SSC Selection Post Phase 14 · Exam Replay

Quantitative Aptitude — Selection Post Phase 14 (2026)

Every shift as it was held, set as 15-minute tests of 25 questions with +2 / −0.5 marking. Graduate and 12th level for Quant and Reasoning; 10th, 12th and Graduate for General Awareness, with an explanation for every question, and English.

Graduate · 17 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

For what value of x is the statement (x/27)(x/108) = 1 true?

  1. 76
  2. 34
  3. 66
  4. 54

Answer: D. x² = 27 × 108 = 2916 → x = 54. ⚡ 108 = 4 × 27, so x = 2 × 27.

Q52 · Ratio, Proportion & Partnership

Two numbers are in the ratio 5: 9. When 4 is subtracted from the first number, and 6 is added to the second number, the resulting ratio becomes 1: 2. Find the sum of the original numbers.

  1. 152
  2. 138
  3. 184
  4. 196

Answer: D. (5k − 4)/(9k + 6) = 1/2 → k = 14 → sum = 14k = 196. ⚡ Sum must be a multiple of 14 — only 196 is.

Q53 · Ratio, Proportion & Partnership

X and Y started a business with investments in the ratio 5 : 4. After 8 months, X withdrew his entire amount. If the profit at the end of the year was shared in the ratio 5 : 9, for how many months did Y invest his money?

  1. 12 months
  2. 14 months
  3. 18 months
  4. 16 months

Answer: C. 5 × 8 : 4 × t = 5 : 9 → 4t × 5 = 360 → t = 18.

Q54 · Percentage

The monthly income of Suresh is ₹18,000, and his monthly expenditure is ₹12,000. Next year, his income increases by 20% and his expenditure increases by 15%. Find the percentage increase in his savings.

  1. 15%
  2. 25%
  3. 30%
  4. 40%

Answer: C. Savings 6000 → 21600 − 13800 = 7800 → +30%. ⚡ Income : exp : savings = 3 : 2 : 1 → 3×20 − 2×15 = 30%.

Q55 · Simple & Compound Interest

A person invested a certain sum of money at 10% per annum simple interest. After 4 years, the interest earned was ₹3,600 less than the sum invested. What was the sum invested?

  1. ₹7000
  2. ₹6000
  3. ₹6500
  4. ₹9000

Answer: B. SI = 40% of P → 0.6P = 3600 → P = 6000.

Q56 · Simple & Compound Interest

Find the amount if ₹6,400 is invested at 5% compound interest for 3 years.

  1. ₹7208.80
  2. ₹7408.80
  3. ₹7308.80
  4. ₹7008.80

Answer: B. 6400 × (21/20)³ = 6400 × 9261/8000 = 7408.80. ⚡ 3-year CI at 5% = 15.7625%.

Q57 · Algebra

If a + 1/a = 2, then find a²⁰²¹ + 1/a²⁰²⁷.

  1. 0
  2. 1
  3. 2
  4. −1

Answer: C. a + 1/a = 2 ⇒ a = 1, so the value is 1 + 1 = 2.

Q58 · Mensuration (2D & 3D)

The side of a regular hexagon is equal to the side of a square. If the perimeter of the square is 24 cm, find the perimeter of the hexagon.

  1. 26 cm
  2. 16 cm
  3. 46 cm
  4. 36 cm

Answer: D. Side = 6 → 6 × 6 = 36 cm.

Q59 · Algebra

If 8x³ − 27y³ = (2x − 3y)(Mx² + Ny² + Oxy), find M² + N² + O².

  1. 118
  2. 125
  3. 133
  4. 140

Answer: C. a³ − b³ = (a − b)(a² + ab + b²) → 4x² + 9y² + 6xy → 16 + 81 + 36 = 133.

Q60 · Average

The average age of a committee of 12 members is 40 years. A member aged 55 years retires and is replaced by a new member aged 31 years. What is the new average age of the committee?

  1. 35 years
  2. 42 years
  3. 38 years
  4. 48 years

Answer: C. Fall = (55 − 31)/12 = 2 → 38.

Q61 · Mensuration (2D & 3D)

In a circle of radius 21 cm, an arc subtends an angle of 120 degrees at the centre. Find the length of the arc. (Take π = 22/7)

  1. 22 cm
  2. 14 cm
  3. 44 cm
  4. 28 cm

Answer: C. (1/3) × 2 × 22/7 × 21 = 44.

Q62 · Profit, Loss & Discount

Given that the cost price of 20 items equals the selling price of x items, and the profit percentage is 25%, determine the value of x.

  1. 14
  2. 16
  3. 12
  4. 18

Answer: B. 20/x = 5/4 → x = 16.

Q63 · Profit, Loss & Discount

An item with a marked price of ₹x was sold for ₹4,400 after a discount of 12%. Find the value of x.

  1. ₹7000
  2. ₹6500
  3. ₹5000
  4. ₹5600

Answer: C. 4400/0.88 = 5000.

Q64 · Trigonometry

Simplify: (sin A + cosec A)² + (cos A + sec A)² − (tan² A + cot² A).

  1. 0
  2. 7
  3. 1
  4. 5

Answer: B. = 1 + 4 + (cosec² + sec²) − (tan² + cot²) = 5 + 2 = 7. ⚡ Put A = 45°: 4.5 + 4.5 − 2 = 7.

Q65 · Geometry (Lines, Triangles, Circles, Polygons)

In △ABC, the lengths of the medians AD, BE, and CF are 9 cm, 12 cm, and 15 cm respectively. Find the area of △ABC.

  1. 64 cm²
  2. 52 cm²
  3. 72 cm²
  4. 85 cm²

Answer: C. Area = 4/3 × area of the triangle formed by the medians. 9-12-15 is right-angled → 54 → 72.

Q66 · Trigonometry

Simplify the expression: (sin θ + cosec θ)² + (cos θ + sec θ)² − (tan θ + cot θ)².

  1. 5
  2. 0
  3. 1
  4. 1/2

Answer: A. = 7 + tan² + cot² − (tan² + cot² + 2) = 5. ⚡ θ = 45°: 9 − 4 = 5.

Q67 · Trigonometry

If sin θ − cos θ = 4/5, then find the value of sin θ + cos θ.

  1. √34/5
  2. 5/√34
  3. √24/5
  4. 5/√24

Answer: A. (s + c)² = 2 − (s − c)² = 2 − 16/25 = 34/25.

Q68 · Trigonometry

If sec² θ + tan² θ = 7/12, find the value of sec⁴ θ − tan⁴ θ.

  1. 7/12
  2. 13/12
  3. 1
  4. 5/12

Answer: A. (sec² − tan²)(sec² + tan²) = 1 × 7/12.

Q69 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of the centre. One chord is 16 cm long and the distance between them is 23 cm. Find the difference between the lengths of the two chords (in cm).

  1. 10 cm
  2. 14 cm
  3. 18 cm
  4. 22 cm

Answer: B. Chord 16 is 15 cm from centre; the other is 8 cm away → half-chord 15 → 30. Difference 14. ⚡ 8-15-17 triplet.

Q70 · Mixture & Alligation

A jar contains a mixture of two liquids A and B in the ratio 3: 1. When 16 liters of the mixture is taken out and 9 liters of liquid B is poured into the jar, the ratio becomes 3: 4. How many liters of liquid A was contained in the jar initially?

  1. 21 liters
  2. 25 liters
  3. 28 liters
  4. 32 liters

Answer: A. Total 4k: A = 3k − 12, B = k + 5. (3k − 12)/(k + 5) = 3/4 → k = 7 → A = 21.

Q71 · Mensuration (2D & 3D)

The total surface area of a hemisphere is 462 cm². What is its curved surface area? (Use π = 22/7)

  1. 283 cm²
  2. 329 cm²
  3. 308 cm²
  4. 258 cm²

Answer: C. TSA = 3πr², CSA = 2πr² → 2/3 × 462 = 308.

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

Consider, a triangle ABC circumscribing a circle having a radius of 4 cm. The lengths of segments BD and DC are 8 cm and 6 cm, respectively. Determine the lengths of sides AB and AC.

  1. 15 cm, 13 cm
  2. 18 cm, 12 cm
  3. 19 cm, 12 cm
  4. 22 cm, 18 cm

Answer: A. AB = x + 8, AC = x + 6, s = 14 + x. r·s = √(s·x·6·8) → s = 3x → x = 7. ⚡ 13-14-15 triangle has inradius 4.

Q73 · Mensuration (2D & 3D)

The ratio of the area of the base of a regular square pyramid to the area of one of its lateral faces is 2:1. Find the angle the lateral face makes with the base.

  1. 30°
  2. 45°
  3. 60°
  4. 75°

Answer: C. a² : ½·a·l = 2 : 1 → l = a. cos φ = (a/2)/l = 1/2 → 60°.

Q74 · Profit, Loss & Discount

A tin of cheese is marked at ₹1050 and is offered at an 11% discount. A tin of butter is marked at ₹1750 and is offered at a 32% discount. If a customer purchases 5 tins of cheese and 4 tins of butter, find the overall effective discount percentage on the total purchase.

  1. 18%
  2. 23%
  3. 28%
  4. 33%

Answer: B. MP 5250 + 7000 = 12250; discount 577.5 + 2240 = 2817.5 → 23%.

Q75 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles have a common external tangent of length 9 and a common internal tangent of length 5. Find the product of the radii of the circles.

  1. 14
  2. 15
  3. 17
  4. 18

Answer: A. (Ext² − Int²)/4 = (81 − 25)/4 = 14.

Graduate · 18 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

The value of (√5 + √2)(√5 - √2) is:

  1. 3
  2. 7
  3. √3
  4. 5

Answer: A. 5 − 2 = 3.

Q52 · Number System & Simplification

What is the binary equivalent of the decimal number 14?

  1. 1101
  2. 1111
  3. 1001
  4. 1110

Answer: D. 8 + 4 + 2 → 1110.

Q53 · Coordinate Geometry

Which of the following lines passes through the origin and forms a 90° angle with the line whose angle of inclination is 30°?

  1. y = tan30°·x
  2. y = −tan30°·x
  3. y = tan60°·x
  4. y = −tan60°·x

Answer: D. Perpendicular slope = −1/tan30° = −√3 = −tan60°.

Q54 · Algebra

Find x: √(x+8) = 10

  1. 92
  2. None
  3. {index}
  4. {index+1}

Answer: A. x + 8 = 100 → 92. (Options 3 and 4 are printed garbled on the official sheet.)

Q55 · Algebra

If x + 1/x = 3, then what is the value of x^2 + 1/x^2?

  1. 7
  2. 9
  3. 5
  4. 6

Answer: A. 3² − 2 = 7.

Q56 · Algebra

In which of the following, the two expressions are like terms?

  1. 7x and 7y
  2. 7x and 9x
  3. 7x and 7xz
  4. 7x and 7xy

Answer: B. Like terms share the same variable part.

Q57 · Mensuration (2D & 3D)

A cylinder has radius 2.5 cm and height 10 cm. Find its volume (use π=3.14).

  1. 196.25 cm³
  2. 178.5 cm³
  3. 198.75 cm³
  4. 200 cm³

Answer: A. 3.14 × 6.25 × 10 = 196.25.

Q58 · Mensuration (2D & 3D)

A giant rotating clock ride completes a 5π/2 radians swing. Each swing spans 40 meters along its arc. What is the radius of the circular path?

  1. 16
  2. 14
  3. 40 ÷ (5π/2)
  4. 40 ÷ (2.5π)

Answer: C / D. r = arc ÷ angle = 40 ÷ (5π/2).

Q59 · Number System & Simplification

Simplify: (8² − 6²)/(8 − 6)

  1. 2
  2. 14
  3. 7
  4. 13

Answer: B. (a² − b²)/(a − b) = a + b = 14.

Q60 · Geometry (Lines, Triangles, Circles, Polygons)

In an optics lab, two precision circular mirrors with radii 6 cm and 10 cm are mounted on a flat bench with their centers exactly 20 cm apart. A laser beam is directed such that it just grazes the edge of both mirrors — touching each mirror tangentially from the outside — forming a direct common external tangent path. What is the length of this direct common external tangent between the two mirrors?

  1. 18.9 cm
  2. 19 cm
  3. 19.6 cm
  4. 20 cm

Answer: C. √(20² − 4²) = √384 ≈ 19.6.

Q61 · Geometry (Lines, Triangles, Circles, Polygons)

A regular polygon has 9 sides. Find the measure of each interior angle

  1. 120°
  2. 135°
  3. 140°
  4. 147°

Answer: C. Exterior 40° → interior 140°.

Q62 · Geometry (Lines, Triangles, Circles, Polygons)

If a regular polygon has interior angle = 179°, find the number of sides.

  1. 180
  2. 360
  3. 540
  4. 720

Answer: B. Exterior 1° → 360 sides.

Q63 · Mensuration (2D & 3D)

If a circular wire is bent to form a square, and the radius of the circle is 14 cm, what is the side of the square?

  1. 14
  2. 22
  3. 44
  4. 28

Answer: B. Circumference 88 ÷ 4 = 22.

Q64 · Mensuration (2D & 3D)

A rectangular prism has volume 288 cm³ and base dimensions 6 cm and 4 cm. Find its height.

  1. 10 cm
  2. 11 cm
  3. 12 cm
  4. 13 cm

Answer: C. 288 ÷ 24 = 12.

Q65 · Mensuration (2D & 3D)

A square pyramid has a base side of 6 cm and height 9 cm. Find the volume.

  1. 118 cm³
  2. 108 cm³
  3. 208 cm³
  4. None

Answer: B. (1/3) × 36 × 9 = 108.

Q66 · Geometry (Lines, Triangles, Circles, Polygons)

Two circular gears with radii 3 cm and 6 cm are mounted on a flat surface such that they just touch externally. To install a belt that runs directly from one gear to the other without wrapping around them, the engineer needs to determine the length of the direct common tangent between the two gears.

  1. 8.49 cm
  2. 7.8 cm
  3. 6.75 cm
  4. 5 cm

Answer: A. Touching circles: 2√(rR) = 2√18 ≈ 8.49.

Q67 · Geometry (Lines, Triangles, Circles, Polygons)

In a satellite imaging system, two base stations A and B are located on the perimeter of a circular ground station with a radius of 30 km. A satellite at point S inside the circle monitors both stations such that angle ASB = 60°. A ground operator walks along the outer ring path (major arc AB) to find the spot P from where the satellite S appears exactly between the two stations. Determine the maximum angle APB the operator can observe.

  1. 90°
  2. 75°
  3. 60°
  4. 120°

Answer: D. Official key: 120°.

Q68 · Profit, Loss & Discount

A shopkeeper bought 5 watches for ₹6000. He sold each at ₹1100. Find the overall profit or loss percentage.

  1. 8% loss
  2. 8.33% loss
  3. 7.5% loss
  4. 6.67% loss

Answer: B. CP 1200 each → loss 100/1200 = 8.33%.

Q69 · Profit, Loss & Discount

A textile trader invested ₹1,00,000: half in designer sarees (sold at 20% profit) and half in casual wear (sold at 10% loss) during a festive season to clear inventory. What was the overall percentage profit or loss?

  1. 2.5% loss
  2. No profit no loss
  3. 5% profit
  4. 7.5% profit

Answer: C. Equal halves → (20 − 10)/2 = 5% profit.

Q70 · Mixture & Alligation

A perfumer blends two perfumes costing ₹900/L and ₹600/L to make 240 L of blend at ₹750/L. Due to poor packaging, 15 L leaks out. How much of the ₹900/L perfume was used?

  1. 100
  2. 110
  3. 120
  4. 130

Answer: C. Alligation 150 : 150 = 1 : 1 → 120 L. The leak doesn't matter.

Q71 · Simple & Compound Interest

A parent invested ₹3,00,000 in a UK education bond at 8% CI for 3 years. Afterward, due to devaluation, the return (in ₹) is converted and reinvested at 10% CI annually in India for 2 more years. If the amount after UK bond matures becomes ₹3,78,000, what will be the amount after 5 years?

  1. ₹4,55,000
  2. ₹4,57,380
  3. ₹4,60,000
  4. ₹4,50,000

Answer: B. 378000 × 1.21 = 457380.

Q72 · Number System & Simplification

A square tile has area 72 cm². What is the length of each side in simplest surd form?

  1. 6√2 cm
  2. √72 cm
  3. 12 cm
  4. 4√3 cm

Answer: A. √72 = 6√2.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles of radii 6 cm and 4 cm touch externally. How many common tangents can be drawn?

  1. 1
  2. 2
  3. 3
  4. 4

Answer: C. 2 direct + 1 transverse = 3.

Q74 · Heights & Distances

A man standing on the deck of a ship (25 m above water level) observes the angle of elevation of the top of a cliff as 60° and the angle of depression of the base as 30°. Find the height of the cliff.

  1. 90 m
  2. 100 m
  3. 103.92 m
  4. 152 m

Answer: B. Distance 25√3; rise above eye = 25√3 × √3 = 75 → 100. ⚡ 30°/60° pair → height = 4 × 25.

Q75 · Mixture & Alligation

A container contains 60 litres of a mixture of milk and water in the ratio 7:3. How many litres of the mixture should be removed and replaced with pure water so that the ratio of milk to water in the resulting mixture becomes 7:5?

  1. 8 litres
  2. 10 litres
  3. 2 litres
  4. 12 litres

Answer: B. Milk share 7/10 → 7/12. Kept = (7/12)/(7/10) = 5/6 → remove 1/6 of 60 = 10.

Graduate · 19 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

Find the number of digits in the square root of 282429536481.

  1. 8
  2. 6
  3. 9
  4. 7

Answer: B. 12 digits → 6 digits in the root.

Q52 · Ratio, Proportion & Partnership

If p: q: r = 1: 3: 4 and 2p + q + 3r = 51, find the value of r.

  1. 20
  2. 16
  3. 24
  4. 12

Answer: D. 2 + 3 + 12 = 17k = 51 → k = 3 → r = 12.

Q53 · Ratio, Proportion & Partnership

A, B, and C enter into a partnership in which A’s capital is used for 5 months, and he claims 1/7 of the profit. B’s capital is used for 7 months, and he claims 1/5 of the profit. If C invested ₹4,600 for 9 months, how much total capital was invested by A?

  1. ₹1,800
  2. ₹2,000
  3. ₹1,500
  4. ₹2,100

Answer: A. C's share = 23/35 ↔ 4600 × 9 = 41400 → 1/35 ↔ 1800. A's 5/35 = 9000 over 5 months → ₹1,800.

Q54 · Percentage

The monthly income of Anita is ₹24,000, and her monthly expenditure is ₹16,000. If her income increases by 25% and her expenditure increases by 10%, find the percentage increase in her savings.

  1. 40%
  2. 75%
  3. 80%
  4. 55%

Answer: D. 8000 → 12400 = +55%. ⚡ 3 × 25 − 2 × 10 = 55.

Q55 · Algebra

If a + b = 3 and ab = 2, find a³ + b³.

  1. 9
  2. 18
  3. 12
  4. 6

Answer: A. 27 − 3 × 2 × 3 = 9.

Q56 · Mensuration (2D & 3D)

If the side of a regular hexagon is doubled, what happens to its area?

  1. Increases 2 times
  2. Increases 3 times
  3. Increases 4 times
  4. Increases 6 times

Answer: C. Area ∝ side².

Q57 · Simple & Compound Interest

A sum of ₹5,000 amounts to ₹6,500 in 3 years at simple interest. If the rate of interest is doubled, what will be the amount of the same sum in 5 years?

  1. ₹9,000
  2. ₹10,000
  3. ₹8,500
  4. ₹11,000

Answer: B. Rate 10% → 20%; SI for 5 yrs = 5000 → ₹10,000.

Q58 · Average

Given that the average of five consecutive odd numbers is 27, determine the product of the first and last numbers.

  1. 713
  2. 654
  3. 852
  4. 546

Answer: A. 23 × 31 = 713. ⚡ 27² − 4².

Q59 · Profit, Loss & Discount

A manufacturer sells an item to a wholesale dealer at a profit of 10%. The wholesaler sells it to a retailer at a profit of 20%. If the retailer pays ₹1,320 for it, find the cost price for the manufacturer.

  1. ₹2000
  2. ₹1000
  3. ₹3000
  4. ₹4000

Answer: B. 1320 ÷ 1.32 = 1000.

Q60 · Mensuration (2D & 3D)

The area of a sector of a circle of radius 28 cm is 308 sq cm. Find the central angle of the sector. (Use π = 22/7)

  1. 75°
  2. 45°
  3. 60°
  4. 90°

Answer: B. 308/2464 = 1/8 → 45°.

Q61 · Simple & Compound Interest

A loan of ₹12,400 is taken at 10% compound interest, payable in two equal annual installments. Find the approximate installment amount.

  1. ₹7,643
  2. ₹7,043
  3. ₹7,743
  4. ₹7,145

Answer: D. x/1.1 + x/1.21 = 12400 → x ≈ 7145. ⚡ At 10% for 2 years, instalment = P × 121/210.

Q62 · Profit, Loss & Discount

A product is sold for ₹8,800 after a 20% discount on its marked price y. Find y.

  1. ₹22,000
  2. ₹17,000
  3. ₹11,000
  4. ₹35,000

Answer: C. 8800 ÷ 0.8.

Q63 · Trigonometry

If 3 sin θ + 5 cos θ = 5, find the value of 5 sin θ − 3 cos θ.

  1. 0
  2. ±1
  3. ±3
  4. ±5

Answer: C. Sum of squares = 3² + 5² = 34 → 25 + x² = 34 → ±3.

Q64 · Trigonometry

What is the value of [sin(18°) cos(72°) + sec(61°) sin(29°) + cos(18°) sin(72°) + cosec(61°) cos(29°)] / [sec²(48°) − cot²(42°)]?

  1. 0
  2. 1
  3. 2
  4. 3

Answer: D. sin²18 + cos²18 = 1, plus 1 + 1 → 3. Denominator = sec²48 − tan²48 = 1.

Q65 · Trigonometry

If cosec θ + cot θ = p, then find the value of (p² − 1)/(p² + 1).

  1. sinθ
  2. tanθ
  3. cosθ
  4. cotθ

Answer: C. Standard result. ⚡ θ = 90° → p = 1 → 0 = cos90°.

Q66 · Mensuration (2D & 3D)

The ratio of the volumes of two hemispheres is 27 : 64. What is the ratio of their total surface areas?

  1. 3:4
  2. 9:16
  3. 27:64
  4. 81:256

Answer: B. Radii 3 : 4 → areas 9 : 16.

Q67 · Trigonometry

Evaluate the value of the expression: 3(sin θ − cos θ)⁴ + 6(sin θ + cos θ)² + 4(sin⁶ θ + cos⁶ θ).

  1. 1
  2. 7
  3. 13
  4. 10

Answer: C. Put θ = 0: 3 + 6 + 4 = 13.

Q68 · Geometry (Lines, Triangles, Circles, Polygons)

In a triangle ABC, D and E are points on sides AB and AC respectively such that DE ∥ BC. If AD = x, DB = x-2, AE = x+2, and EC = x-1, find the value of x.

  1. 4
  2. 2
  3. 10
  4. 7

Answer: A. x(x − 1) = (x − 2)(x + 2) → x = 4.

Q69 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle with centre O and radius 13 cm, two parallel chords AB and CD are drawn on opposite sides of the centre. If AB = 10 cm and CD = 24 cm, find the distance between the two chords (in cm).

  1. 15 cm
  2. 17 cm
  3. 21 cm
  4. 25 cm

Answer: B. 12 + 5 = 17.

Q70 · Mixture & Alligation

A bucket contains a mixture of two liquids P and Q are in the ratio 4 : 1. When 10 liters of the mixture is taken out and 10 liters of liquid Q is poured into the bucket, the ratio becomes 2 : 3. How many liters of liquid P was contained in the bucket?

  1. 14 liters
  2. 16 liters
  3. 18 liters
  4. 20 liters

Answer: B. (4k − 8)/(k + 8) = 2/3 → k = 4 → P = 16.

Q71 · Mensuration (2D & 3D)

The diagonal of the square base of a right square pyramid is 10√2 cm. If the lateral surface area of the pyramid is 260 cm², calculate the volume of the pyramid.

  1. 400 cm³
  2. 300 cm³
  3. 450 cm³
  4. 350 cm³

Answer: A. Side 10, slant 13, height 12 → (1/3) × 100 × 12 = 400.

Q72 · Profit, Loss & Discount

A shopkeeper marks a shirt at ₹1200 and offers a discount of 15%. He marks a pair of trousers at ₹2000 and offers a discount of 25%. If a customer buys 3 shirts and 2 trousers, find the approximate overall discount percentage on the total purchase.

  1. 18.56%
  2. 20.26%
  3. 23.95%
  4. 25.56%

Answer: B. 1540 ÷ 7600 = 20.26%.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles intersect at points P and Q. Their common tangents AB and CD meet the line PQ, extended on both sides, at points X and Y respectively. If PQ = 8 cm and XY = 17 cm, find the length of AB (in cm).

  1. 12 cm
  2. 13 cm
  3. 14 cm
  4. 15 cm

Answer: D. ⚡ AB = √(XY² − PQ²) = √(289 − 64) = 15.

Q74 · Algebra

If x + 1/x = 9, then find the value of x³ + 1/x³ + x² + 1/x².

  1. 702
  2. 729
  3. 779
  4. 781

Answer: D. 702 + 79 = 781.

Q75 · Geometry (Lines, Triangles, Circles, Polygons)

A point P is at a distance of 13 cm from the center of a circle. If the radius of the circle is 5 cm, what is the length of the tangent segment drawn from point P to the circle?

  1. 12 cm
  2. 13 cm
  3. 15 cm
  4. 18 cm

Answer: A. √(169 − 25) = 12.

Graduate · 21 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

Which number system uses digits 0-9 and letters A-F?

  1. Binary
  2. Octel
  3. Decimal
  4. Hexadecimal

Answer: D. Base 16.

Q52 · Number System & Simplification

Simplify (√50 - √8)

  1. 20√2
  2. 3√2
  3. 10√2
  4. 200√2

Answer: B. 5√2 − 2√2.

Q53 · Algebra

If a, b, c are in A.P. and a^2, b^2, c^2 are in G.P., then what is the relation among a, b, c?

  1. a = b = c
  2. a + c = 2b and abc = 0
  3. b² = ac
  4. a² + c² = 2b²

Answer: D. Official key: a² + c² = 2b².

Q54 · Algebra

Solve 3x + 5 = 20.

  1. 5
  2. 6
  3. 10
  4. 15

Answer: A. x = 5.

Q55 · Number System & Simplification

Simplify: 7² + 2 × 7 × 3 + 3²

  1. 100
  2. 121
  3. 64
  4. 169

Answer: A. (7 + 3)².

Q56 · Number System & Simplification

What is the unit digit of 17⁸³?

  1. 1
  2. 2
  3. 3
  4. 4

Answer: C. Cycle 7, 9, 3, 1; 83 mod 4 = 3 → 3.

Q57 · Geometry (Lines, Triangles, Circles, Polygons)

In a regular hexagon, what is the measure of one interior angle?

  1. 120°
  2. 140°
  3. 160°
  4. 100°

Answer: A. 720/6.

Q58 · Mensuration (2D & 3D)

The area of a regular hexagon inscribed in a circle is 200√3 cm². Find the radius of the circle.

  1. 10
  2. 11.54
  3. 14
  4. 16

Answer: B. (3√3/2)r² = 200√3 → r² = 400/3 → 11.54.

Q59 · Mensuration (2D & 3D)

A circular track has a radius of 28 m. What is the distance covered in 2 full rounds?

  1. 176 m
  2. 346 m
  3. 352 m
  4. 564 m

Answer: C. 2 × 176.

Q60 · Geometry (Lines, Triangles, Circles, Polygons)

A chord of length 16 cm is 6 cm away from the center of a circle. Find the radius of the circle.

  1. 10 cm
  2. 12 cm
  3. 8 cm
  4. 14 cm

Answer: A. √(64 + 36).

Q61 · Mensuration (2D & 3D)

A prism has a base of area 35 cm² and height 6.5 cm. What is the volume?

  1. 220 cm³
  2. 227.5 cm³
  3. 230 cm³
  4. 240 cm³

Answer: B. 35 × 6.5.

Q62 · Mensuration (2D & 3D)

An architect is designing a square-based pyramid for a public monument. The base has a perimeter of 60 m, and the total lateral surface area (the sum of the four triangular faces) is 500 m². To finalize the design, the architect needs to find the vertical height of the pyramid.

  1. 15 m
  2. 14.88 m
  3. 16.67 m
  4. 14 m

Answer: B. Side 15, slant 16.67 → h = √(277.8 − 56.25) ≈ 14.88.

Q63 · Profit, Loss & Discount

Two items sold at ₹500 each. One at 25% gain, other at 25% loss. What is the overall result?

  1. 5% loss
  2. 6.25% loss
  3. 7.5% loss
  4. 10% loss

Answer: B. ⚡ Same SP, ±x% → loss x²/100.

Q64 · Profit, Loss & Discount

A pharmacy earns 25% profit on marked price after offering a 20% discount. What is the cost price if the marked price is ₹400?

  1. ₹250
  2. ₹256
  3. ₹260
  4. ₹270

Answer: B. SP 320 = 1.25 CP → 256.

Q65 · Mixture & Alligation

A brine tank has 100 liters of 40% salt solution. Water is added to reduce it to 25%, but then 10 liters are lost due to overflow. What was the volume of water added?

  1. 60
  2. 65
  3. 70
  4. 75

Answer: C. 40 L salt → 160 L total → 60 L water, plus 10 L lost while filling → 70 (official key).

Q66 · Number System & Simplification

A number is written as 3.272727... (repeating). Express it as a fraction.

  1. 327/99
  2. 324/99
  3. 298/91
  4. 333/99

Answer: B. 3 + 27/99 = 324/99 = 36/11.

Q67 · Number System & Simplification

Find the surd value of √75 − √27.

  1. 2√3
  2. 3√2
  3. 4√3
  4. 6√2

Answer: A. 5√3 − 3√3.

Q68 · Algebra

How many solutions does the equation 3x − 2y = 6 have?

  1. None
  2. One
  3. Two
  4. Infinite

Answer: D. One equation, two variables.

Q69 · Trigonometry

Find the number of degrees in 5π/3 radians.

  1. 300°
  2. 200°
  3. 400°
  4. 100°

Answer: A. 5 × 60.

Q70 · Simple & Compound Interest

A sum of ₹20,000 is borrowed at 10% compound interest, to be repaid in two equal annual installments. Find the approximate value of each installment.

  1. ₹11,922
  2. ₹12,522
  3. ₹11,524
  4. ₹11,022

Answer: C. 20000 × 121/210 ≈ 11,524.

Q71 · Geometry (Lines, Triangles, Circles, Polygons)

Two chords AB and CD of a circle intersect internally at a point P. If angle APC = 50° and the minor arc AC subtends a central angle of 60°, find the central angle subtended by the minor arc BD.

  1. 35°
  2. 40°
  3. 45°
  4. 50°

Answer: B. 50 = ½(60 + x) → 40.

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

Two tangents are drawn from an external point T to a circle with center O, touching at A and B. If ∠AOB = 120°, what is ∠ATB?

  1. 30°
  2. 45°
  3. 60°
  4. 90°

Answer: C. 180 − 120.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles cut each other at points M and N. AB and CD are the common tangents to the circles. The line MN, when produced on both sides, intersects tangents AB and CD at points P and Q respectively. If MN = 3 cm and PQ = 5 cm, find the length of AB (in cm).

  1. 2 cm
  2. 3 cm
  3. 4 cm
  4. 5 cm

Answer: C. ⚡ AB = √(PQ² − MN²) = √(25 − 9) = 4.

Q74 · Heights & Distances

A balloon is observed from two points A and B on the ground, 1200 m apart. If the angles of elevation of the balloon from these points are 60° and 30° respectively. If the balloon is between A and B, find its height.

  1. 300√3 m
  2. 200√3 m
  3. 500 m
  4. 600 m

Answer: A. h/√3 + h√3 = 1200 → h = 300√3.

Q75 · Mixture & Alligation

A vessel contains 100 litres of a mixture of milk and water in the ratio 4:1. First, 20 litres of the mixture are removed and replaced with an equal volume of pure water. Then, 25 litres of this new mixture are removed and replaced with an equal volume of pure milk. What is the final ratio of milk to water in the vessel?

  1. 17 : 8
  2. 73 : 27
  3. 19 : 6
  4. 21 : 8

Answer: B. 64 : 36 → remove ¼ → 48 : 27 → +25 milk → 73 : 27.

Graduate · 22 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

For what value of x is the statement (x/16)(x/64) = 1 true?

  1. 48
  2. 32
  3. 68
  4. 52

Answer: B. x² = 1024.

Q52 · Ratio, Proportion & Partnership

If a: b: c = 1: 2: 3 and 3a + 2b + c = 30, find the value of c.

  1. 12
  2. 9
  3. 17
  4. 6

Answer: B. 10k = 30 → c = 9.

Q53 · Ratio, Proportion & Partnership

X, Y, and Z are three partners whose profit-sharing ratio is 5:7:8. Had they invested their capital for 14 months, 8 months, and 7 months, respectively, what would their initial capital investment ratio be?

  1. 35 : 28 : 24
  2. 7 : 5 : 4
  3. 20 : 49 : 64
  4. 5 : 7 : 8

Answer: C. 5/14 : 7/8 : 8/7 → × 56.

Q54 · Percentage

If P is 25% more than Q and R is 40% less than the sum of P and Q, then by what percentage is R more than P?

  1. 6%
  2. 12%
  3. 8%
  4. 14%

Answer: C. Q 100, P 125, R 135 → 8%.

Q55 · Time, Work & Distance

A vehicle travels from city A to city B at a constant speed of 30 km/h and returns from city B to city A at a constant speed of 90 km/h. Determine the average speed for the entire journey.

  1. 35 km/h
  2. 25 km/h
  3. 45 km/h
  4. 15 km/h

Answer: C. 2xy/(x + y) = 45.

Q56 · Simple & Compound Interest

Find the rate of interest if ₹1,000 amounts to ₹1,210 in 2 years, compounded annually.

  1. 7%
  2. 15%
  3. 13%
  4. 10%

Answer: D. 1.21 = 1.1².

Q57 · Algebra

If k − 1/k = 5, find the value of k³ − 1/k³.

  1. 125
  2. 130
  3. 140
  4. 155

Answer: C. 125 + 3 × 5.

Q58 · Geometry (Lines, Triangles, Circles, Polygons)

If the number of diagonals of a regular polygon is 170, what is the measure of each of its interior angles?

  1. 112°
  2. 139°
  3. 162°
  4. 173°

Answer: C. n = 20 → 162°.

Q59 · Simple & Compound Interest

The ratio of the principal and the amount after 5 years is 4 : 7. In how many years will the ratio of the principal and the simple interest become 5 : 6 at the same rate?

  1. 8 years
  2. 10 years
  3. 12 years
  4. 15 years

Answer: A. 15% p.a.; need 120% → 8 years.

Q60 · Mensuration (2D & 3D)

The area of a sector of a circle having radius 21 cm is 231 sq cm. Find the degree measure of the corresponding central angle. (Use π = 22/7)

  1. 90°
  2. 30°
  3. 60°
  4. 45°

Answer: C. 231/1386 = 1/6.

Q61 · Profit, Loss & Discount

By selling a toy at a certain price, a merchant gains 10%. If he increases the price by Rs. 4, his gain becomes 12.5%. Find the cost price of the toy.

  1. ₹180
  2. ₹140
  3. ₹160
  4. ₹120

Answer: C. 2.5% = 4.

Q62 · Trigonometry

If cosec θ − cot θ = √2 − 1, find the value of cosec θ + cot θ.

  1. 0
  2. √2
  3. √2 + 2
  4. √2 + 1

Answer: D. Product is 1.

Q63 · Trigonometry

If sin θ − cos θ = 3/5, find the value of sin θ + cos θ.

  1. √31/5
  2. 5/√41
  3. √41/5
  4. 5/√31

Answer: C. 2 − 9/25 = 41/25.

Q64 · Trigonometry

What is the value of {2[sin(21°) cos(69°) + cos(21°) sin(69°)] + 3 sec(54°) sin(36°)} / [cosec²(15°) − tan²(75°)]?

  1. 1
  2. 2
  3. 4
  4. 5

Answer: D. 2·1 + 3·1 = 5; denominator = 1.

Q65 · Mensuration (2D & 3D)

A hemispherical water tank has an internal radius of 21 m. It is full of water and is being emptied by a pump at a rate of 100 litres per second. How long will it take to drain the entire tank? (Use π = 22/7)

  1. 55 hours 12 minutes
  2. 55 hours 30 minutes
  3. 53 hours 45 minutes
  4. 53 hours 54 minutes

Answer: D. 19404 m³ = 1,94,04,000 L → 1,94,040 s = 53.9 h.

Q66 · Trigonometry

Simplify the expression: (tanθ − secθ + 1)/(tanθ + secθ − 1).

  1. (sinθ + cosθ + 1)/sinθ
  2. 0
  3. 1
  4. (1 − sinθ)/cosθ

Answer: D. It's the reciprocal of (1 + sinθ)/cosθ = (1 − sinθ)/cosθ.

Q67 · Geometry (Lines, Triangles, Circles, Polygons)

In △ABC, the internal bisectors of ∠B and ∠C meet at point O. If the exterior angle at vertex A when side BA is extended is 130°, find the measure of ∠BOC.

  1. 115°
  2. 120°
  3. 110°
  4. 125°

Answer: A. A = 50 → 90 + 25.

Q68 · Geometry (Lines, Triangles, Circles, Polygons)

Two parallel chords are drawn on opposite sides of the centre of a circle of diameter 30 cm. One chord has length 24 cm, and the perpendicular distance between the two chords is 21 cm. Determine the length of the other chord.

  1. 9 cm
  2. 12 cm
  3. 18 cm
  4. 24 cm

Answer: C. Distances 9 and 12 → half-chord 9 → 18.

Q69 · Mixture & Alligation

A bucket contains a mixture of two liquids P and Q in the ratio 5 : 2. If 14 liters of the mixture is taken out and 7 liters of liquid Q is added to the bucket, the ratio of P to Q becomes 2 : 1. Find the initial quantity of liquid P in the bucket.

  1. 30 liters
  2. 50 liters
  3. 80 liters
  4. 100 liters

Answer: C. (5k − 10)/(2k + 3) = 2 → k = 16 → 80.

Q70 · Mensuration (2D & 3D)

A plane parallel to the base of a pyramid cuts it at half its vertical height from the apex. What is the ratio of the volume of the smaller pyramid to the frustum formed?

  1. 1:8
  2. 1:7
  3. 2:9
  4. 2:7

Answer: B. 1 : 8 of whole → 1 : 7.

Q71 · Profit, Loss & Discount

A shopkeeper purchases 220 items but pays only for 198 items at the marked price. He sells each item at a discount of 5%. Find his approximate gain percentage.

  1. 7%
  2. 10%
  3. 6%
  4. 11%

Answer: C. 209/198 → 5.6% ≈ 6%.

Q72 · Profit, Loss & Discount

A saree is purchased for ₹644 after a discount of 8%, and another saree is purchased for ₹594 after a discount of 1%. If both sarees are considered as a single transaction, find the approximate overall discount percentage on the total marked price.

  1. 4.13%
  2. 5.07%
  3. 4.77%
  4. 5.50%

Answer: C. MP 700 + 600; discount 62/1300.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

The length of a common direct tangent to two circles is 25 cm and the length of their common transverse tangent is 15 cm. Find the product of the radii.

  1. 60
  2. 80
  3. 100
  4. 120

Answer: C. (625 − 225)/4.

Q74 · Algebra

If x⁴ + 1/x⁴ = 322 and x > 1, what is the value of the expression x − 1/x?

  1. 4
  2. 8
  3. 12
  4. 16

Answer: A. x² + 1/x² = 18 → (x − 1/x)² = 16.

Q75 · Geometry (Lines, Triangles, Circles, Polygons)

If PA and PB are tangents to a circle with center O from an external point P, and M is a point on the minor arc AB, the tangent at M intersects PA at X and PB at Y. If ∠APB = θ, then ∠XOY is:

  1. 90° − θ/2
  2. θ/2
  3. θ
  4. Variable

Answer: A. ½(180 − θ).

Graduate · 23 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

What is the Hexadecimal representation of 4?

  1. 100
  2. 289
  3. 4
  4. 234

Answer: C. Same as decimal below 10.

Q52 · Coordinate Geometry

Which of the following transformations maps the line y = x onto another line that is perpendicular to it and also passes through the origin?

  1. Rotate 90° about origin
  2. Reflect about x-axis
  3. Translate by (1,1)
  4. Rotate 45° about origin

Answer: A. y = x → y = −x.

Q53 · Algebra

Factorize: x^2 − 10x + 25

  1. (x − 5)²
  2. (x − 10)²
  3. (x − 15)²
  4. (x − 25)²

Answer: A. Perfect square.

Q54 · Algebra

Solve for 'x' 4x - 7 = 5x - 3.

  1. 4
  2. −4
  3. 3
  4. −3

Answer: B. x = −4.

Q55 · Number System & Simplification

Simplify: 1.25 + 2.5 × (1.6 − 0.4) ÷ 0.2

  1. 19.25
  2. 16.25
  3. 15.5
  4. 14

Answer: B. 3 ÷ 0.2 = 15 → 16.25.

Q56 · Algebra

Which of the following represents (x + y)²?

  1. x² + y²
  2. x² + 2xy + y²
  3. x² − 2xy + y²
  4. x² − y²

Answer: B. Identity.

Q57 · Number System & Simplification

Find the unit digit of 999³ + 888² + 777¹.

  1. 4
  2. 6
  3. 2
  4. 0

Answer: D. 9 + 4 + 7 = 20.

Q58 · Geometry (Lines, Triangles, Circles, Polygons)

How many diagonals are there in a regular pentagon?

  1. 5
  2. 7
  3. 10
  4. 15

Answer: A. 5 × 2/2.

Q59 · Geometry (Lines, Triangles, Circles, Polygons)

A regular polygon has 20 diagonals. Find the number of its sides.

  1. 6
  2. 8
  3. 7
  4. 10

Answer: B. 8 × 5/2 = 20.

Q60 · Mensuration (2D & 3D)

Find the area of a quarter-circle with radius 7 cm.

  1. 38.5 cm²
  2. 114 cm²
  3. 14 cm²
  4. 144 cm²

Answer: A. 154/4.

Q61 · Mensuration (2D & 3D)

In a square pyramid, the base side is 6 cm and slant height is 10 cm. Find lateral surface area.

  1. 120 cm²
  2. 130 cm²
  3. 140 cm²
  4. 150 cm²

Answer: A. ½ × 24 × 10.

Q62 · Mensuration (2D & 3D)

A circular park has a radius of 8 cm, and a special garden area is designed as a sector with an area of 32π cm². Find the length of the curved boundary (arc) of this garden sector.

  1. 4π cm
  2. 6π cm
  3. 8π cm
  4. 10π cm

Answer: C. Area = ½ r l → l = 8π.

Q63 · Mensuration (2D & 3D)

An architect is designing a right prism-shaped skylight with a rectangular base measuring 9 cm by 12 cm and a height of 16 cm. Determine the length of the longest diagonal across the prism for structural support planning.

  1. 23 cm
  2. 22.5 cm
  3. 21.93 cm
  4. 20.5 cm

Answer: C. √481 ≈ 21.93.

Q64 · Percentage

Free delivery over ₹500. Customer buys items worth ₹480 and pays ₹50 shipping. What % more should he have bought to avoid shipping?

  1. 4%
  2. 4.17%
  3. 5%
  4. 5.18%

Answer: B. 20/480.

Q65 · Profit, Loss & Discount

A bookstore sells half the books at 20% profit and the rest at 10% loss. Overall, he gains ₹200 on a batch of books worth ₹4000. What is the total selling price?

  1. ₹4,150
  2. ₹4,200
  3. ₹4,250
  4. ₹4,300

Answer: B. 4000 + 200.

Q66 · Mixture & Alligation

An audit shows assets invested in schemes giving 12% and 18% return yielding 15% average return. If total investment is ₹6,00,000, what is investment in the lower-return scheme?

  1. ₹2,00,000
  2. ₹2,50,000
  3. ₹3,00,000
  4. ₹3,50,000

Answer: C. Midpoint → 1 : 1.

Q67 · Trigonometry

Convert −390° into radians.

  1. −13π/6
  2. −11π/6
  3. −7π/6
  4. −15π/6

Answer: A. −390π/180.

Q68 · Simple & Compound Interest

Calculate the compound interest on ₹2,500 at 20% per annum for 1 year 9 months, compounded annually.

  1. ₹1050
  2. ₹950
  3. ₹1000
  4. ₹900

Answer: B. 2500 → 3000 → +15% = 3450.

Q69 · Algebra

If √x + 1/√x = √7, what is the value of x + 1/x?

  1. 1
  2. 2
  3. 4
  4. 5

Answer: D. 7 − 2.

Q70 · Algebra

If x² + 1/x² = 14, find the value of (x + 1/x)².

  1. 10
  2. 12
  3. 14
  4. 16

Answer: D. 14 + 2.

Q71 · Geometry (Lines, Triangles, Circles, Polygons)

A chord of a circle has a length of 6 cm. The angle subtended by the chord at a point on the circumference is 30°. What is the distance from the center of the circle to the chord?

  1. 2 cm
  2. 2√3 cm
  3. 3 cm
  4. 3√3 cm

Answer: D. Central angle 60° → r = 6 → √(36 − 9).

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

If a tangent PQ is drawn at point P to a circle such that ∠OPQ = 90°, and a chord PR is drawn such that ∠RPQ = 30°, what is the angle subtended by the chord PR at the centre O?

  1. 30°
  2. 60°
  3. 90°
  4. 120°

Answer: B. Twice the tangent–chord angle.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles have a common external tangent of length 17 cm and a common internal tangent of length 9 cm. Find the product of the radii of the circles.

  1. 48
  2. 52
  3. 54
  4. 64

Answer: B. (289 − 81)/4.

Q74 · Heights & Distances

Two towers of height h₁ and h₂ subtend angles of 30° and 60° respectively at a point on the line joining their feet. If the distance between the towers is d, what is the ratio of their heights h₁ : h₂ if the point is at the midpoint?

  1. 1:3
  2. 3:1
  3. 4:5
  4. 5:4

Answer: A. tan30 : tan60.

Q75 · Mixture & Alligation

Three solutions contain acid and water in the ratios 1:2, 2:3, and 3:2 respectively. Equal quantities of the first two solutions and twice the quantity of the third solution are mixed together. What is the ratio of acid to water in the final mixture?

  1. 29 : 31
  2. 11 : 14
  3. 17 : 23
  4. 15 : 19

Answer: A. Take 15, 15, 30 L → 29 : 31.

Graduate · 24 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

Find the smallest number which is a perfect square and is divisible by 6, 10, 15, and 30.

  1. 400
  2. 900
  3. 2500
  4. 1600

Answer: B. LCM 30 → 30² = 900.

Q52 · Ratio, Proportion & Partnership

The ratio of juice and water in a mixture is 2: 3. What is the percentage of juice in the mixture?

  1. 55%
  2. 40%
  3. 25%
  4. 60%

Answer: B. 2/5.

Q53 · Ratio, Proportion & Partnership

A and B invest in a business in the ratio 4:5. After 10 months, B leaves the business after withdrawing his investment. In the first year, the business made a profit of ₹49,000. What is B's share?

  1. ₹25,000
  2. ₹20,000
  3. ₹24,000
  4. ₹22,000

Answer: A. 48 : 50 → 50/98.

Q54 · Percentage

In an innings of 108 runs, a batsman hit 9 boundaries and 3 sixes. Find the percentage of runs scored by running.

  1. 50%
  2. 65%
  3. 32%
  4. 48%

Answer: A. 54 boundaries → 50%.

Q55 · Average

The average of 5 consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?

  1. 5
  2. 8
  3. 6
  4. 3

Answer: B. Always 8.

Q56 · Simple & Compound Interest

If ₹2,000 amounts to ₹2,315.25 in 3 years at compound interest, what is the rate percent per annum?

  1. 7%
  2. 5%
  3. 9%
  4. 10%

Answer: B. 1.05³ = 1.157625.

Q57 · Geometry (Lines, Triangles, Circles, Polygons)

If a regular polygon has 90 diagonals, what is the measure of each interior angle?

  1. 126°
  2. 181°
  3. 156°
  4. 140°

Answer: C. n = 15.

Q58 · Simple & Compound Interest

A sum of ₹15,600 is invested in a scheme of simple interest. The person receives ₹4,680 as interest after 3 years. If he had invested the same sum for 5 years at a rate 2% lower than the original rate, what would be the interest?

  1. ₹6,240
  2. ₹5,400
  3. ₹6,500
  4. ₹5,850

Answer: A. 10% → 8% → 6240.

Q59 · Algebra

If x + 1/x = 2, then what is the value of x⁷ + 1/x¹¹⁷?

  1. 2
  2. 1
  3. 3
  4. 4

Answer: A. x = 1.

Q60 · Profit, Loss & Discount

A dealer claims to sell goods at cost price but uses a weight of 960 grams in place of a standard kilogram. Determine the approximate percentage gain achieved by the dealer.

  1. 5.18%
  2. 6.78%
  3. 7.42%
  4. 4.17%

Answer: D. 40/960.

Q61 · Mensuration (2D & 3D)

In a circle of radius 42 cm, an arc subtends an angle of 15 degrees at the centre. Find the length of the arc. (Take π = 22/7)

  1. 33 cm
  2. 11 cm
  3. 22 cm
  4. 44 cm

Answer: B. 264 × 15/360.

Q62 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle with center O, AD is a diameter and AC is a chord. Point B is on AD such that OB = 7 cm and BC = 9 cm. If ∠OBC = 60°, find the radius of the circle.

  1. 16 cm
  2. √90 cm
  3. 25 cm
  4. √67 cm

Answer: D. Cosine rule: 49 + 81 − 63 = 67.

Q63 · Trigonometry

If sin θ + sin³ θ = cos² θ, find the value of cos⁶ θ − 4 cos⁴ θ + 8 cos² θ.

  1. 4
  2. 1
  3. 0
  4. −2

Answer: A. Square both sides with c = cos²θ: (1 − c)(2 − c)² = c² → c³ − 4c² + 8c = 4.

Q64 · Trigonometry

If sin A + cos A = √2, determine the value of tan A + cot A.

  1. 1/√2
  2. 2
  3. 1/2
  4. √2

Answer: B. A = 45°.

Q65 · Trigonometry

What is the value of [sin(42°) sec(48°) + cos(42°) cosec(48°) + tan(38°) tan(52°)] / [cosec²(31°) − tan²(59°)]?

  1. 0
  2. 1
  3. 2
  4. 3

Answer: D. 1 + 1 + 1 over 1.

Q66 · Mensuration (2D & 3D)

If the radius of a hemisphere is 7 cm, what is the difference between its total surface area and its curved surface area?

  1. 154 cm²
  2. 77 cm²
  3. 169 cm²
  4. 88 cm²

Answer: A. πr².

Q67 · Trigonometry

Simplify the expression: (cos³ θ + sin³ θ)/(cos θ + sin θ) + (cos³ θ − sin³ θ)/(cos θ − sin θ).

  1. 1
  2. 0
  3. 2
  4. −2

Answer: C. (1 − sc) + (1 + sc).

Q68 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle with a diameter of 34 cm, two parallel chords are drawn on opposite sides of the center. The length of one chord is 30 cm, and the perpendicular distance between the two chords is 23 cm. Calculate the length of the other chord.

  1. 14 cm
  2. 16 cm
  3. 20 cm
  4. 24 cm

Answer: B. Distances 8 and 15 → 16.

Q69 · Mensuration (2D & 3D)

A square pyramid is sliced by a plane parallel to its base at a point that is one-third of the way down from the apex along its height. If the volume of the original pyramid is 540 cm³, determine the volume of the resulting frustum.

  1. 415 cm³
  2. 578 cm³
  3. 520 cm³
  4. 480 cm³

Answer: C. 540 − 540/27.

Q70 · Profit, Loss & Discount

A shopkeeper earns a profit of 19% on the cost price of an article after giving three consecutive discounts of 11%, 13% and 15% to a customer. What would have been the profit percentage, had the shopkeeper given discounts of 11% and 13% only?

  1. 35%
  2. 40%
  3. 45%
  4. 50%

Answer: B. 119 ÷ 0.85 = 140.

Q71 · Profit, Loss & Discount

A seller offers a 20% discount and still earns a 25% profit. If the profit made is ₹75, find the marked price of the article.

  1. ₹504.25
  2. ₹468.75
  3. ₹490
  4. ₹570

Answer: B. CP 300, SP 375, MP 468.75.

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

The common direct tangent of two circles is 26 cm long, while their common transverse tangent is 10 cm long. Find the product of the radii of the circles.

  1. 72
  2. 86
  3. 100
  4. 144

Answer: D. (676 − 100)/4.

Q73 · Algebra

If p + q + r = 0 and pq + qr + rp = −35, then find p⁴ + q⁴ + r⁴.

  1. 2400
  2. 2450
  3. 3675
  4. 4900

Answer: B. Σp² = 70 → ⚡ when p + q + r = 0, Σp⁴ = (Σp²)²/2 = 2450.

Q74 · Geometry (Lines, Triangles, Circles, Polygons)

Tangents PT and PS are drawn from an external point P to a circle of radius 5 cm. If the distance from P to the center O is 13 cm, find the area of quadrilateral PTOS.

  1. 30 cm²
  2. 45 cm²
  3. 60 cm²
  4. 65 cm²

Answer: C. 2 × ½ × 5 × 12.

Q75 · Mixture & Alligation

Plastic and leather are two types of materials used to manufacture industrial washers. How many kg of pure plastic must be added to a mixture of 16 kg of a first washer material and 25 kg of a second washer material to produce a new batch containing exactly 40% leather? The ratio of plastic to leather by weight is 3:1 in the first material and 6:19 in the second material.

  1. 19.5 kg
  2. 18.5 kg
  3. 17.5 kg
  4. 16.5 kg

Answer: D. Leather 23 kg → total 57.5 → add 16.5.

Graduate · 25 Sep 2026, Shift 1, 10:00 AM

Q51 · Number System & Simplification

What is the Binary representation of 83?

  1. 1010011
  2. 123
  3. 53
  4. 83

Answer: A. 64 + 16 + 2 + 1.

Q52 · Coordinate Geometry

Find the distance between the points where the line y = x intersects x-axis and y-axis.

  1. 1
  2. 2
  3. √5
  4. √2

Answer: D. Official key: √2.

Q53 · Number System & Simplification

Evaluate: (11² + 14²) ÷ 3

  1. 107.67
  2. 104.17
  3. 110.67
  4. 105.67

Answer: D. 317/3.

Q54 · Number System & Simplification

What is the number of zeroes in the product 25 × 20 × 16 × 40?

  1. 4
  2. 6
  3. 2
  4. 8

Answer: A. = 3,20,000.

Q55 · Mensuration (2D & 3D)

Each side of a regular nonagon is 8 cm. Find its perimeter.

  1. 72 cm
  2. 64 cm
  3. 70 cm
  4. 80 cm

Answer: A. 9 × 8.

Q56 · Mensuration (2D & 3D)

Find the radius of a circle whose circumference is 31.4 cm.

  1. 5 cm
  2. 6 cm
  3. 4 cm
  4. 7 cm

Answer: A. 31.4 ÷ 6.28.

Q57 · Mensuration (2D & 3D)

A prism has a parallelogram base with base 6 cm, height 5 cm, and prism height 11 cm. Find the volume.

  1. 280 cm³
  2. 270 cm³
  3. 260 cm³
  4. 330 cm³

Answer: D. 30 × 11.

Q58 · Mensuration (2D & 3D)

A square pyramid has lateral surface area 312 cm² and slant height 13 cm. Find base side.

  1. 12 cm
  2. 14 cm
  3. 16 cm
  4. 18 cm

Answer: A. 2 × a × 13 = 312.

Q59 · Geometry (Lines, Triangles, Circles, Polygons)

A decorative triangular frame is to be fitted with a circular glass piece perfectly inscribed inside it. The triangle's sides measure 13 cm, 14 cm, and 15 cm. To craft the glass precisely, the radius of the inscribed circle needs to be calculated.

  1. 3.5 cm
  2. 4 cm
  3. 4.5 cm
  4. 5 cm

Answer: B. 84 ÷ 21.

Q60 · Profit, Loss & Discount

A combo pack is marked ₹500. A 10% discount is offered on each item and total combo gives extra 5% discount. Find total amount paid.

  1. ₹425.7
  2. ₹427.5
  3. ₹430
  4. ₹435

Answer: B. 500 × 0.9 × 0.95.

Q61 · Profit, Loss & Discount

A home décor exporter sent a fragile mirror set worth an unknown amount. During international transit, part of the packaging was damaged, requiring a ₹500 repacking cost. The buyer agreed to pay ₹20,000, and the seller claimed a 25% profit on his total investment, including the repacking cost. What was the original cost of the goods before repacking?

  1. ₹15,000
  2. ₹15,500
  3. ₹16,000
  4. ₹16,500

Answer: B. 16000 − 500.

Q62 · Mixture & Alligation

A janitorial service company uses a 75-liter drum of industrial bleach (20% concentration) for commercial cleaning. After 15 liters is accidentally spilled, the drum is topped up with pure water. To stay within chemical exposure norms for indoor use, the dilution must be accurately recalculated. What is the new percentage of bleach concentration?

  1. 15%
  2. 16%
  3. 17%
  4. 18%

Answer: B. 20 × 60/75.

Q63 · Algebra

Find the value of (5x + 2)² − (5x − 2)²

  1. 20x
  2. 40x
  3. 50x
  4. 100x

Answer: B. 4ab.

Q64 · Algebra

If a + b = 5 and ab = 6, find a³ + b³.

  1. 35
  2. 36
  3. 40
  4. 45

Answer: A. 125 − 90.

Q65 · Geometry (Lines, Triangles, Circles, Polygons)

If a polygon has 24 sides. How many diagonals does it have?

  1. 252
  2. 262
  3. 272
  4. 282

Answer: A. 24 × 21/2.

Q66 · Mensuration (2D & 3D)

A sector of a circle subtends an angle of π/3 radians at the center. If the radius of the circle is 6 cm, what is the arc length?

  1. 2π/7
  2. 2π/3 m
  3. 42π cm
  4. 2π cm

Answer: D. rθ.

Q67 · Number System & Simplification

Evaluate: (0.064 − 0.027)/(0.16 + 0.12 + 0.09) + (0.125 + 0.008)/(0.25 − 0.10 + 0.04).

  1. 0.4
  2. 0.8
  3. 0.6
  4. 0.2

Answer: B. (a − b) + (a + b) = 0.1 + 0.7.

Q68 · Simple & Compound Interest

What will be the compound interest on ₹8,000 at 5% per annum for 2 years 3 months, compounded annually?

  1. ₹1000.25
  2. ₹930.25
  3. ₹990.25
  4. ₹900.25

Answer: B. 8820 × 1.0125 = 8930.25.

Q69 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle with centre O, PA and PB are tangents touching the circle at A and B respectively. Point C lies on the major arc AB. If ∠ACB = 50°, find ∠APB.

  1. 80°
  2. 100°
  3. 120°
  4. 160°

Answer: A. 180 − 100.

Q70 · Algebra

If x = 6 − 3√3, what is the value of (√x − 3/√x)²?

  1. 1
  2. 2
  3. 4
  4. 6

Answer: D. x + 9/x − 6 = 12 − 6.

Q71 · Algebra

If x + 1/x = 2√5, then determine the value of 2x/(x² − 1).

  1. 1/2
  2. 3/4
  3. 5/6
  4. 7/8

Answer: A. = 2/(x − 1/x) = 2/4.

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

Consider a circle inscribed in ΔABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

  1. 7 cm, 5 cm, 3 cm
  2. 8 cm, 5 cm, 2 cm
  3. 9 cm, 7 cm, 2 cm
  4. 10 cm, 8cm, 2 cm

Answer: A. s − opposite side: 15 − 8, 15 − 10, 15 − 12.

Q73 · Heights & Distances

The angle of elevation of a cloud from a point h m above a lake is α and the angle of depression of its reflection in the lake is β. Find the height of the cloud above the lake.

  1. H = h(tanα + tanβ)/(tanβ − tanα)
  2. H = h(tanα − tanβ)/(tanβ + tanα)
  3. H = h(tanα·tanβ)/(tanβ − tanα)
  4. H = h·tanα/(tanβ − tanα)

Answer: A. Standard result.

Q74 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles with radii R and r (R > r) touch each other externally. If the angle between their two direct common tangents is 60°, find the ratio of their radii, R : r.

  1. 5:1
  2. 3 : 1
  3. 2:7
  4. 3:7

Answer: B. sin30 = (R − r)/(R + r).

Q75 · Mixture & Alligation

A container has 200 litres of a mixture of milk and water in the ratio 3:2. First, 40 litres of the mixture are removed and replaced with an equal volume of pure water. Then, 50 litres of the resulting mixture are removed and replaced with an equal volume of pure milk. Find the final ratio of milk to water in the container.

  1. 109 : 66
  2. 111 : 64
  3. 61 : 39
  4. 47 : 30

Answer: C. 96 : 104 → 72 : 78 → 122 : 78.

Graduate · 26 Sep 2026, Higher Secondary Level

Q51 · Number System & Simplification

What is the result of: (10 + 2) × (6 - 4) ÷ 2?

  1. 6
  2. 12
  3. 10
  4. 8

Answer: B. 12 × 2 ÷ 2.

Q52 · Mixture & Alligation

A shopkeeper combines two qualities of tea, one at Rs.75/kg and the other at Rs.105/kg, in the ratio of 3:2. Calculate the cost price per kg of this tea mixture.

  1. Rs.89/kg
  2. Rs.97/kg
  3. Rs.77/kg
  4. Rs.87/kg

Answer: D. 435 ÷ 5.

Q53 · Number System & Simplification

The next term in the series 1, 4, 36, 576, ..... is:

  1. 3600
  2. 8100
  3. 12100
  4. 14400

Answer: D. 1², 2², 6², 24², 120² (factorials).

Q54 · Algebra

A gardener plants some trees in the form of a perfect rectangle. The number of trees in each row is 6 more than the number of rows. If the total number of trees planted is 135, find the number of rows?

  1. 8
  2. 9
  3. 7
  4. 2

Answer: B. 9 × 15.

Q55 · Simple & Compound Interest

A sum of money becomes Rs. 47,600 at compound interest. If rate of interest in three years is 11.11%, 16.66%, 12.5% respectively. Find the compound interest?

  1. Rs. 13,360
  2. Rs. 15,000
  3. Rs. 14,960
  4. Rs. 17,560

Answer: C. Factor 10/9 × 7/6 × 9/8 = 35/24 → P = 32640.

Q56 · Profit, Loss & Discount

A shopkeeper marks an article at a price such that after giving discount of 20% and he gains k%. If the cost price and the marked price of the article are Rs. 4,400 and Rs. 6,500 respectively. What is the value of k?

  1. 25%
  2. 16.25%
  3. 18.18%
  4. 14.75%

Answer: C. SP 5200 → 800/4400.

Q57 · Mixture & Alligation

A can has a capacity of 300 liters and it is completely filled with pure milk. From this can, 30 liters of milk is removed and the same amount (30 liters) of water is added to fill the can again. This process of removing 30 liters of the mixture and replacing it with 30 liters of water is repeated several times. After repeating the process a certain number of times, the quantity of pure milk left in the can reduces to 218.7 liters. How many times must this process be carried out for the amount of pure milk to become 218.7 liters?

  1. 2
  2. 3
  3. 4
  4. 5

Answer: B. 0.9³ = 0.729.

Q58 · Time, Work & Distance

A company deploys 500 labourers to restore an old fort wall. In the first 15 weeks, they manage to rebuild 2/5 of the total structure. Suddenly, a severe storm hits the region, causing the restoration work to be stopped for 6 weeks. During this period of inactivity, 1/2 of the portion already restored collapses due to the storm damage. When the weather clears and the restoration resumes, only 360 labourers return to work. Assuming that no further interruptions occur, in how many weeks from the beginning will the entire restoration project be completed?

  1. 42.33 weeks
  2. 57.23 weeks
  3. 62.67 weeks
  4. 55.25 weeks

Answer: C. Whole = 18750 man-weeks; remaining 4/5 = 15000 ÷ 360 = 41.67 → 15 + 6 + 41.67.

Q59 · Time, Work & Distance

A man begins his trip 36 minutes later than his regular starting time. To make up for the delay, he travels at 180% of his usual speed and ends up reaching his destination 16 minutes earlier than his usual arrival time. Find the usual time taken for the journey?

  1. 95 minutes
  2. 117 minutes
  3. 104 minutes
  4. 119 minutes

Answer: B. Saved 4/9 of usual = 52 min.

Q60 · Time, Work & Distance

A train going from P to Q, meets an accident after travelling 90 km. Due to the accident, the train reduces its speed to 2/3 of its normal speed and reaches its destination 30 minutes late, had the same accident occurred 60 km further the train would have reached the same destination just 10 min late. What is the distance from P to Q?

  1. 170 km
  2. 180 km
  3. 210 km
  4. 190 km

Answer: B. 60 km saves 20 min → 90 km/h; remaining 90 km → 180.

Q61 · Time, Work & Distance

Three men can build a wall individually in 12 hours, 15 hours and 20 hours, respectively. However, if they work together, they end up using 340 fewer bricks per hour than the sum of their individual rates and complete the wall in 15 hours. Find the total number of bricks in the wall?

  1. 2700
  2. 3250
  3. 2550
  4. 3200

Answer: C. N/5 − N/15 = 340 → N = 2550.

Q62 · Geometry (Lines, Triangles, Circles, Polygons)

In a circle, two chords AB and CD are equal in length. If chord AB subtends an angle of 35° at the centre, find the angle subtended by chord CD at the centre.

  1. 30°
  2. 35°
  3. 40°
  4. 70°

Answer: B. Equal chords, equal angles.

Q63 · Algebra

If y = + 1, then the value of 1 + (1/y) + (1/y²) − (1/y³) + (1/y⁴) − (1/y⁵) is?

  1. 2
  2. −1
  3. 0
  4. 2

Answer: A / D. 1 + 1 + 1 − 1 + 1 − 1 = 2.

Q64 · Ratio, Proportion & Partnership

A, B and C invest ₹24,000, ₹36,000 and ₹12,000 respectively in a business. A is the working partner and receives 26.67% of the total profit for managing the business. The remaining profit is shared among A, B and C in the ratio of their capitals. At the end of the year, A’s total share of profit ₹300 more than the combined shares of B and C. Find the amount that gets by A?

  1. ₹7,500
  2. ₹6,500
  3. ₹6,900
  4. ₹5,600

Answer: C. A = 23P/45, B + C = 22P/45 → P = 13500.

Q65 · Number System & Simplification

If √(8ⁿ) = 512, then the value of n is:

  1. 8
  2. 3
  3. 4
  4. 6

Answer: D. 8^(n/2) = 8³.

Q66 · Geometry (Lines, Triangles, Circles, Polygons)

In ΔABC, a line DE is drawn parallel to BC, meeting AB at D and AC at E. If AD:DB = 2:3 and BC = 35 cm, find DE.

  1. 12 cm
  2. 14 cm
  3. 16 cm
  4. 21 cm

Answer: B. 2/5 × 35.

Q67 · Time, Work & Distance

A is twice as efficient as B, and B is 50% more efficient than C. If A, B and C together complete a work in 12 days, in how many days can B alone complete the work?

  1. 36 days
  2. 40 days
  3. 49 days
  4. 44 days

Answer: D. 6 : 3 : 2 → 132/3.

Q68 · Mensuration (2D & 3D)

A trapezium has parallel sides 18 cm and 32 cm. The distance between the parallel sides is 10 cm. What is the area of the trapezium?

  1. 220 cm²
  2. 240 cm²
  3. 250 cm²
  4. 300 cm²

Answer: C. ½ × 50 × 10.

Q69 · Mensuration (2D & 3D)

The diagonals of a rhombus are in the ratio 11:60 and its perimeter is 244 cm. What is its area?

  1. 1200 cm²
  2. 1320 cm²
  3. 1440 cm²
  4. 1560 cm²

Answer: B. 11-60-61 → diagonals 22, 120.

Q70 · Heights & Distances

A 12 m high tree casts a shadow of length 12√3 m. Find the angle of elevation of the sun.

  1. 30°
  2. 45°
  3. 60°
  4. 90°

Answer: A. tan = 1/√3.

Q71 · Heights & Distances

From the roof of a 20 m high building, the angle of elevation of the top of a tower is 45° and the angle of depression of its foot is 30°. Find the height of the tower.

  1. 20√3 m
  2. 20(√3 + 1) m
  3. 40√3 m
  4. 20(2√3 + 1) m

Answer: B. Distance 20√3 → 20 + 20√3.

Q72 · Trigonometry

A ladder leans against a wall making an angle of 28° with the ground. To calculate stability, the engineer needs the complementary angle. Find the complementary angle.

  1. 46°
  2. 54°
  3. 56°
  4. 62°

Answer: D. 90 − 28.

Q73 · Number System & Simplification

A set is formed as S = (−2, 0, 3/4, √16, √15). Under the usual school convention where natural numbers start from 1, how many elements of S are natural numbers?

  1. 1
  2. 2
  3. 3
  4. 4

Answer: A. Only √16 = 4.

Q74 · Number System & Simplification

A rational number has a terminating decimal expansion only when the denominator in lowest terms has no prime factors other than 2 and 5. Which fraction below has a non-terminating recurring decimal expansion?

  1. 13/40
  2. 7/12
  3. 21/28
  4. 25/125

Answer: B. Denominator has 3. (21/28 = 3/4.)

Q75 · Trigonometry

If sin⁴θ + cos⁴θ = 7/9, then find tan²θ + cot²θ.

  1. 5
  2. 6
  3. 7
  4. 8

Answer: C. s²c² = 1/9 → (7/9) ÷ (1/9).

12th level · 16 Sep 2026, Shift 2, 1:30 PM

Q51 · Algebra

If x = 531, y = −295 and z = −231, find the value of [(x − y)² + (y − z)² + (z − x)²] / (x³ + y³ + z³ − 3xyz).

  1. 0.6
  2. 0.4
  3. 0.5
  4. 0.3

Answer: B. x + y + z = 5. Expression = 2/(x + y + z) = 2/5 = 0.4. ⚡ Numerator is 2(x²+y²+z²−xy−yz−zx).

Q52 · Ratio, Proportion & Partnership

Ravi started a business with an investment of Rs. 90,000 and after 4 months Krishna joined him investing Rs. 1,50,000. If the profit at the end of the year is Rs. 66,500, then find Krishna's profit?

  1. Rs. 31,500
  2. Rs. 35,000
  3. Rs. 27,500
  4. Rs. 21,500

Answer: B. 90,000×12 : 1,50,000×8 = 9 : 10 → Krishna = 10/19 × 66,500 = 35,000.

Q53 · Simple & Compound Interest

At what rate per annum will Rs. 54,000 yield a compound interest of Rs. 39,312 in 9 months compounded quarterly?

  1. 45%
  2. 54%
  3. 72%
  4. 80%

Answer: D. 9 months = 3 quarters. 93,312/54,000 = 1.728 = 1.2³ → 20% per quarter = 80% p.a.

Q54 · Profit, Loss & Discount

Raj purchases an item whose marked price is partly paid in cash and the balance through a credit card. On the cash-paid 30% portion, he receives a 35% discount, while the credit-card-paid 70% portion incurs a 3% surcharge. If the total amount he finally pays is ₹9,160. Find the marked price of the item?

  1. ₹7,500
  2. ₹8,500
  3. ₹9,000
  4. ₹10,000

Answer: D. 0.3×0.65 + 0.7×1.03 = 0.916 of MP = 9,160 → MP = 10,000.

Q55 · Mixture & Alligation

A bottle contains 80 lit of a honey-water mixture and 25% of the mixture is pure honey. Some additional pure honey is added to the bottle so that the final mixture contains 60% honey. What amount of pure honey must be added to achieve this new concentration?

  1. 50 lit
  2. 90 lit
  3. 70 lit
  4. 71 lit

Answer: C. Honey 20, water 60. Water must be 40% → total 150 → add 70 L.

Q56 · Percentage

The income of A is 80% of B's income and the expenditure of A is 60% of B's expenditure. If the income of A is equal to 120% of B's expenditure, then by what percentage are the savings of A more than B's saving?

  1. 15%
  2. 18%
  3. 20%
  4. 22%

Answer: C. B income 100 → A income 80 = 1.2 × B's exp → B exp 66.67, A exp 40. Savings 40 vs 33.33 → 20%.

Q57 · Mixture & Alligation

Five identical vessels each have capacity C. The quantities of milk in them are in the ratio 2:3:4:5:6. The total milk equals to 4/7 of the combined capacity of the five vessels. How many vessels contain at least half of a vessel?

  1. 2
  2. 3
  3. 4
  4. 5

Answer: B. 20k = (4/7)·5C → k = C/7. Vessels hold 2C/7…6C/7; at least C/2 → 4/7, 5/7, 6/7 → 3.

Q58 · Time, Work & Distance

Two stations X and Y are 900 km apart. Train P starts from station X and travels toward Y and at the same time train Q starts from station Y and travels toward X. Train Q is 50% faster than train P and both trains travel at constant speeds. Find the distance from station Y to the point where the two trains meet?

  1. 360 km
  2. 540 km
  3. 180 km
  4. 420 km

Answer: B. Speeds 2 : 3 → Q covers 3/5 × 900 = 540 km.

Q59 · Time, Work & Distance

A and B can do a work in 35 days and 42 days respectively. They began the work together, but A left after some time and B finished the remaining working in 9 days. After how many days did A leave the work?

  1. 14 days
  2. 13 days
  3. 12 days
  4. 15 days

Answer: D. B's 9 days = 9/42. Rest 33/42 at 11/210 per day together → 15 days.

Q60 · Time, Work & Distance

P can complete a work in 25 more days than Q, while P takes 45 more days than R to complete the same work If P and Q work together, they can finish the work at the same time that R can complete it alone. How many days would P alone take to complete the work?

  1. 15 days
  2. 20 days
  3. 30 days
  4. 75 days

Answer: D. P = x, Q = x − 25, R = x − 45; 1/x + 1/(x − 25) = 1/(x − 45) → x = 75. ⚡ Check 75, 50, 30.

Q61 · Geometry (Lines, Triangles, Circles, Polygons)

Two chords AB and CD of a circle subtend angles of 40° and 70° respectively at the centre. Find the difference between the angles subtended by these chords at points on the circle lying on their minor arcs.

  1. 10°
  2. 15°
  3. 20°
  4. 30°

Answer: B. Inscribed angles are half: 20° and 35° → difference 15°.

Q62 · Number System & Simplification

If (48÷36×3) − [15÷9×(40 − 31) − 10] + 2P = 8÷4, then find the value of P?

  1. 5/2
  2. 2/3
  3. 3/2
  4. 7/2

Answer: C. 4 − (15 − 10) + 2P = 2 → 2P = 3 → P = 3/2.

Q63 · Algebra

Simplify: ((a² − b²)³ + (b² − c²)³ + (c² − a²)³)/((a − b)³ + (b − c)³ + (c − a)³).

  1. (a − b)(b + c)(c + a)
  2. (a − b)(b − c)(c − a)
  3. (a + b)(b + c)(c + a)
  4. (a + b)(b + c)(c − a)

Answer: C. If p + q + r = 0, p³ + q³ + r³ = 3pqr → ratio = (a+b)(b+c)(c+a).

Q64 · Number System & Simplification

The product of a number and its square is 729. Find the number.

  1. 9
  2. 3
  3. 2
  4. 6

Answer: A. n³ = 729 → 9.

Q65 · Number System & Simplification

√(6 + √(6 + √(6 + ⋯))) is equal to:

  1. 3
  2. 5
  3. 6
  4. 2

Answer: A. x² = 6 + x → x = 3.

Q66 · Number System & Simplification

Find the smallest number which when divided by 12, 15, and 18 leaves a remainder of 7 in each case.

  1. 181
  2. 185
  3. 183
  4. 187

Answer: D. LCM(12, 15, 18) = 180 → 180 + 7 = 187.

Q67 · Number System & Simplification

What is the value of (0.1̄ + 0.2̄ + 0.3̄ + … + 0.8̄) ÷ 4?

  1. 1
  2. 5
  3. 9
  4. 7

Answer: A. 0.n̄ = n/9 → (1+…+8)/9 = 4 → ÷ 4 = 1.

Q68 · Number System & Simplification

Simplify the expression: √(10 + √24 + √40 + √60) / (√2 + √3 + √5).

  1. √5
  2. 1
  3. 2
  4. √7

Answer: B. (√2 + √3 + √5)² = 10 + √24 + √40 + √60 → value 1.

Q69 · Mensuration (2D & 3D)

For a right prism, the base area is 54 cm², the perimeter of the base is 30 cm and the height is 8 cm. What is its total surface area?

  1. 240 cm²
  2. 294 cm²
  3. 348 cm²
  4. 432 cm²

Answer: C. TSA = 2 × 54 + 30 × 8 = 348.

Q70 · Trigonometry

Evaluate without using decimal values: sin18°·sec72° + cos18°·cosec72° + tan35°·cot35°.

  1. 1
  2. 2
  3. 3
  4. 4

Answer: C. Each pair is complementary → 1 + 1 + 1 = 3.

Q71 · Mensuration (2D & 3D)

The length, breadth and height of a cuboid are in the ratio 2:3:6 and its space diagonal is 21 cm. Find its volume.

  1. 486 cm³
  2. 729 cm³
  3. 972 cm³
  4. 1458 cm³

Answer: C. 7k = 21 → k = 3 → 6 × 9 × 18 = 972.

Q72 · Mensuration (2D & 3D)

A regular square pyramid has base side 12 cm and vertical height 8 cm. What is its total surface area?

  1. 288 cm²
  2. 336 cm²
  3. 384 cm²
  4. 432 cm²

Answer: C. Slant = √(8² + 6²) = 10. 2 × 12 × 10 + 144 = 384.

Q73 · Trigonometry

If sinθ + cosθ = 1, then the value of sinθ cosθ is:

  1. 0
  2. 1/2
  3. −1/2
  4. 1

Answer: A. (s + c)² = 1 → 2sc = 0.

Q74 · Mensuration (2D & 3D)

A hemispherical bowl has radius 9 cm and is filled completely with water. What is its volume?

  1. 243π cm³
  2. 324π cm³
  3. 486π cm³
  4. 729π cm³

Answer: C. (2/3)π·9³ = 486π.

Q75 · Trigonometry

If tan A + tan² A = 1, then find cot² A − cot A.

  1. 0
  2. 1
  3. 2
  4. −1

Answer: B. tanA(1 + tanA) = 1 → cotA = 1 + tanA → cot²A − cotA = cotA·tanA = 1.

12th level · 17 Sep 2026, Shift 2, 1:30 PM

Q51 · Mensuration (2D & 3D)

A dessert consists of a cone having a radius of 3.5 cm and 12 cm high, topped by a hemispherical scoop also with a 3.5 cm radius. Determine the total volume of this dessert.

  1. 243.83 cm³
  2. 678.89 cm³
  3. 220.45 cm³
  4. 324.57 cm³

Answer: A. Cone 154 + hemisphere 89.83 = 243.83 cm³.

Q52 · Mensuration (2D & 3D)

A cylindrical water tank of height 1.5 m and diameter 1.4 m is completely filled. Determine the estimated water does it hold (in liters).

  1. 2200 liters
  2. 2400 liters
  3. 2150 liters
  4. 2310 liters

Answer: D. π × 0.7² × 1.5 = 2.31 m³ = 2,310 L.

Q53 · Mensuration (2D & 3D)

Find the length of the arc which is intercepted by a central angle of 90° in a circle of radius 14 cm. (Use π = 22/7)

  1. 22 cm
  2. 23 cm
  3. 24 cm
  4. 25 cm

Answer: A. ¼ × 2π × 14 = 22.

Q54 · Mensuration (2D & 3D)

If a solid metal sphere with a 4.2 cm radius is reshaped by melting into smaller spheres, each having a radius of 0.7 cm, what will be the total count of these smaller spheres?

  1. 450
  2. 200
  3. 216
  4. 345

Answer: C. (4.2/0.7)³ = 6³ = 216.

Q55 · Mensuration (2D & 3D)

If the height of a cylinder is reduced by 20% and radius increased by 25%, what is the percentage change in curved surface area? (Use approximation only)

  1. 5% increase
  2. 4% decrease
  3. 10% increase
  4. No change

Answer: D. CSA ∝ rh: 1.25 × 0.8 = 1 → no change.

Q56 · Number System & Simplification

Which of the following is equal to the decimal 7.8125?

  1. 63/8
  2. 125/16
  3. 113/14
  4. 105/13

Answer: B. 7.8125 = 7 + 13/16 = 125/16.

Q57 · Number System & Simplification

If 2.3̄6̄ means the digits 36 are repeating after 2., then the value in fraction form is:

  1. 23/9
  2. 78/33
  3. 26/11
  4. 118/45

Answer: B / C. 2 + 36/99 = 2 + 4/11 = 26/11.

Q58 · Simple & Compound Interest

A businessman lent Rs. 10,000 to two individuals, one loan earning simple interest and the other compound interest, both at the same annual interest rate. After 3 years, the difference between the compound interest and simple interest amounts to Rs. 25. After 2 years, this difference is Rs. 8. Determine the annual rate of interest.

  1. 18.65%
  2. 12.5%
  3. 13.42%
  4. 17.26%

Answer: B. For SI vs CI: D₃/D₂ = 3 + r → 25/8 = 3 + r → r = 1/8 = 12.5%.

Q59 · Percentage

A food truck uses 250 kg of flour per month. In a new eco-friendly recipe, it reduces flour usage by 20%. How much flour is saved in one month?

  1. 50
  2. 10
  3. 20
  4. 30

Answer: A. 20% of 250 = 50 kg.

Q60 · Simple & Compound Interest

Raj deposited Rs. 800 in a savings account that earns simple interest. After 3 years, the total amount reached Rs. 956. If the interest rate is raised by 4%, what will be the total amount after 3 years at the new rate?

  1. 1547
  2. 1343
  3. 1052
  4. 1232

Answer: C. SI 156 in 3 yrs → 6.5% → 10.5% → 800 × 31.5% = 252 → 1,052.

Q61 · Number System & Simplification

Which of the following is equal to √5 − √2

  1. √5 + √2
  2. √5 − √2 + 1
  3. (√5 − √2)/1
  4. None

Answer: C. Dividing by 1 changes nothing.

Q62 · Trigonometry

If tan θ = 3/4, what is (sin θ + cos θ)/(sin θ − cos θ)?

  1. −5
  2. −7
  3. 0
  4. −8

Answer: B. Divide by cosθ: (3/4 + 1)/(3/4 − 1) = −7.

Q63 · Geometry (Lines, Triangles, Circles, Polygons)

Two calibration dials of radii 12 cm and 5 cm are attached to a control panel with centers 17 cm apart. To check alignment, an engineer draws tangents. Find the lengths of the direct and transverse tangents.

  1. 18.44 cm, 0
  2. 15.49 cm, 0
  3. 12.34 cm, 1 cm
  4. 16.76 cm, 14.62 cm

Answer: B. d = 17 = r₁ + r₂ → circles touch, transverse tangent 0. Direct = √(17² − 7²) = √240 ≈ 15.49.

Q64 · Time, Work & Distance

A person travels 640 km in 16 hours, partly by train and partly by car. If the train covers 3 times the distance covered by the car and the speed of the train is 60 km/h, find the speed of the car.

  1. 20 km/h
  2. 30 km/h
  3. 35 km/h
  4. 25 km/h

Answer: A. Train 480 km at 60 = 8 h → car 160 km in 8 h = 20 km/h.

Q65 · Mixture & Alligation

A 470 kg mixture of sand and gravel contains 55% gravel. How much gravel must be added to make the mixture contain 65% gravel?

  1. 30 kg
  2. 35 kg
  3. 20 kg
  4. 25 kg

Answer: C. Official key: 20 kg.

Q66 · Ratio, Proportion & Partnership

Aman and Mahesh invest Rs. 65,000 and Rs. 78,000 for 1 year. What is the ratio of their profits?

  1. 5:6
  2. 5:8
  3. 7:6
  4. 6:7

Answer: A. 65 : 78 = 5 : 6.

Q67 · Mensuration (2D & 3D)

If the ratio of the height and base of a parallelogram is 14:9, respectively, and its area is 1134 cm², then find the difference between the height and base of the parallelogram.

  1. 12 cm
  2. 28 cm
  3. 15 cm
  4. 26 cm

Answer: C. 126k² = 1134 → k = 3 → 42 − 27 = 15.

Q68 · Geometry (Lines, Triangles, Circles, Polygons)

The ratio of an interior angle to its corresponding exterior angle in a regular polygon is 5:1. How many sides does it have?

  1. 12
  2. 9
  3. 7
  4. 15

Answer: A. Exterior = 180/6 = 30° → 12 sides.

Q69 · Number System & Simplification

Which of the following statements is true regarding the relationship between rational and irrational numbers?

  1. Rational and irrational numbers belong to the same set.
  2. Rational and irrational numbers are mutually exclusive to each other.
  3. All irrational numbers are rational numbers.
  4. All rational numbers are irrational numbers.

Answer: B. No number is both rational and irrational.

Q70 · Coordinate Geometry

Which of the following equations represents a horizontal line?

  1. 5x + 3y = 12
  2. 4x + 9y = 13
  3. y = 7/3
  4. x = 12/7

Answer: C. y = constant is horizontal.

Q71 · Mixture & Alligation

A milkman has 20 liters of milk. He mixes it with 5 liters of water. What is the percentage of water in the mixture?

  1. 20%
  2. 40%
  3. 60%
  4. 80%

Answer: A. 5/25 = 20%.

Q72 · Profit, Loss & Discount

A shopkeeper sold an article at successive discounts of 20% and 30%. Find the overall discount percentage.

  1. 25%
  2. 44%
  3. 50%
  4. 62%

Answer: B. 1 − 0.8 × 0.7 = 0.44 → 44%.

Q73 · Mensuration (2D & 3D)

Calculate the area of a triangle with sides 7 cm, 9 cm, and 12 cm.

  1. 10√5 cm²
  2. 16√5 cm²
  3. 14√5 cm²
  4. 18√5 cm²

Answer: C. s = 14 → √(14·7·5·2) = 14√5.

Q74 · Number System & Simplification

Simplify: [(0.64 ÷ 0.008) − 18.75% of 320] ÷ [5² − (4³ ÷ 8)]

  1. 20/17
  2. 17/20
  3. 21/17
  4. 19/17

Answer: A. (80 − 60) ÷ (25 − 8) = 20/17.

Q75 · Mensuration (2D & 3D)

The curved surface area of a cone is 220π cm² and its radius is 10 cm. What is the slant height of the cone?

  1. 11 cm
  2. 18 cm
  3. 22 cm
  4. 24 cm

Answer: C. πrl = 220π → l = 22.

12th level · 18 Sep 2026, Shift 2, 1:30 PM

Q51 · Algebra

If (k³⁶ + 1)/(k¹⁸) = 11, then find the value of (k⁷² + 1)/k³⁶?

  1. 131
  2. 119
  3. 124
  4. 121

Answer: B. k¹⁸ + 1/k¹⁸ = 11 → square − 2 = 119.

Q52 · Ratio, Proportion & Partnership

A and B started a business with capitals of Rs. 32,000 and Rs. 48,000 respectively. B took a salary of Rs. 1,200 per month from the profit as he ran the business. They carried a profit of Rs. 24,000 at the end of the year. What is the share of A in the profit?

  1. Rs. 9,200
  2. Rs. 3,540
  3. Rs. 6,000
  4. Rs. 3,840

Answer: D. B's salary 14,400 → 9,600 shared 2 : 3 → A = 3,840.

Q53 · Simple & Compound Interest

The difference between the CI and SI on a certain sum of money for 3 years at 5% per annum is Rs. 244. Find the principal?

  1. Rs. 24,000
  2. Rs. 35,000
  3. Rs. 32,000
  4. Rs. 28,000

Answer: C. 3-yr diff = P·r²(3 + r) = P × 0.007625 = 244 → P = 32,000.

Q54 · Mixture & Alligation

In a pot there is a mixture of milk and water in the ratio of 9:4. By adding 35 lit of water the ratio gets reversed and the pot becomes full. What is the capacity of the pot?

  1. 75 lit
  2. 69 lit
  3. 63 lit
  4. 84 lit

Answer: C. 9x/(4x + 35) = 4/9 → x = 28/13 → capacity 13x + 35 = 63.

Q55 · Algebra

A man participated in a gambling game for three rounds. According to the rules of the game, if he wins a round, he receives ₹200, but after each round he must pay 50% of the total amount he has at that moment. He was lucky and won all three rounds. After completing the three rounds, he found that he had lost three-fourths of his initial amount. Find the initial amount he had before starting the game?

  1. ₹1,250
  2. ₹1,400
  3. ₹1,500
  4. ₹1,600

Answer: B. After 3 rounds: (I + 1400)/8 = I/4 → I = 1,400.

Q56 · Time, Work & Distance

A car travels from city P to city Q at a constant speed. If its speed were increased by 6 km/h, the trip would take 1 hour less. If the speed were further increased by 4 km/h (i.e. 10 km/h more than original), the trip would take an additional 30 minutes less. What is the distance between the two cities?

  1. 360 km
  2. 180 km
  3. 40 km
  4. 200 km

Answer: B. d = s(s + 6)/6; try s = 30 → d = 180, and with +10: 180/30 − 180/40 = 1.5 ✓.

Q57 · Time, Work & Distance

Raj can do 44.44% of a work in 36 days. He works for 24 days and then Karan alone finishes the balance of the work in 38 days. In how many days will both working together complete half of the same work?

  1. 14.2 days
  2. 8.5 days
  3. 16.2 days
  4. 11.8 days

Answer: C. Raj: 81 days. Karan does 19/27 in 38 → 54 days. Together 5/162 per day → half in 16.2 days.

Q58 · Time, Work & Distance

A man works twice as fast as a woman and a woman works twice as fast as a child. If 18 men can complete a job in 10 days, how many days would 36 women and 72 children together require to finish the same job?

  1. 6 days
  2. 8 days
  3. 5 days
  4. 7 days

Answer: C. 1 man = 2 women = 4 children. 180 man-days = 720 child-days ÷ 144 = 5.

Q59 · Profit, Loss & Discount

Find the single equivalent discount for successive discounts of 20%, 25%, and 50% on the marked price of a laptop.

  1. 70%
  2. 60%
  3. 90%
  4. 80%

Answer: A. 1 − 0.8 × 0.75 × 0.5 = 70%.

Q60 · Algebra

If x² − 6x + 1 = 0, then find the value of x⁴ + 1/x⁴.

  1. 1150
  2. 1152
  3. 1154
  4. 1156

Answer: C. x + 1/x = 6 → 34 → 34² − 2 = 1154.

Q61 · Number System & Simplification

A decimal expression is given as (0.125 + 0.333333...) ÷ (0.75 − 0.2). Convert all decimals to fractions and find the simplified value.

  1. 5/6
  2. 6/5
  3. 11/20
  4. 24/55

Answer: A. (1/8 + 1/3) ÷ (11/20) = (11/24) × (20/11) = 5/6.

Q62 · Mixture & Alligation

Two equal quantities of mixtures are mixed together. In the first mixture, milk and water are in the ratio 5 : 3, and in the second mixture, milk and water are in the ratio 7 : 5. What is the ratio of milk to water in the final mixture?

  1. 29 : 19
  2. 17 : 11
  3. 19 : 29
  4. 31 : 17

Answer: A. 5/8 + 7/12 = 29/24 milk, 19/24 water → 29 : 19.

Q63 · Number System & Simplification

Simplify: [(13/15 ÷ 26/45) + (7/12 ÷ 14/9)] × 48/7

  1. 80/7
  2. 85/7
  3. 90/7
  4. 95/7

Answer: C. 3/2 + 3/8 = 15/8 → × 48/7 = 90/7.

Q64 · Mensuration (2D & 3D)

A right prism has an equilateral triangular base of side 12 cm and height 10 cm. Find the exact volume of the prism.

  1. 120√3 cm³
  2. 240√3 cm³
  3. 360√3 cm³
  4. 720√3 cm³

Answer: C. (√3/4)·144 × 10 = 360√3.

Q65 · Number System & Simplification

A positive integer is given by N = 2³ × 3² × 5 × 7³. It is to be multiplied by the least natural number so that the product becomes a perfect square. What is the required least multiplier?

  1. 35
  2. 70
  3. 140
  4. 210

Answer: B. Odd powers: 2, 5, 7 → multiply by 70.

Q66 · Mensuration (2D & 3D)

A rectangular parallelepiped has length 12 cm, breadth 9 cm and height 8 cm. Find its volume.

  1. 729 cm³
  2. 768 cm³
  3. 864 cm³
  4. 936 cm³

Answer: C. 12 × 9 × 8 = 864.

Q67 · Geometry (Lines, Triangles, Circles, Polygons)

A satellite dish is tilted at an angle of 31°. What is the measure of its complementary angle?

  1. 49°
  2. 59°
  3. 69°
  4. 79°

Answer: B. 90 − 31 = 59°.

Q68 · Mensuration (2D & 3D)

A square pyramid has base side 9 cm and vertical height 12 cm. What is its volume?

  1. 243 cm³
  2. 324 cm³
  3. 486 cm³
  4. 972 cm³

Answer: B. (1/3) × 81 × 12 = 324.

Q69 · Number System & Simplification

Three statements are given about number systems. I. Every integer is rational. II. Every whole number is an integer. III. Every irrational number is real. Which statements are always true?

  1. Only I and II
  2. Only II and III
  3. Only I and III
  4. I, II and III

Answer: D. All three are always true.

Q70 · Trigonometry

If sinθ cosθ = 1/3, then find the value of sin⁴θ + cos⁴θ.

  1. 5/9
  2. 7/9
  3. 8/9
  4. 1/9

Answer: B. 1 − 2s²c² = 1 − 2/9 = 7/9.

Q71 · Trigonometry

If α and β are acute angles, α + β = 60° and tan α tan β = 1/3, then find tan α + tan β.

  1. √3/3
  2. 2√3/3
  3. √3
  4. 4√3/3

Answer: B. tan60 = S/(1 − 1/3) → S = 2√3/3.

Q72 · Number System & Simplification

If the value of [(6¹²)^(1/3) × ∛27 ÷ 3²] + 4⁰ − 1000⁰ is equal to 2ᵃ × 3ᵇ × 5ᶜ then a+b−2c equals to

  1. 7
  2. 12
  3. 18
  4. 22

Answer: A. 6⁴ × 3 ÷ 9 = 432 = 2⁴ × 3³ → 4 + 3 − 0 = 7.

Q73 · Number System & Simplification

Simplify: [√(7 + 4√3) − √(7 − 4√3)] / 2

  1. 6√3
  2. √2
  3. √3
  4. 2√3

Answer: C. √(7 ± 4√3) = 2 ± √3 → (2√3)/2 = √3.

Q74 · Mensuration (2D & 3D)

A hemispherical bowl is open at the top and has inner radius 10 cm. What is the exact inner curved surface area?

  1. 100π cm²
  2. 150π cm²
  3. 200π cm²
  4. 300π cm²

Answer: C. 2πr² = 200π.

Q75 · Geometry (Lines, Triangles, Circles, Polygons)

Two chords AB and CD intersect at P inside a circle. If ∠APC = 75° and the ratio of arcs AC : BD = 5:1, find the angle subtended by chord BD at any point on the major arc.

  1. 12.5°
  2. 15°
  3. 25°
  4. 27.5°

Answer: A. AC + BD = 150°, 5 : 1 → BD = 25° → inscribed 12.5°.

12th level · 19 Sep 2026, Shift 2, 1:30 PM

Q51 · Algebra

x and y are positive integers such that x⁴ + y⁴ + x²y² = 473 and xy = 16, then what is the value of x² + xy + y²?

  1. 52
  2. 43
  3. 15
  4. 37

Answer: B. (x² + y²)² − x²y² = 473 → x² + y² = 27 → 27 + 16 = 43.

Q52 · Ratio, Proportion & Partnership

Ram, Ravi, Rahim started a business. Ram invests 37.5% of the total capital, Ravi invested 66⅔% of the remaining capital and the Rahim invested the rest. If the total profit at the end of the year was Rs. 2,040 then find the amount by which the profit Ravi exceeds Raheem?

  1. Rs. 375
  2. Rs. 425
  3. Rs. 500
  4. Rs. 575

Answer: B. Ram 37.5%, Ravi 41.67%, Rahim 20.83% → difference 20.83% of 2,040 = 425.

Q53 · Simple & Compound Interest

A certain sum of money is invested at a rate of 16.67% per annum, with the interest being compounded annually. After being invested for 3 years, the amount accumulated becomes ₹15,000. Find the amount at the end of the 4th year?

  1. ₹18,500
  2. ₹17,500
  3. ₹17,000
  4. ₹17,250

Answer: B. 16.67% = 1/6 → 15,000 × 7/6 = 17,500.

Q54 · Profit, Loss & Discount

The cost price of two articles A and B is the same. Article A is sold at a loss of 30% and Article B is sold for Rs. 2,300 more than the selling price of A. If the net profit made by selling both the articles together is 16%, then what is the selling price of article B?

  1. Rs. 5,400
  2. Rs. 4,250
  3. Rs. 4,050
  4. Rs. 4,500

Answer: C. CP 100 each: A 70, total 232 → B 162 → difference 92 ↔ 2,300 → B = 4,050.

Q55 · Mixture & Alligation

A milk man mixes 40lit of water with 80 lit of milk. After selling 25% of this mixture, he adds water to replenish quantity that he has sold. What is the current proportion of water to milk?

  1. 2:1
  2. 1:2
  3. 1:1
  4. 2:3

Answer: C. After sale: 30 water, 60 milk; add 30 water → 60 : 60 = 1 : 1.

Q56 · Percentage

In an examination 70% of the students passed in Arithmetic, 55% of the students passed in Reasoning, 20% of the students failed in both the subjects. 125 students who passed only in Arithmetic, then find how many students failed only in reasoning?

  1. 145
  2. 120
  3. 125
  4. 225

Answer: C. Both passed 45% → only Arithmetic 25% = 125 → total 500. Failed only Reasoning = only Arithmetic = 125.

Q57 · Time, Work & Distance

Train A takes 1½ hours more than train B to cover a distance of 240 km. If the speed of train A doubles, it then takes 30 minutes less than the time taken by train B for the same distance. What is the speed of train B?

  1. 100 kmph
  2. 84 kmph
  3. 96 kmph
  4. 72 kmph

Answer: C. tA = tB + 1.5 and tA/2 = tB − 0.5 → tB = 2.5 h → 96 km/h.

Q58 · Time, Work & Distance

Ravi is thrice as good as work man as Krishna. If together they can complete a work in 28 days, in how many days Ravi alone completes the work?

  1. 37.33 days
  2. 45.25 days
  3. 39 days
  4. 28 days

Answer: A. 3 : 1 → work 4 × 28 = 112 → Ravi 112/3 = 37.33 days.

Q59 · Time, Work & Distance

The ratio of efficiency of P & Q is 9:5. Working together they can complete a certain work in 7½ days. P alone completed the 3/7 part of the work and after which Q alone completed the remaining work. The total number of days in which the entire work got complete is?

  1. 12 days
  2. 15 days
  3. 17 days
  4. 18 days

Answer: C. Work 14 × 7.5 = 105. P does 45 in 5 days, Q does 60 in 12 → 17.

Q60 · Algebra

If 3x = a + b + c, find the value of (x − a)³ + (x − b)³ + (x − c)³ − 3(x − a)(x − b)(x − c).

  1. a + b + c
  2. (a − b)(b − c)(c − a)
  3. 0
  4. a + b − c

Answer: C. (x − a) + (x − b) + (x − c) = 0 → expression = 0.

Q61 · Number System & Simplification

The product of a positive number and its square is 1331. What is the value of the number?

  1. 11
  2. 13
  3. 17
  4. 19

Answer: A. n³ = 1331 → 11.

Q62 · Ratio, Proportion & Partnership

If x : y : z = 5 : 6 : 7 and 3x − 2y + z = 40, then the value of z is:

  1. 14
  2. 22
  3. 28
  4. 18

Answer: C. 15k − 12k + 7k = 10k = 40 → z = 28.

Q63 · Number System & Simplification

What is the least number that must be subtracted from 9400 to make it divisible by 23?

  1. 16
  2. 18
  3. 24
  4. 20

Answer: A. 9400 = 23 × 408 + 16.

Q64 · Number System & Simplification

Calculate: √0.4̄ × (0.46̄ + 0.03̄).

  1. 1/5
  2. 1/7
  3. 1/3
  4. 1/2

Answer: C. √(4/9) = 2/3; 7/15 + 1/30 = 1/2 → 1/3.

Q65 · Number System & Simplification

Evaluate: ((2.3)³ − 0.027) / ((2.3)² + 0.69 + 0.09).

  1. 2
  2. 7
  3. 1
  4. 9

Answer: A. (a³ − b³)/(a² + ab + b²) = a − b = 2.3 − 0.3 = 2.

Q66 · Number System & Simplification

Evaluate: √(6 + √(6 + √(6 + …∞))).

  1. 6
  2. 3
  3. 8
  4. 9

Answer: B. x² = 6 + x → 3.

Q67 · Mensuration (2D & 3D)

A right prism has a square base of side 9 cm and height 20 cm. Find its total surface area.

  1. 720 cm²
  2. 801 cm²
  3. 882 cm²
  4. 900 cm²

Answer: C. 2 × 81 + 36 × 20 = 882.

Q68 · Number System & Simplification

If a = √3481 and b = √2209, then find the value of (a² − b²) ÷ (a − b).

  1. 96
  2. 104
  3. 106
  4. 112

Answer: C. a + b = 59 + 47 = 106.

Q69 · Trigonometry

If sec(7θ − 11°) = cosec(4θ + 2°), where both angles are acute, then θ is equal to:

  1. 7°
  2. 8°
  3. 9°
  4. 10°

Answer: C. 11θ − 9 = 90 → θ = 9°.

Q70 · Mensuration (2D & 3D)

A cuboid has dimensions 10 cm, 6 cm and 4 cm. What is its total surface area?

  1. 200 cm²
  2. 224 cm²
  3. 248 cm²
  4. 280 cm²

Answer: C. 2(60 + 40 + 24) = 248.

Q71 · Mensuration (2D & 3D)

A regular square pyramid has base side 10 cm and slant height 13 cm. What is its lateral surface area?

  1. 130 cm²
  2. 200 cm²
  3. 260 cm²
  4. 360 cm²

Answer: C. ½ × 40 × 13 = 260.

Q72 · Trigonometry

If sin²θ = 9/25 and cosθ is positive, then the value of sin²θ + cos²θ is:

  1. 9/25
  2. 16/25
  3. 1
  4. 25/16

Answer: C. Always 1.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

In a cyclic quadrilateral, two opposite angles are (2x + 10)° and (3x - 5)°. Find the larger of these two opposite angles.

  1. 70°
  2. 80°
  3. 90°
  4. 100°

Answer: D. Opposite angles sum 180 → x = 35 → 80°, 100°.

Q74 · Trigonometry

Simplify: (cosec A − cot A)² + (cosec A + cot A)² − 4cot² A.

  1. 0
  2. 1
  3. 2
  4. 4

Answer: C. 2cosec² + 2cot² − 4cot² = 2(cosec² − cot²) = 2.

Q75 · Mensuration (2D & 3D)

A closed hemispherical dome has radius 6 cm. Its total surface area includes the curved surface and circular base. What is the total surface area?

  1. 72π cm²
  2. 96π cm²
  3. 108π cm²
  4. 144π cm²

Answer: C. 3πr² = 108π.

12th level · 21 Sep 2026, Shift 2, 1:30 PM

Q51 · Mensuration (2D & 3D)

A plot of land is shaped like a quadrilateral consisting of a rectangle and a right-angled triangle attached to one of its shorter sides. The rectangle is 20 m long and 12 m wide. The right-angled triangle has a base of 12 m (same as rectangle’s width) and a height of 9 m. What is the total area of the quadrilateral-shaped land?

  1. 294 m²
  2. 376 m²
  3. 456 m²
  4. 567 m²

Answer: A. 240 + ½ × 12 × 9 = 294.

Q52 · Number System & Simplification

Identify the irrational number from the list below:

  1. (√49)/2
  2. π/2
  3. 2.5
  4. 0.333...

Answer: B. π is irrational.

Q53 · Number System & Simplification

What is the value of: 3² + 5 × 2 − 4?

  1. 15
  2. 17
  3. 19
  4. 13

Answer: A. 9 + 10 − 4 = 15.

Q54 · Number System & Simplification

If the 3rd and 5th terms of a geometric progression are 9 and 81 respectively, what is the sum of the first 4 terms?

  1. 40
  2. 120
  3. 111
  4. 102

Answer: A. r² = 9 → r = 3, a = 1 → 1 + 3 + 9 + 27 = 40.

Q55 · Trigonometry

If sin A= 1/2 , then the value of cot A is

  1. √3
  2. 1/√3
  3. √3/2
  4. 1

Answer: A. A = 30° → cot = √3.

Q56 · Number System & Simplification

A construction company stores steel rods in bundles, where each rod’s length (in cm) is a 5-digit number. Two types of rods were received from different suppliers, with all rods of the same type having equal length. It was found that: One type has rods of length 11088 cm, and the other 17280 cm. The manager wants to cut both types of rods into smaller rods of equal maximum length (no leftover from any rod), so that they can be used interchangeably in modular construction. What is the maximum length (in cm) of each smaller rod that can be cut from both types?

  1. 138
  2. 144
  3. 150
  4. 145

Answer: B. HCF(11088, 17280) = 144.

Q57 · Time, Work & Distance

Atul covers a distance of 436 km in 8 hours by car. Find the speed of the car.

  1. 54.75 km/h
  2. 54.50 km/h
  3. 65.50 km/h
  4. 64.75 km/h

Answer: B. 436/8 = 54.5.

Q58 · Profit, Loss & Discount

The selling price of a mobile set after a discount of 25% is Rs. 10,600. What was the marked price approximately?

  1. Rs. 14,345.33
  2. Rs. 15,233.33
  3. Rs. 14,133.33
  4. Rs. 14,233.33

Answer: C. 10,600 ÷ 0.75 = 14,133.33.

Q59 · Mixture & Alligation

In a 96-litre solution of milk and water where the milk to water ratio is 5:3, what quantity of water should be mixed in to obtain a final ratio of 3:2?

  1. 6 L
  2. 5 L
  3. 4 L
  4. 7 L

Answer: C. Milk 60 → water needed 40 → add 4 L.

Q60 · Time, Work & Distance

26 men can do a job in 45 days. How many men are needed to do the same work in 15 days?

  1. 78
  2. 68
  3. 48
  4. 58

Answer: A. 26 × 45/15 = 78.

Q61 · Geometry (Lines, Triangles, Circles, Polygons)

In triangle ABC, G is the centroid. If CF, AD and BE are medians on sides AB, BC and CA respectively, and the area of triangle BGF is 24 cm² then find the area of triangle ABG.

  1. 24 cm²
  2. 48 cm²
  3. 144 cm²
  4. 72 cm²

Answer: B. Medians make 6 equal triangles → ABG = 2 × 24 = 48.

Q62 · Number System & Simplification

If the square of a number is 3969, what is the square root of the square of twice that number?

  1. 126
  2. 136
  3. 124
  4. 144

Answer: A. Number 63 → √(126²) = 126.

Q63 · Time, Work & Distance

A and B are in the ratio 7:5 in efficiency. A alone can complete the work in 55 days. How long will B take to finish it alone?

  1. 77 days
  2. 67 days
  3. 57 days
  4. 54 days

Answer: A. Time ∝ 1/efficiency → 55 × 7/5 = 77.

Q64 · Algebra

If the sum of three numbers is zero and the sum of their squares is 36. What is the sum of the product of these numbers, two at a time?

  1. −18
  2. −9
  3. 9
  4. 18

Answer: A. 0 = 36 + 2S → S = −18.

Q65 · Heights & Distances

A wooden cane is leaning against a wall, making an angle of 30° with the ground. If the cane is 15 m long, the distance of the point where it touches the wall and the point on the ground measured vertically is:

  1. 7 m
  2. 7.25 m
  3. 7.5 m
  4. 7.75 m

Answer: C. 15 sin30° = 7.5 m.

Q66 · Heights & Distances

A mirror is placed on the ground facing the roof. A girl sees the top of a tower in the mirror which is at a distance of 210 m from the mirror. The girl is 1 m away from the mirror and her height is 1 m, find the height of the tower in meters.

  1. 105 m
  2. 150 m
  3. 200 m
  4. 210 m

Answer: D. Similar triangles: 1/1 = h/210 → 210 m.

Q67 · Number System & Simplification

Simplify the expression: (6.38 × 56 + 6.38 × 44) ÷ [(8.19)² − (1.81)²]

  1. 8
  2. 9
  3. 10
  4. 11

Answer: C. 638 ÷ (10 × 6.38) = 10.

Q68 · Simple & Compound Interest

A principal sum of ₹24,000 is invested at 10% per annum, with interest compounded annually. What is the difference between the compound interest earned in the third year and that earned in the fourth year?

  1. ₹290.4
  2. ₹300.5
  3. ₹275.4
  4. ₹280.5

Answer: A. CI 3rd year = 2,904; 4th = 3,194.4 → 290.4. ⚡ Difference = 10% of 2,904.

Q69 · Mixture & Alligation

A seller deals with three different items named A, B and C. Each of these items earns a different percentage of profit when sold: item A gives him an 18% profit, item B gives him a 32% profit and item C gives him a 35% profit. When the seller considers only the items A and C together, the overall profit percentage from these two items turns out to be 27%. In addition to this, when he considers all three items A, B and C together, the overall profit percentage becomes 29%. It is also given that the total number of items sold, including A, B and C is 170. Determine how many items of type A were sold?

  1. 68
  2. 48
  3. 54
  4. 50

Answer: B. A : C = 8 : 9 (alligation at 27). (A + C) : B = 3 : 2 at 29 → A + C = 102 → A = 48.

Q70 · Ratio, Proportion & Partnership

A and B started a business together by investing money in partnership. A contributed 5/9th of the total capital and kept his investment in the business for 48 months. At the end of the business period, the profit earned was shared between A and B and it was found that B's share of the profit was 3/7th of the total profit. How many months B had invested his money in the business?

  1. 42 months
  2. 45 months
  3. 35 months
  4. 24 months

Answer: B. A : B = (5×48) : (4×t) = 4 : 3 → t = 45.

Q71 · Time, Work & Distance

Ravi and Krishna working together can complete a job in 7 days. If Ravi works thrice as efficiently as he actually did and Krishna work 1/4 efficiently as he actually did, then the work would have been completed in 4 days. Then Krishna alone can complete the work in how many days?

  1. 12.5 days
  2. 15.4 days
  3. 14.5 days
  4. 13.5 days

Answer: B. 7(R + K) = 4(3R + K/4) → R = 1.2K → Krishna alone 7 × 2.2 = 15.4 days.

Q72 · Time, Work & Distance

A, B and C can do a piece of work in 12 days, 18 days and 24 days respectively. They all start the work together, but A leaves after 3 days and B leaves 4 days before the work is completed. In how many days is the work completed?

  1. 12 days
  2. 10 days
  3. 15 days
  4. 20 days

Answer: B. Rates 6, 4, 3 of 72: 18 + 4(T − 4) + 3T = 72 → T = 10.

Q73 · Geometry (Lines, Triangles, Circles, Polygons)

A chord AB subtends an angle of 70° at the centre of the circle. Find the angle subtended by the same chord at a point on the major arc of the circle.

  1. 35°
  2. 70°
  3. 110°
  4. 145°

Answer: A. Angle on the major arc = ½ × 70° = 35°.

Q74 · Mensuration (2D & 3D)

In a trapezium, the parallel sides are 20 cm and 10 cm long. If the non-parallel sides are equal and the area is 180 cm², what is the distance between the parallel sides?

  1. 15 cm
  2. 12 cm
  3. 18 cm
  4. 10 cm

Answer: B. ½ × 30 × h = 180 → 12.

Q75 · Trigonometry

If p + q = 90° and all terms are defined, find the value of: [cosec p − sec q]¹⁰ + [cot p − tan q]⁶ + [sin²p + sin²q][cos²p + cos²q].

  1. 0
  2. 1
  3. 2
  4. 3

Answer: B. cosec p = sec q and cot p = tan q → 0 + 0 + 1 × 1 = 1.

12th level · 22 Sep 2026, Shift 2, 1:30 PM

Q51 · Mensuration (2D & 3D)

A conical vessel of radius 10 cm and height 24 cm is completely filled with water. How many cylindrical bottles of radius 2.5 cm and height 6 cm can be filled from it? (Use π = 3.14)

  1. 29
  2. 21
  3. 34
  4. 25

Answer: B. 800π ÷ 37.5π = 21.3 → 21 bottles.

Q52 · Mensuration (2D & 3D)

A right circular cylinder has the same height and radius as a cone. What is the ratio of their volumes?

  1. 2:1
  2. 1:3
  3. 1:2
  4. 3:1

Answer: D. πr²h : ⅓πr²h = 3 : 1.

Q53 · Mensuration (2D & 3D)

If the radius of a circle is 10.5 cm, what is the length of the arc formed by a central angle of 60°? (Use π = 22/7)

  1. 11 cm
  2. 13 cm
  3. 11.5 cm
  4. 12 cm

Answer: A. (60/360) × 2 × 22/7 × 10.5 = 11.

Q54 · Number System & Simplification

Identify the correct relationship:

  1. Every natural number is an integer, but not every integer is a natural number.
  2. Every integer is a whole number.
  3. Every rational number is an integer.
  4. Every irrational number is a rational number.

Answer: A. Natural ⊂ integers, not the reverse.

Q55 · Number System & Simplification

If a decimal number is written as 0.ababab... (repeating block of 2 digits), its equivalent fraction will have a denominator of:

  1. 100
  2. 99
  3. 990
  4. 9

Answer: B. Two-digit repeating block → /99.

Q56 · Number System & Simplification

Which of the following numbers cannot be expressed as the sum of two odd natural numbers?

  1. 12
  2. 26
  3. 50
  4. 33

Answer: D. Odd + odd = even → 33 is impossible.

Q57 · Geometry (Lines, Triangles, Circles, Polygons)

Each exterior angle of a regular polygon is 30°. How many sides does the polygon have?

  1. 12
  2. 18
  3. 24
  4. 36

Answer: A. 360/30 = 12.

Q58 · Geometry (Lines, Triangles, Circles, Polygons)

A surveillance system uses two circular zones: Circle C₁ has a radius of 10 m Circle C₂ has a radius of 6 m The distance between their centers is 26 m From a point P outside both circles, two direct tangents are drawn — one to each circle — touching C₁ at point A and C₂ at point B. Let O₁ and O₂ be the centers of the circles. The tangents PA and PB form two right triangles: △PO₁A and △PO₂B. Find the ratio of lengths O₁A : O₂B

  1. 5/3
  2. 8/7
  3. 2/5
  4. 7/3

Answer: A. O₁A and O₂B are the radii → 10 : 6 = 5/3.

Q59 · Ratio, Proportion & Partnership

Amit invests Rs. 26,000 for 6 months and Bablu invests Rs. 46,000 for 8 months. Find the ratio of profits.

  1. 38:92
  2. 39:94
  3. 39:92
  4. 49:72

Answer: C. 26×6 : 46×8 = 156 : 368 = 39 : 92.

Q60 · Mensuration (2D & 3D)

The length and the breadth of a rectangle are 'x' cm and 16 cm, respectively. If the perimeter of the rectangle is 80 cm, then find the area of the rectangle.

  1. 254 cm²
  2. 144 cm²
  3. 294 cm²
  4. 384 cm²

Answer: D. x = 24 → 24 × 16 = 384.

Q61 · Mensuration (2D & 3D)

The total surface area of a hemisphere is 1,360.80 cm². Find the volume of a sphere whose radius is 10 cm less than that of the given hemisphere. (Take π = 3.15)

  1. 48.5 cm³
  2. 33.6 cm³
  3. 32.4 cm³
  4. 42.6 cm³

Answer: B. 3 × 3.15 × r² = 1360.8 → r = 12 → sphere r = 2 → 33.6.

Q62 · Mixture & Alligation

You have 90 ml of a sugar solution that contains 38% sugar. How much pure water must be added so that the final solution becomes 17.1% sugar?

  1. 90 ml
  2. 110 ml
  3. 140 ml
  4. 160 ml

Answer: B. Sugar 34.2 → 17.1% → total 200 → add 110 ml.

Q63 · Percentage

A distance of 120 km is wrongly measured as 126 km. The error percentage is:

  1. 7%
  2. 5%
  3. 8%
  4. 6%

Answer: B. 6/120 = 5%.

Q64 · Profit, Loss & Discount

Find the single equivalent discount for successive discounts of 10%, 15%, and 20% on the marked price of a television.

  1. 54.6%
  2. 41.9%
  3. 63.2%
  4. 38.8%

Answer: D. 0.9 × 0.85 × 0.8 = 0.612 → 38.8%.

Q65 · Number System & Simplification

Simplify: 5/(1 + 3√4).

  1. 7/8
  2. 4/7
  3. 5/7
  4. 3/8

Answer: C. √4 = 2 → 5/7.

Q66 · Algebra

Given the equations 3x + 4y = 10 and -x + 2y = 0, where (a, b) is the solution, determine the value of a + b.

  1. 4
  2. 2
  3. 3
  4. 1

Answer: C. x = 2y → y = 1, x = 2 → 3.

Q67 · Mensuration (2D & 3D)

Find the area of a triangle with sides 13 cm, 14cm, and 15 cm.

  1. 48 cm²
  2. 84 cm²
  3. 96 cm²
  4. 72 cm²

Answer: B. s = 21 → √(21·8·7·6) = 84.

Q68 · Mensuration (2D & 3D)

Three solid spheres of radii 3 cm, 4 cm, and 5 cm are melted to form a single large solid sphere. What is the radius of the new sphere?

  1. 6 cm
  2. 8 cm
  3. 2 cm
  4. 4 cm

Answer: A. 27 + 64 + 125 = 216 = 6³.

Q69 · Time, Work & Distance

Two cars start at the same time from A and B, 120 km apart. If they drive towards each other, they meet in 1 hour. If they drive in the same direction, the faster car overtakes the slower one in 6 hours. What is the speed of the faster car?

  1. 50 km/h
  2. 60 km/h
  3. 70 km/h
  4. 80 km/h

Answer: C. Sum 120, difference 20 → 70 km/h.

Q70 · Simple & Compound Interest

A sum amounts to ₹16,900 in 2 years and ₹21,970 in 3 years at compound interest, compounded annually. What is the annual rate of interest?

  1. 20%
  2. 25%
  3. 35%
  4. 30%

Answer: D. 21,970/16,900 = 1.3 → 30%.

Q71 · Mixture & Alligation

A container has 120 litres of a spirit-water mixture in the ratio 7 : 5. Some litres of the mixture is withdrawn and replaced by the same quantity of water. Then 24 litres of pure spirit is added. If the final ratio of spirit to water becomes 5 : 4, how many litres of the mixture was withdrawn?

  1. 18 litres
  2. 21 litres
  3. 30 litres
  4. 24 litres

Answer: D. (94 − 7x/12)/(50 + 7x/12) = 5/4 → x = 24.

Q72 · Simple & Compound Interest

A total sum is divided between A and B such that A receives ₹6,000 more than B. A's part is lent at 8% per annum and B's part at 11% per annum, both at simple interest for 3 years. If the total interest earned is ₹8,280, find the total sum invested.

  1. ₹28,000
  2. ₹30,000
  3. ₹32,000
  4. ₹36,000

Answer: B. 0.24A + 0.33B = 8280, A = B + 6000 → B = 12,000 → total 30,000.

Q73 · Mensuration (2D & 3D)

A cone has radius 9 cm and slant height 15 cm. Find its total surface area.

  1. 135π cm²
  2. 216π cm²
  3. 270π cm²
  4. 324π cm²

Answer: B. πrl + πr² = 135π + 81π = 216π.

Q74 · Trigonometry

If θ is acute and 2sinθ + 3cosθ = √13, then find tanθ.

  1. 2/3
  2. 3/2
  3. √13/3
  4. 3/√13

Answer: A. Max of 2s + 3c is √13, reached when tanθ = 2/3.

Q75 · Number System & Simplification

Simplify: [(3/5 + 2/3) × 15/8] − [7/6 ÷ 14/9 + 1/2]

  1. 1/3
  2. 4/7
  3. 9/8
  4. 2/11

Answer: C. 19/8 − 5/4 = 9/8.

12th level · 23 Sep 2026, Shift 2, 1:30 PM

Q51 · Ratio, Proportion & Partnership

A, B, C invested their capitals in the ratio of 3:4:5. The ratio of time for which A, B, C invested is 2:1:4. If A gets a share of profit which is Rs. 8,500 more than B's profit, then C's profit?

  1. Rs. 85,000
  2. Rs. 65,250
  3. Rs. 92,500
  4. Rs. 80,000

Answer: A. Profit 6 : 4 : 20 → 2 parts = 8,500 → C = 85,000.

Q52 · Number System & Simplification

A gardener has several pots of flowers. He decides to place the same number of flowers in each pot, equal to the total number of pots he has. After arranging all the flowers, he finds that exactly 12 baskets, each containing 75 flowers are used completely. Find the number of pots?

  1. 30
  2. 28
  3. 32
  4. 25

Answer: A. n² = 900 → 30.

Q53 · Simple & Compound Interest

What is the difference between the compound interest earned in one year when the interest is compounded annually and when it is compounded semi-annually on Rs. 14,500 for 1 year at 9% per annum?

  1. Rs. 30.21
  2. Rs. 30.56
  3. Rs. 30.98
  4. Rs. 29.36

Answer: D. Annual 1,305; half-yearly 1,334.36 → 29.36.

Q54 · Profit, Loss & Discount

The marked price of an article is Rs. 3,750. If the shopkeeper offers two successive discounts, each of k% on the MP is equal to a single discount of Rs. 1,104. If he offers only one discount of K% on MP, what will be the new selling price of the article?

  1. Rs. 2,540
  2. Rs. 3,150
  3. Rs. 2,640
  4. Rs. 2,900

Answer: B. (1 − k)² = 0.7056 → k = 16% → 3,750 × 0.84 = 3,150.

Q55 · Mixture & Alligation

A milk man has two types of milk. In the first container percentage of milk is 70% and the second container percentage of milk is 85%. If he mixes 35 lit from the first container to mix with 75 lit from the second container then the percentage of milk in the mixture?

  1. 74.88%
  2. 89.4%
  3. 75.6%
  4. 80.2%

Answer: D. (24.5 + 63.75)/110 = 80.2%.

Q56 · Percentage

A salesman is allowed 7.5% commission of the total sales made by him and a extra bonus of 0.5% on the sales beyond the amount of Rs. 20,000. If his total earning is Rs. 1920. Find the total value of sales made by him.

  1. Rs. 23,000
  2. Rs. 24,450
  3. Rs. 25,250
  4. Rs. 22,500

Answer: C. 0.075S + 0.005(S − 20,000) = 1,920 → S = 25,250.

Q57 · Time, Work & Distance

In a race of 1000 m, A beats B by 35 seconds and beats C by 200 m. If Band Crun a 1000 m race, B beats C by 35 seconds. Find the time taken by A to run the race.

  1. 240 sec
  2. 250 sec
  3. 270 sec
  4. 280 sec

Answer: D. A beats C by 70 s ≡ 200 m → C takes 350 s → A 280 s.

Q58 · Time, Work & Distance

A and B can do a piece of work in 28 days. B alone can do 83.33% of the same work in 25 days, in how many days can A alone do 8/15th part of the same work?

  1. 124 days
  2. 150 days
  3. 224 days
  4. 228 days

Answer: C. B: 30 days. A = 1/28 − 1/30 = 1/420 → 8/15 × 420 = 224.

Q59 · Time, Work & Distance

Rohit started a certain piece of work and continued for 6 days. After that, he had to leave, so Suresh was called in and he completed the remaining work in 24 days. If instead Rohit had worked for 9 days before leaving, then Suresh would have completed the remaining work in just 12 days. In how many days can Rohit alone finish the entire work?

  1. 48 days
  2. 12 days
  3. 36 days
  4. 24 days

Answer: B. 6R + 24S = 9R + 12S → R = 4S → work 48S → Rohit 12 days.

Q60 · Ratio, Proportion & Partnership

If P₁ : P₂ = 3 : 5 and P₁ : P₃ = 2 : 7, then P₂ : P₃ is

  1. 11:19
  2. 10:21
  3. 10:13
  4. 20:21

Answer: B. P₁ = 6 → P₂ = 10, P₃ = 21.

Q61 · Number System & Simplification

Find the unit digit of the product of the first 10 odd natural numbers.

  1. 5
  2. 0
  3. 1
  4. 2

Answer: A. Product contains 5 and is odd → ends in 5.

Q62 · Algebra

If a + b + c = 3 and a² + b² + c² = 16, determine the value of (a − b)² + (b − c)² + (c − a)².

  1. 32
  2. 39
  3. 26
  4. 28

Answer: B. ab + bc + ca = −3.5 → 2(16 + 3.5) = 39.

Q63 · Number System & Simplification

Simplify: √(9 + 4√5) + √(9 − 4√5).

  1. √5
  2. 2√5
  3. 4√5
  4. 5√2

Answer: B. (√5 + 2) + (√5 − 2) = 2√5.

Q64 · Number System & Simplification

A number is increased by 2⅓ of itself. Then 3/10 of the new value is subtracted and the result becomes 147. What was the original number?

  1. 54
  2. 63
  3. 70
  4. 81

Answer: B. x × 10/3 × 7/10 = 7x/3 = 147 → 63.

Q65 · Number System & Simplification

Simplify: (√2025 + ∛1728) × (8/19) − (2⁵ − 3³).

  1. 19
  2. 18
  3. 24
  4. 21

Answer: A. 57 × 8/19 − 5 = 24 − 5 = 19.

Q66 · Mensuration (2D & 3D)

A right triangular prism has a right-triangle base with perpendicular sides 6 cm and 8 cm. The length of the prism is 15 cm. What is its volume?

  1. 240 cm³
  2. 300 cm³
  3. 360 cm³
  4. 480 cm³

Answer: C. ½ × 6 × 8 × 15 = 360.

Q67 · Trigonometry

If θ is acute and sin(θ + 22°) = cos(3θ − 8°), then find θ.

  1. 17°
  2. 18°
  3. 19°
  4. 21°

Answer: C. θ + 22 + 3θ − 8 = 90 → θ = 19°.

Q68 · Mensuration (2D & 3D)

A rectangular box has dimensions 6 cm, 8 cm and 24 cm. What is the length of the longest rod that can fit inside it?

  1. 24 cm
  2. 25 cm
  3. 26 cm
  4. 28 cm

Answer: C. √(36 + 64 + 576) = 26.

Q69 · Mensuration (2D & 3D)

A regular right pyramid has an equilateral triangular base of side 6 cm and vertical height 4 cm. What is its volume?

  1. 9√3 cm³
  2. 12√3 cm³
  3. 18√3 cm³
  4. 36√3 cm³

Answer: B. ⅓ × 9√3 × 4 = 12√3.

Q70 · Number System & Simplification

Four expressions are given in different forms. Select the number which is rational but not an integer.

  1. √49
  2. −15/5
  3. 0/7
  4. 14/9

Answer: D. 14/9 is rational, not an integer.

Q71 · Trigonometry

Simplify: (1 − sin²θ)/cos²θ

  1. sin²θ
  2. cos²θ
  3. 1
  4. tan²θ

Answer: C. 1 − sin²θ = cos²θ → 1.

Q72 · Geometry (Lines, Triangles, Circles, Polygons)

Points C and D lie on the same segment of a circle with chord AB. If ∠ACB = 55°, what is ∠ADB?

  1. 45°
  2. 55°
  3. 65°
  4. 110°

Answer: B. Angles in the same segment are equal.

Q73 · Mensuration (2D & 3D)

A solid hemisphere has radius 7 cm. Find its curved surface area.

  1. 49π cm²
  2. 98π cm²
  3. 147π cm²
  4. 196π cm²

Answer: B. 2πr² = 98π.

Q74 · Trigonometry

Simplify: cosecA/(cosecA − 1) + cosecA/(cosecA + 1).

  1. 2sec² A
  2. 2cosec² A
  3. 2tan² A
  4. 2cot² A

Answer: A. 2cosec²A/cot²A = 2sec²A.

Q75 · Number System & Simplification

Evaluate: (√324/√81 + √196/√49) ÷ (√16 − √25/√5)

  1. (12 + 2√3)/11
  2. (12 + 2√3)/7
  3. (16 + 4√3)/7
  4. (16 + 4√5)/11

Answer: D. 4 ÷ (4 − √5) = (16 + 4√5)/11.

12th level · 24 Sep 2026, Shift 2, 1:30 PM

Q51 · Ratio, Proportion & Partnership

Two alloys P and Q are made of metals X, Y, and Z. In P, the ratio of masses of X:Y:Z is 2:3:5, and in Q, it is 3:5:7. If 12 kg of P and 18 kg of Q are melted together to form a new alloy R, find the ratio of masses of X:Y:Z in R.

  1. 5:8:12
  2. 13:22:32
  3. 12:21:31
  4. 15:25:35

Answer: A. X 2.4 + 3.6 = 6, Y 9.6, Z 14.4 → 5 : 8 : 12.

Q52 · Number System & Simplification

What is the missing number in the equation: 8 + __ × 3 = 20?

  1. 2
  2. 4
  3. 6
  4. 5

Answer: B. 8 + 4 × 3 = 20.

Q53 · Algebra

Two twins, Alpha and Beta, were asked to calculate the square of numbers symmetrically placed around a mysterious number x. According to given problem => (x + 3)² − (x − 3)² ?

  1. 6x
  2. 9x
  3. 12x
  4. 18x

Answer: C. 4ab = 12x.

Q54 · Time, Work & Distance

A cyclist travels a distance of 36 km in 9 hours. What is his average speed?

  1. 4 km/h
  2. 6 km/h
  3. 5 km/h
  4. 7 km/h

Answer: A. 36/9 = 4.

Q55 · Mixture & Alligation

In a 104-litre solution of milk and water where the milk to water ratio is 8:5, what quantity of water should be mixed in to obtain a final ratio of 4:3?

  1. 8 L
  2. 7 L
  3. 6 L
  4. 9 L

Answer: A. Milk 64 → water for 4 : 3 = 48 → add 8 L.

Q56 · Mensuration (2D & 3D)

The sum of the length and breadth of a rectangle is 28 cm and sum of the perimeters of the rectangle and a square is 96 cm. Find the diagonal of square.

  1. 15√2 cm
  2. 11√2 cm
  3. 10√2 cm
  4. 12√2 cm

Answer: C. Square perimeter 40 → side 10 → 10√2.

Q57 · Number System & Simplification

Which of the following G.P. series has a common ratio which is not a perfect square?

  1. 1, 4, 16, 64, ....
  2. 2, 18, 162, 1458, .....
  3. 2, 2.88, 4.1472, ....
  4. 6, 21.6, 77.76, .....

Answer: D. Ratios 4, 9, 1.44 (=1.2²) are squares; 3.6 is not.

Q58 · Number System & Simplification

If 2² + 4² + 6² + 8² ……… + 50² = 5525, then find the value of 1² + 2² + 3² ……… + 25² = ?

  1. 1340.25
  2. 1215.25
  3. 1381.25
  4. 1524.75

Answer: C. Even squares = 4 × (1² + … + 25²) → 5525/4 = 1381.25.

Q59 · Simple & Compound Interest

Michael takes a loan from a finance company at a compound interest rate of 8.33% per annum. He agrees to clear the loan in two instalments ₹6,500 at the end of the first year and ₹8,450 at the end of the second year. Assuming the interest is compounded annually, how much interest did Michael pay in total over the two years?

  1. ₹1,960
  2. ₹1,850
  3. ₹1,750
  4. ₹1,820

Answer: C. Loan = 6500 × 12/13 + 8450 × (12/13)² = 13,200. Paid 14,950 → interest 1,750.

Q60 · Profit, Loss & Discount

After allowing a discount of 20%, the value of an item is Rs. 36,800. If no discount is allowed, then the shopkeeper gain 15%. Find the cost price of the item?

  1. Rs. 42,000
  2. Rs. 45,000
  3. Rs. 40,000
  4. Rs. 41,500

Answer: C. MP 46,000 = 1.15 CP → 40,000.

Q61 · Mixture & Alligation

A container holds a mixture of salt and water in which 8% of the mixture is salt. Some water is evaporated, but the amount of salt remains the same. After 12 litres of water evaporate, the salt concentration rises to 20%. What was the initial volume (in litres) of the salt-water solution?

  1. 24 lit
  2. 18 lit
  3. 20 lit
  4. 21 lit

Answer: C. 0.08V = 0.2(V − 12) → V = 20.

Q62 · Ratio, Proportion & Partnership

A, B and C together start a business by investing a total amount of ₹4.5 lakhs. A invests some amount of money; B invests ₹75,000 more than A and C invests ₹30,000 less than B. After one year the business earns a total profit of ₹16,200, which has to be shared among the partners in the ratio of their investments. Find the profit of C?

  1. ₹4,580
  2. ₹6,500
  3. ₹5,580
  4. ₹6,540

Answer: C. A = 1.1 L, B 1.85 L, C 1.55 L → 155/450 × 16,200 = 5,580.

Q63 · Time, Work & Distance

Two boats go downstream from point X to point Y. The faster boat covers the distance from X to Y is 1.5 times as fast as the slower boat. It is known that for every hour the slower boat lags behind the faster boat by 12 km. However, if they go up stream then the faster boat covers the distance from Y to X in half the time as the slower boat. Find the speed of the faster boat in still water?

  1. 24 kmph
  2. 30 kmph
  3. 28 kmph
  4. 42 kmph

Answer: B. Downstream 36 & 24 → stream 6 (from upstream condition) → faster boat 30.

Q64 · Time, Work & Distance

Ravi, Suresh and Mahesh work at a juice unit. Ravi takes 2 hours to extract as much juice as Suresh can extract in 3 hours. Mahesh takes 6 hours to extract as much juice as Ravi extracts in 4 hours. Working together, they fill a storage tank in 6 hours. How long will Mahesh take to fill the tank alone?

  1. 18 hours
  2. 14 hours
  3. 21 hours
  4. 25 hours

Answer: C. Rates R : S : M = 3 : 2 : 2 → work 42 → Mahesh 21 h.

Q65 · Geometry (Lines, Triangles, Circles, Polygons)

A chord of a circle subtends an angle of 40° at a point on the circle. Find the angle subtended by the same chord at a point on the opposite segment.

  1. 40°
  2. 80°
  3. 140°
  4. 160°

Answer: C. Opposite segment → 180 − 40 = 140°.

Q66 · Number System & Simplification

The smallest number to be added to 697221 to make the sum a perfect square is:

  1. 6
  2. 4
  3. 8
  4. 5

Answer: B. 835² = 697225 → add 4.

Q67 · Number System & Simplification

A number leaves a remainder of 17 when divided by 36. What is the remainder when the same number is divided by 12?

  1. 2
  2. 5
  3. 3
  4. 7

Answer: B. 36 is a multiple of 12 → 17 mod 12 = 5.

Q68 · Ratio, Proportion & Partnership

A, B, and C are employed to do a piece of work for ₹529. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. What amount should be paid to A?

  1. ₹450
  2. ₹275
  3. ₹345
  4. ₹425

Answer: C. A's share = 1 − 8/23 = 15/23 → 345.

Q69 · Geometry (Lines, Triangles, Circles, Polygons)

Triangles ABC and PQR are similar in the order ABC ~ PQR. If AB = 8 cm, BC = 10 cm, CA= 12 cm and PQ = 12 cm, what is the perimeter of triangle PQR?

  1. 36 cm
  2. 42 cm
  3. 45 cm
  4. 54 cm

Answer: C. Scale 12/8 = 1.5 → 30 × 1.5 = 45.

Q70 · Trigonometry

Evaluate: sin²18° + sin² 72° + cos² 36° + cos² 54° + tan15° tan75°.

  1. 2
  2. 5/2
  3. 3
  4. 4

Answer: C. 1 + 1 + 1 = 3.

Q71 · Mensuration (2D & 3D)

A rhombus has diagonals 16 cm and 30 cm. Use half-diagonals to find its side and perimeter. What is the perimeter?

  1. 60 cm
  2. 64 cm
  3. 68 cm
  4. 72 cm

Answer: C. Side √(8² + 15²) = 17 → 68.

Q72 · Heights & Distances

The angle of elevation of the top of a building from a point 24 m away is 60°. What is the height of the building?

  1. 8√3 m
  2. 12√3 m
  3. 24√3 m
  4. 48√3 m

Answer: C. 24 tan60° = 24√3.

Q73 · Heights & Distances

The angle of elevation of the top of a vertical cliff from a point is 30°. After moving 60 m towards the cliff, the angle becomes 60°. Find the height of the cliff.

  1. 20√3 m
  2. 30√3 m
  3. 40√3 m
  4. 60√3 m

Answer: B. ⚡ 30°/60° with gap d → h = (√3/2)d = 30√3.

Q74 · Number System & Simplification

A student adds an integer and an irrational number and claims that the result may become rational. If the integer is −3 and the irrational number is √11, what is the nature of −3 + √11?

  1. Natural number
  2. Integer
  3. Irrational number
  4. Terminating decimal

Answer: C. Integer + irrational = irrational.

Q75 · Trigonometry

If sinθ + cosθ = √6/2, then find tanθ + cotθ.

  1. 3
  2. 4
  3. 5
  4. 6

Answer: B. sc = (6/4 − 1)/2 = 1/4 → tan + cot = 1/(sc) = 4.

12th level · 25 Sep 2026, Shift 2, 1:30 PM

Q51 · Mensuration (2D & 3D)

A tent is shaped like a right circular cone with a radius of 7 m and a height of 24 m. The canvas covers only the curved surface, and it costs ₹84 per m². What is the total cost of the canvas required? (Use π = 22/7)

  1. ₹45,200
  2. ₹67,800
  3. ₹46,200
  4. ₹67,589

Answer: C. Slant 25 → π × 7 × 25 = 550 m² × 84 = 46,200.

Q52 · Number System & Simplification

Which of the following represents a non-terminating but repeating decimal?

  1. 11/13
  2. 9/2
  3. 0.625
  4. √3

Answer: A. 13 has factors other than 2 and 5 → recurring.

Q53 · Number System & Simplification

Which of the following fractions has a terminating decimal representation?

  1. 17/45
  2. 23/125
  3. 11/18
  4. 7/33

Answer: B. 125 = 5³ → terminating.

Q54 · Ratio, Proportion & Partnership

Amit started a business with Rs. 70,000. Brijesh joined after 5 months with Rs. 40,000. At the end of the year, total profit is Rs. 54,000. What is Brijesh's share?

  1. Rs. 13,500
  2. Rs. 14,500
  3. Rs. 13,600
  4. Rs. 14,600

Answer: A. 70×12 : 40×7 = 3 : 1 → 13,500.

Q55 · Percentage

An interval of 2 hours 30 minutes is wrongly estimated as 2 hours 36 minutes. The error percentage is:

  1. 3%
  2. 6%
  3. 4%
  4. 7%

Answer: C. 6/150 = 4%.

Q56 · Number System & Simplification

Find the value of the expression: (0.3̄ + 0.6̄) ÷ (0.13̄ × 7.5).

  1. 1
  2. 3
  3. 7
  4. 4

Answer: A. 1 ÷ (2/15 × 7.5) = 1 ÷ 1 = 1.

Q57 · Algebra

Given the equations 5x + 2y = 16 and 3x − 2y = 0, where (a, b) is the solution, determine the value of a² − b.

  1. 2
  2. 1
  3. 6
  4. 4

Answer: B. x = 2, y = 3 → 4 − 3 = 1.

Q58 · Mensuration (2D & 3D)

Given a cone and a sphere with equal radii and equal volumes, find the ratio between the diameter of the sphere and the height of the cone.

  1. 1:2
  2. 2:1
  3. 3:2
  4. 2:3

Answer: A. ⅓πr²h = 4/3πr³ → h = 4r → 2r : 4r = 1 : 2.

Q59 · Time, Work & Distance

Aman walks to his office at three-fourths of his normal speed and arrives 20 minutes later than usual. Determine the time he normally takes to reach his office.

  1. 80 minutes
  2. 30 minutes
  3. 60 minutes
  4. 45 minutes

Answer: C. Extra time = ⅓ of usual = 20 → 60 min.

Q60 · Mensuration (2D & 3D)

In a parallelogram, the lengths of adjacent sides are 12 cm and 8 cm. If the distance between the longer sides is 6 cm, what is the distance between the shorter sides?

  1. 7 cm
  2. 9 cm
  3. 13 cm
  4. 11 cm

Answer: B. 12 × 6 = 72 = 8 × h → 9.

Q61 · Simple & Compound Interest

A sum invested at 20% per annum compound interest, compounded half-yearly, amounts to ₹26,620 in 1.5 years. Find the principal.

  1. ₹18,000
  2. ₹20,000
  3. ₹21,000
  4. ₹22,000

Answer: B. 10% per half-year, 3 periods → 1.331 → 20,000.

Q62 · Profit, Loss & Discount

The original marked price of an article is first increased by 25%. Then two discounts of 20% and 5% are given successively on the increased marked price. If the final selling price is ₹7,600, find the original marked price.

  1. ₹7,600
  2. ₹8,000
  3. ₹8,400
  4. ₹9,000

Answer: B. 1.25 × 0.8 × 0.95 = 0.95 → 8,000.

Q63 · Number System & Simplification

If x = √7 + √3, then find the exact value of x² + 16/x².

  1. 24
  2. 20
  3. 22
  4. 18

Answer: B. x² = 10 + 2√21, 16/x² = 10 − 2√21 → 20.

Q64 · Mixture & Alligation

A 45-litre mixture contains milk and water in the ratio 7 : 2. Some litres of water is added to it. After that, the same number of litres of the new mixture is removed. If the final ratio of milk to water becomes 5 : 4, how many litres of water was added?

  1. 12 litres
  2. 15 litres
  3. 18 litres
  4. 21 litres

Answer: C. Removing mixture keeps the ratio → 35 : (10 + x) = 5 : 4 → x = 18.

Q65 · Mixture & Alligation

A vessel contains 96 litres of a milk-water mixture in the ratio 5 : 3. x litres of water is added to it. Then 24 litres of the resulting mixture is withdrawn and replaced by 24 litres of pure milk. If the final ratio of milk to water is 3 : 2, find x.

  1. 12 litres
  2. 18 litres
  3. 24 litres
  4. 30 litres

Answer: C. x = 24: 120 L, remove ⅕ → 48 + 24 milk : 48 water = 3 : 2.

Q66 · Geometry (Lines, Triangles, Circles, Polygons)

Two circles have radii 8 cm and 7 cm and their centres are 25 cm apart. Find the length of a transverse common tangent.

  1. 15 cm
  2. 18 cm
  3. 20 cm
  4. 24 cm

Answer: C. √(25² − 15²) = 20.

Q67 · Simple & Compound Interest

A sum of money lent at simple interest amounts to ₹18,720 in 4 years and to ₹21,120 in 6 years. If the same sum is lent at 12% per annum simple interest, what will be the amount after 5 years?

  1. ₹21,600
  2. ₹22,272
  3. ₹22,800
  4. ₹23,040

Answer: B. SI 1,200/yr → P = 13,920 → 60% → 22,272.

Q68 · Mensuration (2D & 3D)

A triangular field has sides 20 m, 21 m and 29 m. After identifying the triangle as right-angled, find the altitude drawn to the hypotenuse.

  1. 210/29 m
  2. 420/29 m
  3. 29/420 m
  4. 29/21 m

Answer: B. 20 × 21/29 = 420/29.

Q69 · Mensuration (2D & 3D)

A closed cylindrical tin has radius 5 cm and height 12 cm. What is its total surface area?

  1. 120π cm²
  2. 150π cm²
  3. 170π cm²
  4. 240π cm²

Answer: C. 2πr(r + h) = 170π.

Q70 · Trigonometry

If X° 48′ is equal to 719π/900 radians, find the value of X.

  1. 142
  2. 143
  3. 144
  4. 145

Answer: B. 719π/900 rad = 143.8° = 143° 48′.

Q71 · Mensuration (2D & 3D)

A right circular cone has radius 6 cm and height 14 cm. What is its volume?

  1. 144π cm³
  2. 168π cm³
  3. 196π cm³
  4. 504π cm³

Answer: B. ⅓π × 36 × 14 = 168π.

Q72 · Mensuration (2D & 3D)

A regular hexagonal tile has side 10 cm. Find its exact area using the standard formula for a regular hexagon.

  1. 100√3 cm²
  2. 150√3 cm²
  3. 200√3 cm²
  4. 300√3 cm²

Answer: B. (3√3/2) × 100 = 150√3.

Q73 · Trigonometry

If θ is acute and cosecθ + cotθ = 4, then find cosθ.

  1. 8/17
  2. 15/17
  3. 17/15
  4. 7/15

Answer: B. cosec − cot = 1/4 → cot = 15/8, cosec = 17/8 → cos = 15/17.

Q74 · Mensuration (2D & 3D)

A hemisphere has volume 486π cm³. What is its curved surface area?

  1. 81π cm²
  2. 162π cm²
  3. 243π cm²
  4. 324π cm²

Answer: B. r³ = 729 → r = 9 → 2πr² = 162π.

Q75 · Number System & Simplification

Find an approximate value of what should come in place of question mark (?) 50.012 x 15.68 - 30.013 x 1.000 = (20 + ?) x 5.23

  1. 124.20
  2. 193.05
  3. 154.35
  4. 200.05

Answer: A. 784.2 − 30 = 754.2 ÷ 5.23 ≈ 144.2 → ? ≈ 124.2.