SSC CGL Mock – Tier II Paper I Mock Test 07 – Section I · Part A · Mathematical Abilities | Online Quiz

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SSC CGL Mock – Tier II Paper I Mock Test 07 – Section I · Part A · Mathematical Abilities – 30 questions, subject: Full Mock Tests. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

A loan is taken at 8% per annum compound interest. The borrower pays ₹ 21,600 at the end of the first year and clears the loan with ₹ 29,160 at the end of the second year. What was the loan?

Correct Answer: D [₹ 45,000]

Explanation:

Balance after year 1 = 29,160 ÷ 1.08 = 27,000; loan = (27,000 + 21,600) ÷ 1.08 = 45,000.

A trader stocks 60 kg of rice. Some of it he sells at a 6% profit and the remainder at a 15% profit, and on the whole stock his profit works out to 12%. How many kg did he sell at 15% profit?

Correct Answer: A [40 kg]

Explanation:

Alligation: (12 − 6) : (15 − 12) = 6 : 3 for the 15% part → 6/9 × 60 = 40 kg.

For an acute angle θ, cos θ + cos²θ = 1. What is sin²θ + sin⁴θ?

Correct Answer: C [1]

Explanation:

cos θ = 1 − cos²θ = sin²θ → sin²θ + sin⁴θ = cos θ + cos²θ = 1.

Evaluate the product sin 10° × sin 30° × sin 50° × sin 70°.

Correct Answer: B [1/16]

Explanation:

sin 10° sin 50° sin 70° = sin 30°/4 = 1/8 (identity sin θ sin(60° − θ) sin(60° + θ) = sin 3θ/4) → × ½ = 1/16.

A lighthouse is 100 m tall. Looking down from its top, a keeper sees two boats, both on the same side of it and in line with its base, at depression angles of 45° and 30°. What is the distance between the boats?

Correct Answer: B [100(√3 − 1) m]

Explanation:

100 cot 30° − 100 cot 45° = 100√3 − 100 = 100(√3 − 1) m.

A right prism 10 cm high has as its base a right triangle with legs 5 cm and 12 cm. Find its total surface area.

Correct Answer: D [360 cm²]

Explanation:

Two bases 2 × 30 = 60; three faces (5 + 12 + 13) × 10 = 300 → 360 cm².

A cylinder 12 cm high has a volume of 1,848 cm³. What is its curved surface area (π = 22/7)?

Correct Answer: C [528 cm²]

Explanation:

r² = 1,848 × 7/(22 × 12) = 49 → r = 7 → CSA = 2 × 22/7 × 7 × 12 = 528 cm².

A cone and a hemisphere have the same base and the same volume. What is the ratio of the height of the cone to the radius?

Correct Answer: A [2 : 1]

Explanation:

1/3 πr²h = 2/3 πr³ → h = 2r → 2 : 1.

Two inlet pipes fill a cistern in 10 minutes and 14 minutes. With the waste pipe also open, the cistern fills in 7 minutes. How long would the waste pipe alone take to empty the full cistern?

Correct Answer: A [35 minutes]

Explanation:

Waste rate = 1/10 + 1/14 − 1/7 = 2/70 = 1/35 → 35 minutes.

10.

The mean and standard deviation of 10 observations are 20 and 2. What is the sum of the squares of the observations?

Correct Answer: A [4,040]

Explanation:

σ² = Σx²/n − mean² → Σx² = 10 × (4 + 400) = 4,040.

11.

Two-quantity comparison
Scores of seven players: 12, 15, 9, 20, 15, 18, 11.
Quantity I: the score in the middle when they are arranged in order
Quantity II: the score that occurs most often

Correct Answer: C [Quantity I = Quantity II]

Explanation:

Arranged: 9, 11, 12, 15, 15, 18, 20 → median 15; 15 occurs twice → mode 15.

12.

A 3-member team is picked at random from a group of 6 men and 4 women. Find the probability that the team contains exactly two women.

Correct Answer: C [3/10]

Explanation:

⁴C₂ × ⁶C₁/¹⁰C₃ = 36/120 = 3/10.

13.

The average of three numbers a, b, c is M, and ab + bc + ca = 0. What is the average of a², b² and c²?

Correct Answer: D [3M²]

Explanation:

a + b + c = 3M → a² + b² + c² = 9M² − 2 × 0 = 9M² → average 3M².

14.

A's and B's monthly pay are in the ratio 2 : 3. After both receive an increment of ₹ 4,000, the ratio of their pay becomes 22 : 31. How much does B earn now (before the increment)?

Correct Answer: B [₹ 27,000]

Explanation:

(2x + 4,000)/(3x + 4,000) = 22/31 → 4x = 36,000 → x = 9,000 → B = 27,000.

15.

If x = (√3 + 1)/(√3 − 1) and y = (√3 − 1)/(√3 + 1), what is x² + y²?

Correct Answer: B [14]

Explanation:

x = 2 + √3, y = 2 − √3 → x + y = 4, xy = 1 → x² + y² = 16 − 2 = 14.

16.

If a + b + c = 6, a² + b² + c² = 14 and a³ + b³ + c³ = 36, find abc.

Correct Answer: D [6]

Explanation:

ab + bc + ca = (36 − 14)/2 = 11; a³ + b³ + c³ − 3abc = 6 × (14 − 11) = 18 → 3abc = 18 → abc = 6.

17.

Statement-basedx is a real number with x + 1/x = 2. Consider the statements:
I. x²⁰²⁶ + 1/x²⁰²⁶ = 2
II. x³ − 1/x³ = 0
Which of them is/are true?

Correct Answer: C [Both I and II]

Explanation:

x + 1/x = 2 forces x = 1, so both I (1 + 1 = 2) and II (1 − 1 = 0) are true.

18.

Raising the numerator of a certain fraction by 25% while lowering its denominator by 10% gives the fraction 5/6. Find the original fraction.

Correct Answer: A [3/5]

Explanation:

f × 1.25/0.9 = 5/6 → f = 5/6 × 0.9/1.25 = 3/5.

19.

A trader buys rice at ₹ 40 per kg and sells it at ₹ 45 per kg, but his 'kilogram' weight weighs only 900 g. What is his total gain per cent?

Correct Answer: C [25%]

Explanation:

For ₹ 45 he gives 0.9 kg costing ₹ 36 → gain 9/36 = 25%.

20.

By allowing a discount of 10% on the marked price, a merchant makes a profit of 26%. What would his profit per cent have been without any discount?

Correct Answer: B [40%]

Explanation:

0.9 MP = 1.26 CP → MP = 1.4 CP → 40%.

21.

Two trains, 200 m and 250 m long, running in opposite directions on parallel tracks, cross each other in 9 seconds. Their speeds are in the ratio 3 : 2. What is the speed of the faster train?

Correct Answer: D [108 km/h]

Explanation:

Relative speed = 450/9 = 50 m/s = 180 km/h → faster = 3/5 × 180 = 108 km/h.

22.

Directions (Q 22–24): The pie chart shows how 1,200 candidates were distributed among five examination centres; the table gives the pass percentage at each centre (fictional data).

Centre	A	B	C	D	E
Pass (%)	60	48	55	40	75

Mixed DIWhich two centres had the same number of successful candidates?

Correct Answer: A [B and D]

Explanation:

Passed: A 108, B 144, C 132, D 144, E 90 → B and D.

23.

(Use the directions above – Q 22–24)
Mixed DIWhat was the overall pass percentage of the 1,200 candidates?

Correct Answer: C [51.5%]

Explanation:

Passed = 618 → 618/1,200 × 100 = 51.5%.

24.

(Use the directions above – Q 22–24)
Mixed DIWhat is the ratio of the candidates who failed at centre C to those who passed at centre E?

Correct Answer: C [6 : 5]

Explanation:

C failed = 240 − 132 = 108; E passed = 90 → 6 : 5.

25.

13²⁰²⁶ × 17²⁰²⁷ is multiplied out in full. Which digit stands in the units place of the result?

Correct Answer: B [7]

Explanation:

3²⁰²⁶ ends like 3² = 9 (2026 = 4k + 2); 7²⁰²⁷ ends like 7³ → 3; 9 × 3 = 27 → 7.

26.

x is the largest four-digit number that leaves remainder 3 when divided by each of 12, 18, 21 and 28. What is the sum of the digits of x?

Correct Answer: D [21]

Explanation:

LCM = 252; 252 × 39 = 9,828 → x = 9,831 → digit sum 21.

27.

Find the value of (1 − 1/2²)(1 − 1/3²)(1 − 1/4²) … (1 − 1/10²).

Correct Answer: A [11/20]

Explanation:

(1 − 1/k²) = (k − 1)(k + 1)/k²; the product telescopes to (1/2)(11/10) = 11/20.

28.

Diagram-basedThree coins (circles) of radius 7 cm are placed so that each touches the other two (see figure). Find the area of the shaded region enclosed between them (π = 22/7).

Correct Answer: C [(49√3 − 77) cm²]

Explanation:

Equilateral triangle of side 14: area 49√3; minus three 60° sectors = half a circle = ½ × 22/7 × 49 = 77 → (49√3 − 77) cm².

29.

In triangle ABC, AB = 10 cm, AC = 14 cm and BC = 16 cm. Find the length of the median from A to BC.

Correct Answer: B [2√21 cm]

Explanation:

AD² = (2 × 100 + 2 × 196 − 256)/4 = 84 → AD = 2√21 cm.

30.

The angles of a triangle ABC are in the ratio A : B : C = 2 : 3 : 4. The bisectors of ∠B and ∠C meet at I. Find ∠BIC.

Correct Answer: A [110°]

Explanation:

∠A = 40°, ∠B = 60°, ∠C = 80° → ∠BIC = 90° + ∠A/2 = 110°.

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