SSC CGL Mock – Tier II Paper I Mock Test 02 – Section I · Part A · Mathematical Abilities | Online Quiz

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SSC CGL Mock – Tier II Paper I Mock Test 02 – 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.

Diagram-basedA circle is inscribed in a right triangle whose legs are 8 cm and 15 cm (see figure). Find the radius r of the circle.

Correct Answer: A [3 cm]

Explanation:

Hypotenuse = 17; for a right triangle r = (a + b − c)/2 = (8 + 15 − 17)/2 = 3 cm.

In ΔPQR the sides are PQ = 14 cm, PR = 10 cm and QR = 18 cm. The internal bisector of angle P cuts QR at S. Find the length QS.

Correct Answer: C [10.5 cm]

Explanation:

QS : SR = PQ : PR = 7 : 5 → QS = 7/12 × 18 = 10.5 cm.

Chords AB and CD of a circle cut each other at P. If AP = 9 cm, PB = 4 cm and CP = 6 cm, what is PD?

Correct Answer: B [6 cm]

Explanation:

AP × PB = CP × PD → 36 = 6 × PD → PD = 6 cm.

A milkman has 60 litres of milk diluted with water in the ratio 5 : 1 (milk : water). How many litres of water should he pour in so that the ratio becomes 5 : 3?

Correct Answer: D [20 litres]

Explanation:

Milk 50 L, water 10 L; for 5 : 3 water must be 30 L → add 20 litres.

Pipe A can fill a tank in 6 hours and pipe B in 8 hours, while pipe C can empty the full tank in 12 hours. All three are opened at 9 a.m. on an empty tank. When will it be full?

Correct Answer: D [1:48 p.m.]

Explanation:

Net rate = 1/6 + 1/8 − 1/12 = 5/24 per hour → 24/5 h = 4 h 48 min after 9 a.m.

If cos θ/(1 − sin θ) + cos θ/(1 + sin θ) = 4 and θ is acute, find θ.

Correct Answer: C [60°]

Explanation:

LHS = 2 cos θ/cos²θ = 2 sec θ = 4 → sec θ = 2 → θ = 60°.

As θ varies, what is the largest value that the expression 20 sin θ + 21 cos θ can take?

Correct Answer: B [29]

Explanation:

Maximum of a sin θ + b cos θ is √(a² + b²) = √841 = 29.

A man sees the top of a tower at an elevation of 30°. After he walks 20 m straight towards the tower, the elevation becomes 60°. Find the height of the tower.

Correct Answer: A [10√3 m]

Explanation:

h cot 30° − h cot 60° = 20 → h(√3 − 1/√3) = 20 → h = 10√3 m.

A frequency distribution is moderately skewed. Its arithmetic mean is 26 and its median is 27. Estimate its mode from the empirical formula.

Correct Answer: C [29]

Explanation:

Mode = 3 Median − 2 Mean = 81 − 52 = 29.

10.

The values 10, 20, 30 and 40 occur with frequencies 3, 5, 8 and 4 respectively. Find the mean.

Correct Answer: B [26.5]

Explanation:

Σfx = 30 + 100 + 240 + 160 = 530; Σf = 20 → 26.5.

11.

A box holds 7 red and 5 green marbles. Priya pulls out two marbles at the same time without looking. What is the probability that both are red?

Correct Answer: A [7/22]

Explanation:

Answer: 7/22. ⁷C₂/¹²C₂ = 21/66 = 7/22.

12.

10% of the electorate stayed away from the poll and 6% of the votes polled were rejected as invalid. The winning candidate secured 54% of the valid votes and beat the only other candidate by 1,692 votes. How large was the electorate?

Correct Answer: D [25,000]

Explanation:

Margin = 8% of valid votes = 0.08 × 0.94 × 0.9 × N = 0.06768N = 1,692 → N = 25,000.

13.

Three sections of a class have 40, 50 and 60 students with average marks 70, 80 and 75. What is the average mark of all the students?

Correct Answer: C [75 1/3]

Explanation:

(2,800 + 4,000 + 4,500)/150 = 11,300/150 = 75 1/3.

14.

Rehana sold a sewing machine at a loss of 15%. Had she charged ₹ 360 more, she would have made a profit of 9%. What did the machine cost her?

Correct Answer: B [₹ 1,500]

Explanation:

9% − (−15%) = 24% of CP = ₹ 360 → CP = 1,500.

15.

An article costs a shopkeeper ₹ 640. At what price must he mark it so that he can allow a 20% discount and still gain 20%?

Correct Answer: D [₹ 960]

Explanation:

SP = 640 × 1.2 = 768 = 80% of MP → MP = 960.

16.

Given x = 3 + 2√2, evaluate √x − 1/√x.

Correct Answer: A [2]

Explanation:

x = (1 + √2)² → √x = 1 + √2, 1/√x = √2 − 1 → difference 2.

17.

Real numbers x and y satisfy 2x + 3y = 13 and xy = 6. Without finding x and y, compute 8x³ + 27y³.

Correct Answer: B [793]

Explanation:

(2x + 3y)³ = 8x³ + 27y³ + 18xy(2x + 3y) → 2,197 = S + 18 × 6 × 13 → S = 793.

18.

The pair of lines 2x + 3y = 5 and 4x + ky = 10 coincide (the system has infinitely many solutions) for which value of k?

Correct Answer: A [6]

Explanation:

For infinitely many solutions 2/4 = 3/k = 5/10 → k = 6.

19.

Two trains start at the same time from towns P and Q towards each other. After they meet, they take 9 hours and 16 hours respectively to reach Q and P. What is the ratio of their speeds?

Correct Answer: C [4 : 3]

Explanation:

Speed ratio = √(time of second after meeting) : √(time of first) = √16 : √9 = 4 : 3.

20.

A's age and B's age today are in the ratio 5 : 7. In 8 years' time the ratio will have changed to 7 : 9. Together, how old are they now?

Correct Answer: D [48 years]

Explanation:

(5x + 8)/(7x + 8) = 7/9 → 45x + 72 = 49x + 56 → x = 4 → 20 + 28 = 48 years.

21.

How many of the numbers 1, 2, 3, …, 500 are divisible by 3 or by 5 but not by 15?

Correct Answer: B [200]

Explanation:

Multiples of 3: 166, of 5: 100, of 15: 33 → (166 + 100 − 33) − 33 = 200.

22.

7,500 is not a perfect square. What is the smallest number we must add to it to reach a perfect square?

Correct Answer: C [69]

Explanation:

86² = 7,396 < 7,500 < 87² = 7,569 → add 7,569 − 7,500 = 69.

23.

Which of the following surds has the greatest value?

Correct Answer: D [∛3]

Explanation:

Raise each to the 24th power: √2 → 2¹² = 4,096, ∛3 → 3⁸ = 6,561, ⁶√6 → 6⁴ = 1,296, ⁸√8 → 8³ = 512 → ∛3 is the greatest.

24.

A solid right circular cone stands 24 cm high on a base of radius 7 cm. Taking π = 22/7, its total surface area (curved surface plus base) is:

Correct Answer: A [704 cm²]

Explanation:

Slant height = 25 → πr(l + r) = 22/7 × 7 × 32 = 704 cm².

25.

A metal sphere of radius 6 cm is melted and recast into a cylinder of radius 4 cm. What is the height of the cylinder?

Correct Answer: A [18 cm]

Explanation:

4/3 π × 216 = π × 16 × h → h = 288/16 = 18 cm.

26.

A pipe 21 cm long has inner radius 3 cm and outer radius 4 cm. What volume of metal does it contain (π = 22/7)?

Correct Answer: C [462 cm³]

Explanation:

π(R² − r²)h = 22/7 × 7 × 21 = 462 cm³.

27.

On ₹ 40,000 for one year at 10% per annum, how much more interest is earned when it is compounded half-yearly instead of annually?

Correct Answer: B [₹ 100]

Explanation:

40,000 × (1.1025 − 1.10) = 100.

28.

Directions (Q 28–30): The bar chart shows the production and sales (in thousand units) of a company over five years. Units not sold in a year are added to stock (fictional data).

Bar chartIn which year were the sales the highest percentage of that year's production?

Correct Answer: D [2024]

Explanation:

Sales/production: 90%, 83.3%, 90%, 92.3%, 90% → 2024.

29.

(Use the directions above – Q 28–30)
Bar chartIf the company had no stock at the start of 2021, how many units were in stock at the end of 2025?

Correct Answer: C [35,000]

Explanation:

(50 − 45) + (60 − 50) + (70 − 63) + (65 − 60) + (80 − 72) = 35 thousand.

30.

(Use the directions above – Q 28–30)
Bar chartIf sales in 2026 grow at the same rate as from 2024 to 2025, what will the 2026 sales be?

Correct Answer: B [86.4 thousand]

Explanation:

Growth 72/60 = 1.2 → 72 × 1.2 = 86.4 thousand units.

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