SSC CGL Mock – Tier II Paper I Mock Test 04 – Section I · Part A · Mathematical Abilities | Online Quiz

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SSC CGL Mock – Tier II Paper I Mock Test 04 – 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.

If sin(A + B) = 1 and cos(A − B) = √3/2, where 0° < B < A ≤ 90°, find A.

Correct Answer: A [60°]

Explanation:

A + B = 90°, A − B = 30° → A = 60°.

Evaluate the product of the cosines of every whole-degree angle from 1° to 179°, that is cos 1° · cos 2° · … · cos 179°.

Correct Answer: B [0]

Explanation:

The product contains cos 90° = 0.

From a point on level ground, the top of a building is seen at an elevation of 30° and the top of a 10 m flagstaff fixed on the building at 45°. Find the height of the building.

Correct Answer: C [5(√3 + 1) m]

Explanation:

If the point is d m away: d/√3 = h and d = h + 10 → h(√3 − 1) = 10 → h = 5(√3 + 1) m.

One candidate scores 30% of the maximum marks and fails by 15 marks; another scores 40% and gets 35 marks more than the pass mark. What percentage is needed to pass?

Correct Answer: D [33%]

Explanation:

10% of maximum = 15 + 35 = 50 → maximum = 500; pass mark = 150 + 15 = 165 → 33%.

After three successive discounts – 10%, 25% and a third one – an item marked ₹ 1,000 sells for ₹ 540. What is the third discount?

Correct Answer: B [20%]

Explanation:

1,000 × 0.9 × 0.75 = 675; 540/675 = 0.8 → third discount 20%.

A sells a cycle to B at a profit of 20%; B sells it to C at a loss of 10%. If C pays ₹ 594, how much did A pay for it?

Correct Answer: A [₹ 550]

Explanation:

594 ÷ (1.2 × 0.9) = 594 ÷ 1.08 = 550.

Eight even numbers follow one another without a gap and have an average of 47. Which is the biggest of them?

Correct Answer: C [54]

Explanation:

They are symmetric about 47: 40, …, 54.

Three positive numbers are proportional to 3, 4 and 6, and when each is squared the squares total 976. The biggest of the three numbers is:

Correct Answer: D [24]

Explanation:

9k² + 16k² + 36k² = 61k² = 976 → k² = 16 → k = 4 → largest = 6 × 4 = 24.

Diagram-basedIn triangle ABC, ∠A = 56°. The altitudes BE and CF meet at H (see figure). Find ∠BHC.

Correct Answer: B [124°]

Explanation:

In quadrilateral AFHE, ∠F = ∠E = 90°, so ∠FHE = 180° − 56° = 124° = ∠BHC (vertically opposite).

10.

The sides of ΔABC are AB = 8 cm, AC = 6 cm and BC = 10 cm, and D is the midpoint of BC. How long is AD?

Correct Answer: A [5 cm]

Explanation:

Apollonius: AB² + AC² = 2(AD² + BD²) → 100 = 2(AD² + 25) → AD = 5 cm (also the circumradius of this right triangle).

11.

A regular polygon has each of its interior angles equal to 160°. Count its diagonals.

Correct Answer: C [135]

Explanation:

Exterior angle 20° → n = 18 → diagonals = 18 × 15/2 = 135.

12.

A cyclist rides along the four equal sides of a square park at 10, 20, 30 and 60 km/h respectively. What is his average speed for the full round?

Correct Answer: D [20 km/h]

Explanation:

Average = 4 ÷ (1/10 + 1/20 + 1/30 + 1/60) = 4 ÷ (12/60) = 20 km/h.

13.

Find the variance of the observations 1, 3, 4, 8, 9 (divide by the number of observations).

Correct Answer: B [9.2]

Explanation:

Mean 5; squared deviations 16, 4, 1, 9, 16 → 46/5 = 9.2.

14.

Two-quantity comparison
Seven observations are 2, 3, 3, 5, 7, 10 and 12.
Quantity I: their arithmetic mean
Quantity II: their middle value (median)

Correct Answer: A [Quantity I > Quantity II]

Explanation:

Mean = 42/7 = 6; median = 5 → Quantity I is greater.

15.

Three fair coins are flipped together. Find the probability that heads show on two or more of them.

Correct Answer: A [1/2]

Explanation:

HHT, HTH, THH, HHH → 4/8 = 1/2.

16.

A bucket in the shape of a frustum has radii 20 cm (top) and 8 cm (bottom) and depth 16 cm. What is its capacity?

Correct Answer: C [3,328π cm³]

Explanation:

V = πh/3 (R² + Rr + r²) = π × 16/3 × 624 = 3,328π cm³.

17.

A circle is inscribed in a square of side 28 cm. What is the area of the square lying outside the circle (π = 22/7)?

Correct Answer: D [168 cm²]

Explanation:

784 − 22/7 × 196 = 784 − 616 = 168 cm².

18.

Find the perimeter of a sector of a circle of radius 14 cm whose angle is 135° (π = 22/7).

Correct Answer: B [61 cm]

Explanation:

Arc = 3/8 × 2 × 22/7 × 14 = 33 → perimeter = 33 + 2 × 14 = 61 cm.

19.

A works one and a half times as fast as B. Jointly they complete an assignment in 12 days. How many days would A take working alone?

Correct Answer: A [20 days]

Explanation:

A = 1.5B → 2.5B per day = 1/12 → B alone 30 days, A alone 30/1.5 = 20 days.

20.

Data sufficiencyFind x + y.
Statement I: the squares of x and y differ by 24, that is, x² − y² = 24
Statement II: x exceeds y by 4

Correct Answer: D [Both statements together are needed; neither alone is sufficient]

Explanation:

I alone: many pairs (7, 5), (5, 1) …; II alone: any pair 4 apart.

21.

If x + y + z = 0 (x, y, z not all zero), what is (x² + y² + z²)/(xy + yz + zx)?

Correct Answer: C [−2]

Explanation:

0 = (x + y + z)² = Σx² + 2Σxy → Σx²/Σxy = −2.

22.

For some real x greater than 1, x⁴ + 1/x⁴ = 119. Determine x − 1/x.

Correct Answer: D [3]

Explanation:

x² + 1/x² = √(119 + 2) = 11; (x − 1/x)² = 11 − 2 = 9 → x − 1/x = 3.

23.

A chemist has 75 litres of a solution that is 20% alcohol by volume. How much pure alcohol must she mix in so that the solution becomes 40% alcohol?

Correct Answer: B [25 litres]

Explanation:

15 + x = 0.4(75 + x) → 0.6x = 15 → x = 25 litres.

24.

Find the highest common factor of the two numbers 2¹² − 1 and 2⁸ − 1.

Correct Answer: C [15]

Explanation:

HCF(2ᵃ − 1, 2ᵇ − 1) = 2 HCF(a, b) − 1 = 2⁴ − 1 = 15.

25.

What is the product of all the positive divisors of 36?

Correct Answer: D [6⁹]

Explanation:

36 has 9 divisors that pair up to 36 → product = 36 9/2 = 6⁹.

26.

Find the value of √(12 + √(12 + √(12 + …))) (continuing without end).

Correct Answer: A [4]

Explanation:

x = √(12 + x) → x² − x − 12 = 0 → x = 4 (positive root).

27.

Directions (Q 27–29): The line graph shows the percentage profit of two companies A and B, where profit % = (Income − Expenditure)/Expenditure × 100 (fictional data).

Line graphIf company A's expenditure in 2022 was ₹ 50 lakh, what was its income that year?

Correct Answer: D [₹ 65 lakh]

Explanation:

Answer: ₹ 65 lakh. Income = 50 × 1.30 = 65.

28.

(Use the directions above – Q 27–29)
Line graphCompany B's income was the same in 2023 and 2024. What is the ratio of its expenditure in 2023 to that in 2024?

Correct Answer: B [9 : 8]

Explanation:

E₂₀₂₃ × 1.20 = E₂₀₂₄ × 1.35 → E₂₀₂₃ : E₂₀₂₄ = 1.35 : 1.20 = 9 : 8.

29.

(Use the directions above – Q 27–29)
Line graphIn 2025 both companies had the same income. What is the ratio of A's expenditure to B's expenditure in 2025?

Correct Answer: C [29 : 27]

Explanation:

Expenditure = Income/(1 + profit %): A : B = 1/1.35 : 1/1.45 = 145 : 135 = 29 : 27.

30.

Rohit borrows ₹ 2,10,000 at 10% per annum, compounded annually, and clears the debt with two equal payments made at the end of the first and second years. How much is each payment?

Correct Answer: A [₹ 1,21,000]

Explanation:

x/1.1 + x/1.21 = 2,10,000 → x × 2.1/1.21 = 2,10,000 → x = 1,21,000.

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