SSC CGL Mock – Tier II Paper I Mock Test 01 – Section I · Part A · Mathematical Abilities | Online Quiz

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SSC CGL Mock – Tier II Paper I Mock Test 01 – 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.

For an angle θ, sec θ + tan θ = 4. Work out sin θ.

Correct Answer: A [15/17]

Explanation:

sec θ − tan θ = 1/4 → sec θ = 17/8, tan θ = 15/8 → sin θ = tan θ/sec θ = 15/17.

Without using tables, add up the squares of the sines of all the angles 5°, 10°, 15°, …, 80°, 85° (seventeen terms in steps of 5°). The total is:

Correct Answer: C [8 1/2]

Explanation:

17 terms; sin²θ + sin²(90° − θ) = 1 gives 8 pairs plus sin²45° = ½ → 8½.

A 60 m high cliff overlooks a tower. Seen from the cliff top, the tower's top and foot have angles of depression of 30° and 60°. How tall is the tower?

Correct Answer: B [40 m]

Explanation:

Distance = 60/√3 = 20√3 m; the top of the tower is 20√3 × tan 30° = 20 m below the cliff top → 60 − 20 = 40 m.

Diagram-basedIn triangle ABC, ∠B = 70° and ∠C = 50°. AD is perpendicular to BC and AE bisects ∠A (see figure). Find ∠DAE.

Correct Answer: D [10°]

Explanation:

∠BAE = 60°/2 = 30° and ∠BAD = 90° − 70° = 20° → ∠DAE = 30° − 20° = 10° (= (∠B − ∠C)/2).

Circles with centres P and Q have radii 13 cm and 15 cm, and PQ = 14 cm. The circles cross at two points. How long is the chord joining those two points?

Correct Answer: B [24 cm]

Explanation:

If the chord is at distance x from P: 169 − x² = 225 − (14 − x)² → x = 5 → half-chord = √(169 − 25) = 12 → chord 24 cm.

In parallelogram ABCD, P is the midpoint of BC and Q is the midpoint of CD. What fraction of the area of the parallelogram is the area of triangle APQ?

Correct Answer: C [3/8]

Explanation:

Triangles ABP and ADQ are 1/4 each and CPQ is 1/8 → APQ = 1 − 1/4 − 1/4 − 1/8 = 3/8.

What remainder does 7¹⁰⁰ + 11¹⁰⁰ leave when it is divided by 12?

Correct Answer: A [2]

Explanation:

7² = 49 ≡ 1 and 11 ≡ −1 (mod 12), so both powers leave 1 → 1 + 1 = 2.

Find the sum of all two-digit numbers that are multiples of 7.

Correct Answer: D [728]

Explanation:

14, 21, …, 98: 13 terms → 13 × (14 + 98)/2 = 728.

Evaluate √0.0169 × √1.44 + √0.0081.

Correct Answer: C [0.246]

Explanation:

0.13 × 1.2 + 0.09 = 0.156 + 0.09 = 0.246.

10.

Find the median of the data 13, 21, 17, 25, 30, 19, 23, 28.

Correct Answer: D [22]

Explanation:

Arranged: 13, 17, 19, 21, 23, 25, 28, 30; median = (21 + 23)/2 = 22.

11.

Find the standard deviation (divide by n) of 2, 4, 6, 8, 10.

Correct Answer: B [2√2]

Explanation:

Mean 6; variance = (16 + 4 + 0 + 4 + 16)/5 = 8 → SD = 2√2.

12.

Ravi rolls a pair of fair six-faced dice once. What is the chance that the two faces shown add up to exactly 8?

Correct Answer: A [5/36]

Explanation:

(2, 6), (3, 5), (4, 4), (5, 3), (6, 2) → 5/36.

13.

A, B and C invest capitals in the ratio 3 : 4 : 5 for periods in the ratio 4 : 3 : 2. Out of a profit of ₹ 85,000, what is C's share?

Correct Answer: C [₹ 25,000]

Explanation:

Profit ratio = 12 : 12 : 10 = 6 : 6 : 5 → C = 5/17 × 85,000 = 25,000.

14.

A metal cube is heated so that each of its edges becomes 10% longer. Its volume therefore grows by:

Correct Answer: B [33.1%]

Explanation:

1.1³ = 1.331 → volume rises by 33.1%.

15.

What is the length of the longest rod that can be placed inside a box measuring 12 cm × 9 cm × 8 cm?

Correct Answer: D [17 cm]

Explanation:

Space diagonal = √(144 + 81 + 64) = √289 = 17 cm.

16.

A pencil-shaped solid is a right prism 15 cm tall whose cross-section is a regular hexagon of side 2 cm. Its volume is:

Correct Answer: A [90√3 cm³]

Explanation:

Base = 6 × (√3/4) × 2² = 6√3 cm² → volume = 6√3 × 15 = 90√3 cm³.

17.

A train crosses a 320 m long platform in 25 seconds, and overtakes a man walking at 7.2 km/h in the same direction in 10 seconds. How long is the train?

Correct Answer: D [180 m]

Explanation:

Man's speed = 2 m/s. L + 320 = 25v and L = 10(v − 2) → 15v = 300 → v = 20 m/s → L = 180 m.

18.

Working in pairs, A and B finish a job in 20 days, B and C in 12 days and C and A in 15 days. How many days would C need if he worked on his own?

Correct Answer: B [20 days]

Explanation:

2(A + B + C) = 1/20 + 1/12 + 1/15 = 1/5 → A + B + C = 1/10; C = 1/10 − 1/20 = 1/20 → 20 days.

19.

A deposit grows at compound interest, compounded annually. Its value at the end of the second year is ₹ 26,460 and at the end of the third year ₹ 27,783. How much was deposited?

Correct Answer: A [₹ 24,000]

Explanation:

Rate = 1,323/26,460 = 5% → sum = 26,460 ÷ 1.05² = 24,000.

20.

A dairy can is filled with 80 litres of pure milk. A worker removes 8 litres and tops the can up with water, and repeats this operation twice more. What quantity of milk remains in the can?

Correct Answer: C [58.32 litres]

Explanation:

Each operation keeps 72/80 = 0.9 of the milk → 80 × 0.9³ = 80 × 0.729 = 58.32 litres.

21.

A trader marks his goods 40% above cost. He allows a trade discount of 10% and then a further cash discount of 5% on the reduced price. What is his profit per cent?

Correct Answer: C [19.7%]

Explanation:

1.40 × 0.90 × 0.95 = 1.197 → profit 19.7% (not 40 − 10 − 5 = 25%).

22.

A toy seller buys toys at 12 for ₹ 10 and sells them at 10 for ₹ 12. What is his gain per cent?

Correct Answer: B [44%]

Explanation:

CP of one toy = 10/12 = 5/6, SP = 12/10 = 6/5 → (6/5)/(5/6) = 36/25 = 1.44 → 44%.

23.

52 numbers have a mean of 40. When the numbers 61 and 69 are struck off the list, what is the mean of those left?

Correct Answer: D [39]

Explanation:

(52 × 40 − 61 − 69)/50 = (2,080 − 130)/50 = 39.

24.

A earns 25% more than B, and B earns 20% more than C. If A earns ₹ 9,000 more than C, what does C earn?

Correct Answer: A [₹ 18,000]

Explanation:

A = 1.25 × 1.2 C = 1.5C → 0.5C = 9,000 → C = 18,000.

25.

Directions (Q 25–27): The table shows the number of students who appeared for and who passed a board examination from two schools A and B (fictional data).

Year	A: appeared	A: passed	B: appeared	B: passed
2021	400	300	350	280
2022	450	360	380	285
2023	500	380	420	336
2024	480	408	400	340
2025	520	442	450	342

Data tableIn how many of the five years was school A's pass percentage higher than school B's?

Correct Answer: D [2]

Explanation:

Pass %: A 75, 80, 76, 85, 85; B 80, 75, 80, 85, 76 → higher only in 2022 and 2025 (2024 is equal).

26.

(Use the directions above – Q 25–27)
Data tableBy what per cent did the number of students passing from school A increase from 2021 to 2025?

Correct Answer: B [47 1/3%]

Explanation:

(442 − 300)/300 × 100 = 47 1/3%.

27.

(Use the directions above – Q 25–27)
Data tableWhat is the ratio of the students who failed from school A to those who failed from school B, taking 2022 and 2023 together?

Correct Answer: A [210 : 179]

Explanation:

A: 90 + 120 = 210; B: 95 + 84 = 179 → 210 : 179.

28.

It is given that x + 1/x = 4. Compute x³ + 1/x³.

Correct Answer: C [52]

Explanation:

x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 64 − 12 = 52.

29.

Three numbers a, b, c have the sum 15, and the sum of their squares is 83. What is ab + bc + ca?

Correct Answer: B [71]

Explanation:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) → 225 = 83 + 2S → S = 71.

30.

Two-quantity comparison
Quantity I: the positive root of x² − x − 12 = 0.
Quantity II: a + b, where a and b are positive numbers with a² + b² = 10 and ab = 3.

Correct Answer: C [Quantity I = Quantity II]

Explanation:

Quantity I: (x − 4)(x + 3) = 0 → 4.

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