SSC CGL Mock – Tier I Mock Test 04 – Section C · Quantitative Aptitude
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Answer: 15 : 14. 45 : 42 = 15 : 14.
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SSC CGL Mock – Tier I Mock Test 04 – Section C · Quantitative Aptitude – 25 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.
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1.
For an acute angle θ, sec² θ − tan² θ + cosec² θ − cot² θ equals:
Correct Answer: A [2]
Explanation:
Each pair equals 1 → 1 + 1 = 2.
2.
θ is an acute angle whose tangent is 8/15. Find sin θ + cos θ.
Correct Answer: D [23/17]
Explanation:
Hypotenuse 17 → 8/17 + 15/17 = 23/17.
3.
How much interest does ₹ 16,000 earn in two years at 5% a year if the interest is added to the principal at the end of each year?
Correct Answer: B [₹ 1,640]
Explanation:
16,000 × 1.05² = 17,640 → CI = 1,640.
4.
Selling a lamp for ₹ 1,150 gives a profit of 15%. At what price should it be sold to make a profit of 25%?
Correct Answer: C [₹ 1,250]
Explanation:
Cost = 1,150 ÷ 1.15 = 1,000; 25% profit → 1,250.
5.
A bag marked ₹ 640 is sold for ₹ 544. What is the rate of discount?
Correct Answer: B [15%]
Explanation:
Answer: 15%. Discount 96 on 640 = 15%.
6.
Thirty-five per cent of a certain number equals 84. Find eighty-five per cent of that number.
Correct Answer: A [204]
Explanation:
Number = 84 × 100/35 = 240; 85% of it = 204.
7.
Working together, A and B finish a task in 12 days; A working alone needs 20 days. How long will B need on his own?
Correct Answer: D [30 days]
Explanation:
Answer: 30 days. 1/12 − 1/20 = 1/30 → 30 days.
8.
A ferry moves at 15 km/h in still water. On a river flowing at 3 km/h, how long does it take to travel 54 km with the current?
Correct Answer: D [3 hours]
Explanation:
Downstream speed 18 km/h → 54/18 = 3 hours.
9.
If x = 5 + 2√6, what is √x?
Correct Answer: B [√3 + √2]
Explanation:
5 + 2√6 = 3 + 2 + 2√(3 × 2) = (√3 + √2)².
10.
The sum of three numbers a, b, c is 12 and the sum of their squares is 50. Find ab + bc + ca, the sum of their products taken two at a time.
Correct Answer: C [47]
Explanation:
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) → 144 = 50 + 2S → S = 47.
11.
Which equation represents the straight line passing through the points (1, 2) and (3, 8)?
Correct Answer: A [y = 3x − 1]
Explanation:
Slope = (8 − 2)/(3 − 1) = 3; y − 2 = 3(x − 1) → y = 3x − 1.
12.
A and B start a business with ₹ 15,000 and ₹ 20,000 respectively for one year. Out of a profit of ₹ 10,500, what is A's share?
Correct Answer: B [₹ 4,500]
Explanation:
Ratio 3 : 4 → A = 3/7 × 10,500 = 4,500.
13.
The perimeter of a rectangle is 46 cm and its length is 15 cm. What is its area?
Correct Answer: A [120 cm²]
Explanation:
Breadth = 23 − 15 = 8 cm → area = 120 cm².
14.
A solid ball has a radius of 3 cm. Express its volume in terms of π.
Correct Answer: C [36π cm³]
Explanation:
Answer: 36π cm³. (4/3)π × 27 = 36π cm³.
15.
When N is divided by 36 the remainder is 29. Find the remainder when N is divided by 12.
Correct Answer: D [5]
Explanation:
36 is a multiple of 12, so the remainder is 29 mod 12 = 5.
16.
Find the least number which, when divided by 12, 16 and 20, leaves a remainder of 5 in each case.
Correct Answer: D [245]
Explanation:
LCM(12, 16, 20) = 240; required number = 240 + 5 = 245.
17.
In triangle ABC, ∠A = 70° and the internal bisectors of ∠B and ∠C cross at I. What is ∠BIC?
Correct Answer: B [125°]
Explanation:
∠BIC = 90° + ∠A/2 = 90° + 35° = 125°.
18.
Six straight sides enclose a polygon. What do all its interior angles add up to?
Correct Answer: C [720°]
Explanation:
(n − 2) × 180° = 4 × 180° = 720°.
19.
Diagram-basedTwo circles of radii 9 cm and 4 cm touch each other externally. PQ is a direct common tangent (see figure). Find PQ.
Correct Answer: A [12 cm]
Explanation:
PQ = √(d² − (r₁ − r₂)²) = √(13² − 5²) = 12 cm.
20.
After 16 innings Rohan's batting average is 38. In his 17th innings he makes 72 runs. Find his average after 17 innings.
Correct Answer: A [40]
Explanation:
(16 × 38 + 72)/17 = 680/17 = 40.
21.
Two vessels of equal size are full of milk-water mixtures in the ratios 4 : 1 and 3 : 7. Both are emptied into a third vessel. What is the ratio of milk to water in it?
Correct Answer: B [11 : 9]
Explanation:
Milk = 4/5 + 3/10 = 11/10, water = 1/5 + 7/10 = 9/10 → 11 : 9.
22. Line graphIn which year did Factory B produce more than Factory A?
Directions (Q 72–75): The line graph shows the production (in thousand units) of two factories A and B from 2020 to 2025 (fictional data).
Correct Answer: D [2023]
Explanation:
Answer: 2023. Only in 2023 (55 against 48).
23.
(Use the directions above – Q 72–75)
Line graphWhat was the total production of Factory A over the six years?
Line graphWhat was the total production of Factory A over the six years?
Correct Answer: C [309 thousand]
Explanation:
40 + 45 + 50 + 48 + 60 + 66 = 309 thousand units.
24.
(Use the directions above – Q 72–75)
Line graphBy what percentage did Factory A's production rise from 2024 to 2025?
Line graphBy what percentage did Factory A's production rise from 2024 to 2025?
Correct Answer: D [10%]
Explanation:
Answer: 10%. (66 − 60)/60 × 100 = 10%.
25.
(Use the directions above – Q 72–75)
Line graphIn 2021, Factory A's output stood to Factory B's output in what ratio?
Line graphIn 2021, Factory A's output stood to Factory B's output in what ratio?
Correct Answer: C [15 : 14]
Explanation:
Answer: 15 : 14. 45 : 42 = 15 : 14.
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