SSC CGL Mock – Tier II Paper I Mock Test 08 – Section I · Part A · Mathematical Abilities

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SSC CGL Mock – Tier II Paper I Mock Test 08 – 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.

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1.  
The ten numbers 1, 2, 3, …, 10 form a data set. Calculate their standard deviation (population formula, dividing by n).

Correct Answer: C [√33/2]

Explanation:

Variance = (n² − 1)/12 = 99/12 = 33/4 → SD = √33/2 ≈ 2.87.

2.  
Two-quantity comparison
For the data 5, 7, 7, 8, 10, 11, 15, 17:
Quantity I: the mean
Quantity II: the median

Correct Answer: A [Quantity I > Quantity II]

Explanation:

Mean = 80/8 = 10; median = (8 + 10)/2 = 9 → Quantity I is greater.

3.  
From a full pack of 52 cards, Arun draws one card, keeps it aside, and then draws a second card. What is the probability that he gets two aces?

Correct Answer: D [1/221]

Explanation:

Answer: 1/221. 4/52 × 3/51 = 1/221.

4.  
Divide the sum of cubes 1³ + 2³ + 3³ + … + 20³ by 7. What remainder is left?

Correct Answer: B [0]

Explanation:

Sum = (20 × 21/2)² = 210² and 210 = 7 × 30 → remainder 0.

5.  
4,620 is to be split as a × b, where a and b are co-prime natural numbers. How many such unordered pairs {a, b} are there?

Correct Answer: A [16]

Explanation:

4,620 = 2² × 3 × 5 × 7 × 11: five prime powers to share between two groups → 2⁵⁻¹ = 16.

6.  
Find the value of 1/(3 − √8) − 1/(√8 − √7) + 1/(√7 − √6) − 1/(√6 − √5) + 1/(√5 − 2).

Correct Answer: D [5]

Explanation:

Rationalise each: (3 + √8) − (√8 + √7) + (√7 + √6) − (√6 + √5) + (√5 + 2) = 5.

7.  
If sec θ − cos θ = 3/2 and θ is acute, find sin θ.

Correct Answer: C [√3/2]

Explanation:

1/c − c = 3/2 → 2c² + 3c − 2 = 0 → cos θ = ½ → θ = 60° → sin θ = √3/2.

8.  
If A + B = 45°, what is the value of (1 + tan A)(1 + tan B)?

Correct Answer: A [2]

Explanation:

tan(A + B) = 1 → tan A + tan B = 1 − tan A tan B → product = 1 + 1 = 2.

9.  
A tower stands on level ground. From points 4 m and 25 m away from its foot, on the same side and in line with it, the angles of elevation of its top add up to 90°. Find the height of the tower.

Correct Answer: B [10 m]

Explanation:

tan α = h/4 and tan(90° − α) = h/25 → h²/(4 × 25) = 1 → h = 10 m.

10.  
Diagram-basedABCD is a square of side 10 cm and E is the midpoint of AB. DE cuts the diagonal AC at F (see figure). Find the area of the shaded triangle AEF.

Correct Answer: A [25/3 cm²]

Explanation:

ΔAFE ~ ΔCFD with ratio AE : CD = 1 : 2, so F is 1/3 of the way from A → height of F above AB = 10/3 → area = ½ × 5 × 10/3 = 25/3 cm².

11.  
An isosceles triangle has sides 5 cm, 5 cm and 6 cm. Find the radius of the circle passing through its three vertices.

Correct Answer: D [25/8 cm]

Explanation:

Area = ½ × 6 × 4 = 12 → R = abc/(4 × area) = 150/48 = 25/8 cm.

12.  
In triangle ABC with AB = 12 cm, BC = 14 cm and CA = 10 cm, the inscribed circle meets side BC at D. How long is BD?

Correct Answer: B [8 cm]

Explanation:

Tangent lengths: BD = s − CA = 18 − 10 = 8 cm.

13.  
Data sufficiencyWhat is the value of a² + b²?
Statement I: a + b = 7 and ab = 12
Statement II: a − b = 1

Correct Answer: A [Statement I alone is sufficient, but Statement II alone is not]

Explanation:

I: a² + b² = 49 − 24 = 25 – sufficient.

14.  
If x + 1/x = √3, find the value of x¹⁸ + x¹² + x⁶ + 1.

Correct Answer: C [0]

Explanation:

x³ + 1/x³ = (√3)³ − 3√3 = 0 → x⁶ = −1 → x¹⁸ + x¹² + x⁶ + 1 = −1 + 1 − 1 + 1 = 0.

15.  
p and q are the roots of x² − 5x + 3 = 0. What is p³ + q³?

Correct Answer: D [80]

Explanation:

p + q = 5, pq = 3 → p³ + q³ = 125 − 3 × 3 × 5 = 80.

16.  
Six equilateral triangles of side 8 cm fit together to form a regular hexagon. What is the area of the hexagon?

Correct Answer: C [96√3 cm²]

Explanation:

Six equilateral triangles: 6 × (√3/4) × 64 = 96√3 cm².

17.  
Water flows at 5 m/s through a pipe of radius 7 cm into a rectangular tank 50 m long and 44 m wide. In how much time will the water level in the tank rise by 7 cm (π = 22/7)?

Correct Answer: A [33 min 20 s]

Explanation:

Volume needed = 50 × 44 × 0.07 = 154 m³; flow = 22/7 × 0.0049 × 5 = 0.077 m³/s → 2,000 s = 33 min 20 s.

18.  
What is the area of the largest triangle that can be inscribed in a semicircle of radius 10 cm?

Correct Answer: B [100 cm²]

Explanation:

Base = diameter 20, height = radius 10 → ½ × 20 × 10 = 100 cm².

19.  
A shopkeeper marks his goods 60% above cost, allows a discount of 25%, and also uses a weight of 900 g in place of 1 kg. What is his overall gain per cent?

Correct Answer: C [33 1/3%]

Explanation:

SP of 1 kg-price = 1.6 × 0.75 = 1.2 × cost of 1 kg, but he gives only 0.9 kg → 1.2/0.9 = 4/3 → 33 1/3%.

20.  
A grocer blends two kinds of rice, one costing ₹ 56 a kg and the other ₹ 70 a kg, in the ratio 3 : 4, and sells the blend at ₹ 72 a kg. Find his percentage profit.

Correct Answer: D [12.5%]

Explanation:

Cost of the mixture = (3 × 56 + 4 × 70)/7 = ₹ 64 per kg → profit = 8/64 = 12.5%.

21.  
In an election between two candidates, 20% of the voters on the list did not vote and 500 votes were invalid. The winner got 60% of the valid votes and won by 1,800 votes. How many voters were on the list?

Correct Answer: B [11,875]

Explanation:

Valid votes = 1,800/0.2 = 9,000; votes cast = 9,500 = 80% of the list → 11,875.

22.  
A boatman takes 10 hours in all to row 36 km downstream and come back the same distance upstream. In the time he rows 3 km downstream he can row only 2 km upstream. Find the speed of the current.

Correct Answer: A [1.5 km/h]

Explanation:

Downstream 3k, upstream 2k: 36/3k + 36/2k = 30/k = 10 → k = 3 → 9 and 6 km/h → current = 1.5 km/h.

23.  
Invested at compound interest, a sum grows to ₹ 9,680 after 2 years and to ₹ 10,648 after 3 years. If instead it earned simple interest at that same annual rate, how much interest would it earn in 4 years?

Correct Answer: B [₹ 3,200]

Explanation:

Rate = 968/9,680 = 10%; sum = 9,680 ÷ 1.21 = 8,000; SI = 8,000 × 0.1 × 4 = 3,200.

24.  
A invests twice as much as B, and B invests three-fourths of what C invests. After 6 months A withdraws half of his capital. Out of a year-end profit of ₹ 46,000, what is C's share?

Correct Answer: A [₹ 16,000]

Explanation:

Take C = 4, B = 3, A = 6: A = 6 × 6 + 3 × 6 = 54, B = 36, C = 48 → 9 : 6 : 8 → C = 8/23 × 46,000 = 16,000.

25.  
A and B together can finish some work in 24 days. They work together for 6 days; then A leaves and B finishes the rest in 30 days. In how many days could A alone have done the whole work?

Correct Answer: D [60 days]

Explanation:

After 6 days 3/4 remains; B does it in 30 days → B alone 40 days; A = 1/24 − 1/40 = 1/60 → 60 days.

26.  

Directions (Q 26–28): The line graph shows the exports and imports of a country (in ₹ thousand crore) from 2020 to 2025 (fictional data).

Line graphOver the six years shown, how many times was the value of exports higher than that of imports in the same year?

Correct Answer: C [3]

Explanation:

2022 (150 > 145), 2024 (180 > 175) and 2025 (210 > 200) → 3.

27.  
(Use the directions above – Q 26–28)
Line graphWhat were the average annual exports over the six years?

Correct Answer: D [₹ 160 thousand crore]

Explanation:

Answer: ₹ 160 thousand crore. 960/6 = 160.

28.  
(Use the directions above – Q 26–28)
Line graphImports changed from each year to the next. In which year did they record their biggest percentage rise over the year before?

Correct Answer: C [2023]

Explanation:

Imports: +7.1%, −3.3%, +17.2%, +2.9%, +14.3% → 2023.

29.  
The mean of 20 observations is 15. One observation, 15, is removed and two observations x and 2x are added; the mean of the 21 observations becomes 16. What is x?

Correct Answer: B [17]

Explanation:

Answer: 17. 300 − 15 + 3x = 336 → x = 17.

30.  
Three equal-sized vessels are each full of a milk-water mixture, in the ratios 2 : 1, 3 : 2 and 5 : 3 respectively. All three are poured into one large tank. Find the milk : water ratio in the tank.

Correct Answer: A [227 : 133]

Explanation:

Milk = 2/3 + 3/5 + 5/8 = 227/120, water = 1/3 + 2/5 + 3/8 = 133/120 → 227 : 133 (not 10 : 6).

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