SSC CGL Mock – Tier II Paper I Mock Test 06 – Section I · Part A · Mathematical Abilities

← Back

SSC CGL Mock – Tier II Paper I Mock Test 06 – 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.

Get daily current affairs & exam alerts – follow us YouTube WhatsApp Channel Telegram Channel Facebook Page Instagram
Share with friends & study groups
Link to this page from your website / blog (HTML code)
1.  
The marked price of a cooler is ₹ 4,050, which is 35% above its cost. What discount per cent must be given on it to earn a profit of 8%?

Correct Answer: B [20%]

Explanation:

CP = 4,050 ÷ 1.35 = 3,000; SP = 3,240 → discount = 810/4,050 = 20%.

2.  
A shopkeeper who allows a 20% discount on the marked price earns a profit of 12%. What would be the result if he allowed a 30% discount instead?

Correct Answer: B [A loss of 2%]

Explanation:

0.8 MP = 1.12 CP → MP = 1.4 CP; 0.7 × 1.4 = 0.98 → a loss of 2%.

3.  
For 2 years at the same rate, the compound interest (compounded annually) on a sum is ₹ 2,520 and the simple interest is ₹ 2,400. What is the sum?

Correct Answer: D [₹ 12,000]

Explanation:

Extra ₹ 120 = interest on one year's SI (₹ 1,200) → rate 10% → sum = 1,200 ÷ 0.1 = 12,000.

4.  
If cosec θ + cot θ = 5/2, find cos θ.

Correct Answer: A [21/29]

Explanation:

cosec θ − cot θ = 2/5 → cosec θ = 29/20, cot θ = 21/20 → cos θ = cot θ/cosec θ = 21/29.

5.  
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, then x² − y² equals:

Correct Answer: A [a² − b²]

Explanation:

x² − y² = a²(sec²θ − tan²θ) − b²(sec²θ − tan²θ) = a² − b² (the 2ab sec θ tan θ terms cancel).

6.  
The shadow of a tower is 40 m longer when the sun's elevation is 30° than when it is 60°. Find the height of the tower.

Correct Answer: C [20√3 m]

Explanation:

h(√3 − 1/√3) = 40 → h × 2/√3 = 40 → h = 20√3 m.

7.  
A distribution has mean 40 and standard deviation 6. What is its coefficient of variation?

Correct Answer: B [15%]

Explanation:

CV = SD/mean × 100 = 6/40 × 100 = 15%.

8.  
Find the mean deviation about the mean of 3, 5, 7, 9, 11.

Correct Answer: C [2.4]

Explanation:

Mean 7; |deviations| 4, 2, 0, 2, 4 → 12/5 = 2.4.

9.  
A pair of fair dice is rolled and the two numbers shown are multiplied. What is the probability that this product is an even number?

Correct Answer: D [3/4]

Explanation:

Odd product needs both odd: 9/36 → even = 27/36 = 3/4.

10.  
A batsman scores 86 in an innings and this raises his average by 2 to 30. How many innings has he now played?

Correct Answer: A [29]

Explanation:

28n + 86 = 30(n + 1) → n = 28 earlier innings → 29 now.

11.  
Find the sum of the first 50 terms of the sequence 3, 7, 11, 15, …

Correct Answer: D [5,050]

Explanation:

S = n/2 × [2a + (n − 1)d] = 25 × (6 + 196) = 5,050.

12.  
Of all the divisors of N = 2⁴ × 3⁵ × 5², how many are themselves perfect squares?

Correct Answer: A [18]

Explanation:

Even exponents only: 2 → {0, 2, 4}, 3 → {0, 2, 4}, 5 → {0, 2} → 3 × 3 × 2 = 18.

13.  
If 2ᵃ = 3ᵇ = 6ᶜ (all non-zero), then c is equal to:

Correct Answer: B [ab/(a + b)]

Explanation:

Let the common value be k: 2 = k 1/a , 3 = k 1/b , 6 = k 1/c → 1/c = 1/a + 1/b → c = ab/(a + b).

14.  
30 litres of brine contain 10% salt. How much water must evaporate to make the salt content 15%?

Correct Answer: C [10 litres]

Explanation:

Salt stays 3 L = 15% of the new volume → 20 L → evaporate 10 litres.

15.  
A and B are partners with capitals in the ratio 3 : 2. A, the working partner, first takes 10% of the profit as salary; the rest is shared in the capital ratio. If A receives ₹ 32,000 in all, what is the total profit?

Correct Answer: B [₹ 50,000]

Explanation:

A gets 0.1P + 0.6 × 0.9P = 0.64P = 32,000 → P = 50,000.

16.  
x satisfies the quadratic x² − 3x + 1 = 0. What is x⁶ + 1/x⁶?

Correct Answer: A [322]

Explanation:

x + 1/x = 3 → x³ + 1/x³ = 27 − 9 = 18 → x⁶ + 1/x⁶ = 18² − 2 = 322.

17.  
For real a, b and c it is known that a² + b² + c² − 2a + 4b − 6c + 14 = 0. Find a + b + c.

Correct Answer: D [2]

Explanation:

(a − 1)² + (b + 2)² + (c − 3)² = 0 → a = 1, b = −2, c = 3 → sum 2.

18.  
Find the HCF of the polynomials x² − 4 and x² + x − 6.

Correct Answer: A [x − 2]

Explanation:

x² − 4 = (x − 2)(x + 2), x² + x − 6 = (x − 2)(x + 3) → common factor x − 2.

19.  
Suresh spends 40% of his income on the household, 25% of the remainder on education and 20% of what is then left on travel. He saves ₹ 14,400. What is his income?

Correct Answer: C [₹ 40,000]

Explanation:

Left = 0.6 × 0.75 × 0.8 = 0.36 of income → 14,400 ÷ 0.36 = 40,000.

20.  
The areas of three adjacent faces of a cuboid are 24 cm², 32 cm² and 48 cm². Find its volume.

Correct Answer: B [192 cm³]

Explanation:

(lb)(bh)(hl) = (lbh)² → V = √(24 × 32 × 48) = √36,864 = 192 cm³.

21.  
A cart wheel 70 cm across rolls without slipping for a distance of 1.1 km. Taking π = 22/7, how many full turns does it make?

Correct Answer: D [500]

Explanation:

Circumference = 22/7 × 70 = 220 cm; 1,10,000/220 = 500.

22.  
The radius of a cone is increased by 50% and its height is reduced by 50%. What happens to its volume?

Correct Answer: A [It increases by 12.5%]

Explanation:

V ∝ r²h → 1.5² × 0.5 = 1.125 → the volume rises by 12.5%.

23.  
A and B can do a job in 6 days and 8 days respectively. With the help of C they finish it in 3 days and receive ₹ 24,000 in all. What is C's fair share?

Correct Answer: A [₹ 3,000]

Explanation:

In 3 days A does 1/2, B 3/8, so C does 1/8 → 1/8 × 24,000 = 3,000.

24.  

Directions (Q 24–26): The bar chart shows the number of employees in five departments of a firm in 2024 and 2025 (fictional data).

Bar chartMeasured against its own 2024 strength, which department grew the most by 2025?

Correct Answer: C [IT]

Explanation:

HR 12.5%, IT 25%, Sales −10%, Operations 10%, Finance 8.9% → IT.

25.  
(Use the directions above – Q 24–26)
Bar chartBy what per cent did the firm's total staff grow from 2024 to 2025?

Correct Answer: B [10%]

Explanation:

Answer: 10%. 500 → 550: 50/500 = 10%.

26.  
(Use the directions above – Q 24–26)
Bar chartIn 2025 the average monthly salary is ₹ 80,000 in IT and ₹ 50,000 in Operations. What is the combined monthly salary bill of these two departments?

Correct Answer: A [₹ 2.08 crore]

Explanation:

150 × 80,000 + 176 × 50,000 = 1,20,00,000 + 88,00,000 = ₹ 2,08,00,000.

27.  
A thief is 200 m ahead of a policeman when the chase begins. The thief runs at 10 km/h and the policeman at 12 km/h. How far will the thief have run when he is caught?

Correct Answer: C [1,000 m]

Explanation:

Gap closes at 2 km/h → 0.2/2 = 0.1 h; thief runs 10 × 0.1 = 1 km = 1,000 m.

28.  
Diagram-basedTA touches the circle at A. B and C are points on the circle with ∠TAB = 65° and ∠BAC = 40° (see figure). Find ∠ABC.

Correct Answer: D [75°]

Explanation:

Alternate segment: ∠ACB = ∠TAB = 65° → ∠ABC = 180° − 65° − 40° = 75°.

29.  
The diagonals of a rhombus are 30 cm and 16 cm. What is the distance between two opposite sides (its height)?

Correct Answer: A [240/17 cm]

Explanation:

Side = √(15² + 8²) = 17; area = ½ × 30 × 16 = 240 = 17 × h → h = 240/17 cm.

30.  
In right triangle PQR, right-angled at Q, QS is the perpendicular from Q to the hypotenuse PR. If PS = 3 cm and SR = 12 cm, find QS.

Correct Answer: D [6 cm]

Explanation:

QS² = PS × SR = 36 → QS = 6 cm.

➤ All 38 papers with every answer explained, score tracker and OMR sheet – SSC CGL 2026 Full Mock Test Papers book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-full-mock-test-papers

📘 SSC CGL 2026 – Full Mock Test Papers (Tier I + Tier II – 38 Full Mock Papers)
Here you get the answer with a one-line explanation. 3,640 new questions in 38 full papers – 15 Tier I, 8 Tier II Paper I, 5 Computer Knowledge, 5 Paper II Statistics, 5 Paper III Finance & Economics · answer key with a one-line reason · score tracker and OMR sheet
Get the book – ₹149 ₹299 →
Score: 0 Answered: 0 / 0