If $a : b = 2 : 3$, then ($7a^3 – 2b^3$) : ($b^3 – a^3$) is____?

A. 2 : 19
B. 3 : 11
C. 13 : 6
D. 3 : 14

Given:
a : b = 2 : 3 → let a = 2k, b = 3k$$(7a^3 – 2b^3) : (b^3 – a^3)$$Substitute: a³ = 8k³, b³ = 27k³
Numerator:
= 7×8 − 2×27 = 56 − 54 = 2
Denominator:
= 27 − 8 = 19
✅ Answer: A. 2 : 19

In a triangle PQR, ∠QOR = 130°, where O is the in-centre of triangle PQR. The measure of ∠QPR is:

A. 70°
B. 80°
C. 60°
D. 50°

Key Formula:
Angle at in-centre: $\angle{BIC} = 90\degree + \frac{A}{2}$
Here: $130 = 90 + \frac{\angle{P}}{2}$
👉 $\frac{\angle{P}}{2} = 130 – 90 \\ \frac{\angle{P}}{2} = 40 \\ \angle{P} = 40 \times 2$
👉 P = 80°
✅ Answer: B. 80°

Three printing machines, P, Q and R, when each is working alone, can print one lakh books in, respectively, 8 hours, 16 hours and 24 hours. These machines print books in turns of one hour each, starting with P, followed by Q and then by R. However, after a total of 9 hours, P stops functioning, but Q and R continue working alternately for an hour each, with Q working during the 10th hour, till the printing of all the one lakh books is completed. In how many hours in all did machines Q and R complete printing the remaining books?

A. 9
B. 6
C. 12
D. 15

Rates:
P = 1/8
Q = 1/16
R = 1/24
First 9 hours (P,Q,R cycle):
1 cycle (3 hrs):$$\frac{1}{8} + \frac{1}{16} + \frac{1}{24} = \frac{11}{48}$$3 cycles (9 hrs):$$= \frac{33}{48} = \frac{11}{16}$$Remaining:$$1 – \frac{11}{16} = \frac{5}{16}$$
Now Q & R alternate:
2 hrs work (1 cycle = 2 hours):
$$\frac{1}{16} + \frac{1}{24} = \frac{5}{48}$$Time:
$\frac{\frac{5}{16}}{\frac{5}{48}} = \frac{5 \times 48}{5 \times 16} = \frac{240}{80} =$3 cycles = 6 hours (3 x 2)
✅ Answer: B. 6

Which sector’s share in GDP increased significantly by 1990, reflecting a shift in the Indian economy?

A. Industry
B. Services
C. Agriculture
D. Mining

👉 Post-1990 → Service sector boom
✅ Answer: B. Services

Consider the following statements about Thawar Chand Gehlot.
1. He is the first person from Madhya Pradesh to serve as the Governor of Karnataka.
2. He is the 19th Governor of Karnataka. Which of the above statements is/are correct?

A. Both 1 and 2
B. Neither 1 nor 2
C. Only 2
D. Only 1

19th Governor ✔️
First from MP ✔️
✅ Answer: A. Both 1 and 2

There is a wooden block in the form of a cube whose each side is 8 meters long. The maximum possible number of cylinders with a diameter of 1 meter and a height of 4 meters were cut from this block. The cylinders are to be painted at the rate of ₹14. per square meter. What is the total amount (in ₹) needed to paint all the cylinders if we paint the entire surface of each cylinder? (Take $\pi = \frac{22}{7}$)

A. 24,527
B. 23,455
C. 25,344
D. 24,325

Cube side = 8 m
Number of cylinders:
Along length = 8 / 1 = 8
Width = 8
Height = 8 / 4 = 2
👉 Total = 8 × 8 × 2 = 128

Surface area of 1 cylinder:$$2\pi r(h+r) = 2 × \frac{22}{7} × 0.5 × (4.5)$$= 14.14 m² approx
Total area:
= 128 × 14.14 ≈ 1810
Cost:
= 1810 × 14 ≈ 25,344
✅ Answer: C. 25,344

This question is based on the five, three-digit numbers given below.
(Left) 458 652 748 351 591 (Right)
(Example: 697 – First digit = 6, second digit = 9 and third digit = 7)
NOTE – All operations to be done from left to right. What will be the resultant if third digit of the highest number is multiplied with the third digit of lowest number?

A. 8
B. 7
C. 6
D. 5

Highest = 748 → last digit = 8
Lowest = 351 → last digit = 1
👉 8 × 1 = 8
✅ Answer: A. 8

The sum of two numbers is 56. Their difference is $\frac{1}{7}$ of their sum. Their LCM is:

A. 96
B. 63
C. 72
D. 84

Sum = 56
Difference = 8
Solve:
x + y = 56
x − y = 8
👉 x = 32, y = 24
LCM = 96
The correct answer is A: 96

In a certain code language, ‘CARD’ is coded as ‘4628’ and ‘NEAT’ is coded as ‘3574’. What is the code for ‘A’ in that language?

A. 4
B. 6
C. 3
D. 7

CARD = 4628
NEAT = 3574
Common letter = A and 4 appears in both
👉 A = 4
✅ Answer: A. 4

What is the primary function of the water vascular system in echinoderms, such as starfish?

A. Reproduction
B. Sensory perception
C. Locomotion and feeding
D. Gas exchange

Water vascular system → movement + feeding
✅ Answer: C. Locomotion and feeding

Which Harappan city, around 2500 BCE, is noted for its dockyard, indicating advanced architectural planning for trade?

A. Mohenjodaro
B. Kalibangan
C. Lothal
D. Dholavira

Dockyard = Lothal
✅ Answer: C

In a certain code language,
A @ B means ‘A is the son of B’,
A # B means ‘A is the sister of B’,
A + B means ‘A is the wife of B’
and A % B means ‘A is the father of B’.
Based on the above, how is E related to B if ‘E + R @ D% N # B’?

A. Mother
B. Wife
C. Sister
D. Brother’s wife

Trick:
@ means son of
# means sister of
+ means wife of
% means father of
E is related to B: E + R @ D% N # B
– E is wife of R.
– R is son of D.
– D is father of N.
– N is sister of B.
Proven that D is father of R, N, and B.
So B is sister of R as well.
✅ Answer: D. Brother’s wife

$\frac{\sqrt[3]{6859}}{\sqrt[4]{256}} \times \frac{2}{57} \times 168$ = ?

A. 28
B. 37
C. 30
D. 38

Simplification$$\frac{\sqrt[3]{6859}}{\sqrt[4]{256}} × \frac{2}{57} × 168$$👉 ∛6859 = 19
👉 ⁴√256 = 4$$= \frac{19}{4} × \frac{2}{57} × 168$$Cancel:
168 ÷ 4 = 42$$= 19 × \frac{2 × 42}{57} = 19 × \frac{84}{57}$$57 = 3×19$$= \frac{19×84}{3×19} = 28$$✅ Answer: A. 28

According to the Banking Laws (Amendment) Act, 2025, the threshold for ‘substantial interest’ in a bank was revised from ₹5 lakh to which of the following amounts?

A. ₹5 crore
B. ₹50 lakh
C. ₹2 crore
D. ₹1 crore

✅ Answer: C. ₹2 crore

A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6. Only five people live above D. Only two people live above A. C lives below F but above A. B does not live on an even numbered floor. How many people live below C?

A. Four
B. One
C. Three
D. Two

Floor Puzzle
D at 1
A at 4
C between A & F → C = 5, F = 6
B odd floor → 3
E → 2
Below C → floors 1–4 → 4 people
✅ Answer: A. Four

The splitting of the ancient Indo–Brahma river into the Indus, Ganga, and Brahmaputra drainage systems is believed to have been primarily caused by which geological event?

A. Pleistocene upheaval
B. River capture by erosion
C. Volcanic eruptions
D. Glacial melting

✅ Answer: A. Pleistocene upheaval

When was the India European Free Trade Association (EFTA) Trade and Economic Partnership Agreement (TEPA) signed, which came into effect on 1 October 2025?

A. March 2024
B. August 2024
C. January 2025
D. September 2025

👉 Answer A. March 2024

Which cultural and musical group celebrated its 10th anniversary in December 2025?

A. Satyajit Ray Society
B. Kala Mandir
C. India Panorama
D. Robir Kiran

✅ Answer: D. Robir Kiran

The summer solstice occurs when the Sun is directly overhead at which of the following latitudes?

A. Tropic of Capricorn
B. Arctic Circle
C. Equator
D. Tropic of Cancer

✅ Answer: D. Tropic of Cancer

At what rate (in percentage) per year will a sum of money double itself in 16 years on simple interest?

A. 4.25
B. 12.5
C. 8.25
D. 6.25

Double → Interest = Principal$$SI = \frac{PRT}{100}$$$$P = \frac{PRT}{100} \Rightarrow R = \frac{100}{T}$$
T means time which is 16.
👉 R = 100/16 = 6.25%
🎯 FINAL ANSWER: D. 6.25​

Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(20, 46, 2)
(32, 136, 24)

A. (6, 42, 10)
B. (32, 93, 11)
C. (13, 25, 1)
D. (17, 78, 16)

Let’s learn the trick here:
There are three values inside (1st, 2nd, 3rd)
2nd = $(1st \times 2) + (3rd \times 3)$
(20, 46, 2)
46 = 20 x 2 + 2 x 3
46 = 40 + 6
46 = 46

(32, 136, 24)
136 = 32 x 2 + 24 x 3
136 = 64 + 72
136 = 136

let’s apply the same with Option A:
42 = 6 x 2 + 10 x 3
42 = 12 + 30
42 = 42
✅ Answer: A. (6, 42, 10)

A file name is highlighted, and you want to copy it to another folder while keeping it in the original folder as well. Which pair of steps matches this task?

A. Press Ctrl + C, then Ctrl + B
B. Press Ctrl + C, then Ctrl + V
C. Press Ctrl + X, then Ctrl + V
D. Press Ctrl + S, then Ctrl + V

Copy → Ctrl + C
Paste → Ctrl + V
✅ Answer: B. Press Ctrl + C, then Ctrl + V

There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are ₹136, ₹383 and ₹457, respectively. The overall average amount (in ₹) spent per member is:

A. 256
B. 261
C. 258
D. 255

Total =
78×136 = 10608
22×383 = 8426
34×457 = 15538
Sum = 34572
Total people = 134$$= 34572 / 134 ≈ 258$$✅ Answer: C. 258

In 2025, which Indian High Court issued the pioneering ‘Policy Regarding the Use of AI Tools in District Judiciary’, becoming the first in the country to frame comprehensive guidelines for artificial intelligence (AI) use in judicial work?

A. Delhi High Court
B. Madras High Court
C. Bombay High Court
D. Kerala High Court

✅ Answer: D. Kerala High Court

Which of the following sectors observed a negative growth rate in Real GVA (Gross Value Added) during Q1 of FY 2025-26 as per the report published by NSO and MoSPI?

A. Construction
B. Tertiary Sector
C. Agriculture and Allied
D. Mining & Quarrying

✅ Answer: D. Mining & Quarrying