The following dataset represents the number of books read by 25 students in a month:
2 , 4 , 4 , 5 , 5 , 5 , 6 , 7 , 7 , 7 , 7 , 8 , 8 , 9 , 9 , 10 , 10 , 11 , 11 , 12 , 13 , 13 , 13 , 15 , 16.
Calculate the mode of the dataset.

A. 11
B. 13
C. 7
D. 5

Mode (Ungrouped Data)
Concept:
Mode = most frequent value

Frequency check:
7 appears 4 times (highest)
✅ Answer: C. 7

In 2025, which city topped the National Air Quality Index released for major Indian cities?

A. Mumbai
B. Shillong
C. Kolkata
D. Ranchi

✅ Answer: B. Shillong

At what rate (in percentage) per year will a sum of money 5 times itself in 16 years on simple interest?

A. 23
B. 25
C. 50
D. 27

Simple Interest
5 times ⇒ Interest = 4P
SI = $\frac{P\times R\times T}{100}$

​4p = $\frac{P\times R\times 16}{100}$

$4 = \frac{P\times R\times 16}{100 \times P} \\ \frac{1}{R} = \frac{16}{100 \times 4} \\ R = \frac{400}{16}$
= 25%
✅ Answer: B. 25

Along a circular running track, P can complete 5 rounds in 40 minutes. Time taken by R to complete 7 rounds is equal to time taken by P to complete 6 rounds. If they start running in the same direction from two different ends of a diameter, then they will meet for the first time after __ minutes.

A. 28
B. 30
C. 24
D. 20

Circular Track
P speed:
5 rounds in 40 min → 1 round = 8 min

R:
7 rounds = 6 rounds of P
→ 1 round R = (6×8)/7 = 48/7 min

Relative speed:
P = 1/8
R = 7/48

Relative =​ $\frac{7}{48} – \frac{1}{8} = \frac{7 – 6}{48} = \frac{1}{48}$

Distance = half circle

Time to meet
They need to cover 1/2 round gap$$\text{Time} = \frac{\text{Distance}}{\text{Relative speed}}$$
$\text{Time} = \frac{\frac{1}{2}}{\frac{1}{48}}$$$= \frac{1}{2} × 48 = 24$$Time = 24 min
✅ Answer: C. 24

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.
Statements: All tigers are wolves. All jackals are wolves. All animals are wolves.
Conclusions:
(I) Some animals are tigers.
(II) Some jackals are animals.

A. Only conclusion (I) follows.
B. Neither conclusion (I) nor (II) follows.
C. Both conclusions (I) and (II) follow.
D. Only conclusion (II) follows.

Syllogism
Given:
All tigers → wolves
All animals → wolves
❌ No direct relation between animals & tigers
(I) ❌
(II) ❌
👉 Answer B. Neither conclusion (I) nor (II) follows.

Which statement is True or False regarding file management in Windows 11?
(i) When a file is deleted and moved to the Recycle Bin, its contents are immediately and permanently erased from the storage disk.
(ii) The file path (C: > Users > Documents > file.txt) is a strictly hierarchical structure, meaning each file has one unique path.

A. (i) True, (ii) True
B. (i) False, (ii) False
C. (i) True, (ii) False
D. (i) False, (ii) True

File Management
(i) ❌ False → recycle bin ≠ permanent delete
(ii) ✔️ True → file path is unique
✅ Answer: D. (i) False, (ii) True

If 3 is added to each even digit and 2 is subtracted from each odd digit in the number 5723946, how many digits will appear more than once in the new number thus formed?

A. None
B. Two
C. One
D. Three

Digit Operation
Number: 5723946
Even +3 → 5→(odd) no, 2→5, 4→7, 6→9
Odd -2 → 5→3, 7→5, 3→1, 9→7

New number: 3,5,5,1,7,7,9
Repeated digits → 5,7 → 2 digits
✅ Answer: B. Two

Jaspreet deposited a sum of ₹28,450 at 20% rate of interest per annum, compounded annually. The total amount received by Jaspreet after 2 years is:

A. ₹40,624
B. ₹40,968
C. ₹40,958
D. ₹41,126

Compound Interest$$A = 28450 × (1.2)^2 = 28450 × 1.44$$$$= 40968$$✅ Answer: B. ₹40,968

Which provision of the Indian Council Act of 1909 was most criticised for weakening the unity of the Indian nationalist movement?

A. Creation of separate electorates
B. Introduction of executive councils in presidencies
C. Expansion of legislative councils
D. Inclusion of Indians in the Governor-General’s Council

✅ Answer: A. Creation of separate electorates

Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?
: OIM :: ICG : %

A. # = MKO, % = GMJ
B. # = MKO, % = GMK
C. # = QKO, % = GAE
D. # = LPO, % = GJH

Pattern:
O, I (-6), M (+4)
I, C (-6), G (+4)

Option C matches the pattern.
✅ Answer: C. # = QKO, % = GAE

Between 2001 and 2011, the male-female gap in the literacy rate of India __.

A. became zero
B. increased
C. remained the same
D. decreased

Literacy Gap
2001 → high gap
2011 → gap reduced
✅ Answer: D. decreased

Based on the English alphabetical order, three of the following four letter cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?
(Note: The odd man out is not based on the number of consonants/vowels or their position in the letter cluster)

A. LN-MO
B. HJ-IK
C. DF-EG
D. KM-NP

Odd Pair
Check:
LN→MO (+1,+1)
HJ→IK (+1,+1)
DF→EG (+1,+1)
KM→NP (+3,+3) ❌
✅ Answer: D. KM-NP

In 2025, which country officially became the 90th State Member of the International Union for Conservation of Nature (IUCN)?

A. Tuvalu
B. Maldives
C. Nauru
D. Kiribati

In October 2025, the Pacific island nation of Tuvalu officially became the 90th State Member of the International Union for Conservation of Nature (IUCN). As a low-lying nation, Tuvalu’s membership strengthens its efforts in biodiversity protection, climate adaptation, and marine conservation within the Pacific region.
🎯 FINAL ANSWER: A. Tuvalu

How often does India submit its Biennial Update Reports (BURs) to the UNFCCC?

A. Every two years
B. Every three years
C. Every year
D. Every five years

✅ Answer: A. Every two years

Simplify the following expression: $[3.75 + \frac{4}{5}] – [3.5 – \frac{8}{20}]$

A. 1.45
B. 1.4
C. 1.35
D. 1.5

Simplify
(3.75 + 0.8) − (3.5 − 0.4)
= 4.55 − 3.1
= 1.45
✅ Answer: A. 1.45

Which Constitutional Amendment Act added Bodo, Dogri, Maithili, and Santhali to the Eighth Schedule of the Indian Constitutional?

A. 93rd Amendment Act, 2005
B. 86th Amendment Act, 2002
C. 92nd Amendment Act, 2003
D. 91st Amendment Act, 2003

✅ Answer: C. 92nd Amendment Act, 2003

Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?
# : ZJR :: PZH : %

A. # = TDL % = VFN
B. # = UDL % = VFN
C. # = TDM % = VFN
D. # = TDL % = VCN

The Pattern Trick:
Z, J (+10), R (+8)
P, Z (+10), H (+8)
The Option A matches the pattern.
👉 Answer A. = TDL % = VFN

Who were the “Samantas” in the post-Gupta period?

A. Religious heads
B. Farmers
C. Architects
D. Feudal lords

✅ Answer: D. Feudal lords

Simplify $\frac{732 \times 732 \times 732 + 268 \times 268 \times 268}{73.2 \times 73.2 + 26.8 \times 26.8 – 73.2 \times 26.8}$

A. 100
B. 10000
C. 100000
D. 1000

🧠 Step 1: Notice the trick (VERY IMPORTANT)
👉 Look carefully:
732 and 268
73.2 and 26.8
👉 They are just 10× smaller in denominator
So:$$732 = 10 × 73.2,\quad 268 = 10 × 26.8$$
🧠 Step 2: Use identities
Numerator:$$a^3 + b^3$$
Denominator:$$a^2 + b^2 – ab$$
👉 This matches identity:
$a^3 + b^3 = (a + b)(a^2 – ab + b^2)$

🧠 Step 3: Apply scaling properly
Let:$$a = 73.2,\quad b = 26.8$$
Then:$$732 = 10a,\quad 268 = 10b$$
Numerator becomes:$$(10a)^3 + (10b)^3 = 1000(a^3 + b^3)$$
Denominator:$$a^2 + b^2 – ab$$
🧠 Step 4: Apply identity$$a^3 + b^3 = (a + b)(a^2 – ab + b^2)$$
👉 Denominator = same expression
✔️ So it cancels

🧠 Step 5: Final simplification$$\frac{1000(a^3 + b^3)}{a^2 + b^2 – ab} = 1000(a + b)$$
🧠 Step 6: Add values$$a + b = 73.2 + 26.8 = 100$$
✅ Final Answer:$$1000 × 100 = \boxed{100000}$$
✅ Answer: C. 100000

In a certain code language, ‘ALIT’ is coded as ‘2159’ and ‘HILT’ is coded as ‘6912’. What is the code for ‘H’ in the given code language?

A. 2
B. 9
C. 6
D. 1

Coding
ALIT → 2159
HILT → 6912
So it is clear the position has nothing to do here, but pattern value does, so:
H = 6
🎯 FINAL ANSWER: C. 6

A major characteristic of computer systems is Diligence. Which of the following scenarios primarily highlights a limitation of the computer system that is not overcome by its diligence?

A. A computer is used to book flights in the morning and write code in the afternoon.
B. A computer performs trillions of calculations a second, much faster than any human.
C. A computer continues processing data for 72 hours straight without any loss of attention.
D. A computer generates incorrect output because the initial data entered was flawed.

✅ Answer: D. A computer generates incorrect output because the initial data entered was flawed.

Which of the following cabinet committees is NOT headed by the Prime Minister?

A. Cabinet committee on employment and skill development
B. Cabinet committee on economic affairs
C. Cabinet committee on investment and growth
D. Cabinet committee on parliamentary affairs

✅ Answer: D. Cabinet committee on parliamentary affairs

Seven people B, C, O, P, Q, R and S are sitting around a circular table facing the center of the table. Only two people sits between P and B when counted from the right of P. Only S sits between O and P. Q sits to the immediate left of B. C is not an immediate neighbor of P. Who sits third to the left of R?

A. P
B. O
C. C
D. B

Pattern:
Right of = clockwise
Left of = anti-clockwise
Seven People = B,C,O,P,Q,R,S
Sitting Circular:
1 = P
2 = R
3 = Q
4 = B
5 = C
6 = O
7 = S

Let’s breakdown: 1, 2, 3, 4, 5, 6, 7, 1
Two between P – B (right of P)
P, 2, 3, B, 5, 6, 7, P

Only S between O – P (Nothing mention, so Start from O)
P, 2, 3, B, 5, O, S, P

Q – B (left of)
P, 2, Q, B, 5, O, S, P

C (not immediate of P)
P, 2, Q, B, C, O, S, P

Only one place left that is for R.
P, R, Q, B, C, O, S, P

The question is: who sits third left of R?
P, R, Q, B, C, O, S, P
Third left of R:
R, P, S, O, C, B, Q, R
✅ Answer: B. O

A boy flying a kite holds the string of length 24.4 m such that it makes an angle of 30° with the ground. Find the height of the kite from the ground.

A. 13.6 m
B. 13.2 m
C. 12.2 m
D. 11.5 cm

This is a right triangle (height problem) — the kite string is the hypotenuse, and the height is the vertical side.

🔴 Given
Length of string = 24.4 m (hypotenuse)
Angle with ground = 30°
Need: height (opposite side)

🧠 Core Concept
In a right triangle:$$\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$$
$\sin\theta = \frac{\text{height}}{\text{hypotenuse}}$

🧠 Step (direct application)$$\sin 30^\circ = \frac{\text{height}}{24.4}$$
We know:$$\sin 30^\circ = \frac{1}{2}$$
✏️ Solve$$\frac{1}{2} = \frac{h}{24.4}$$$$h = 24.4 × \frac{1}{2} = 12.2$$✅ Answer: C. 12.2 m

What should come in place of ‘?’ in the given series?
3 10 24 45 73 ?

A. 109
B. 111
C. 104
D. 108

Series
Differences:
7, 14, 21, 28
Next = +35$$73 + 35 = 108$$✅ Answer: D. 108