A ladder is placed against a wall. If the ladder makes an angle of 45° with the ground and its foot is 8 m away from the wall, what is the length of the ladder?

A. $8\sqrt{2}$ m
B. 8 m
C. 16 m
D. $4\sqrt{2}$ m

Ladder Length (Trigonometry)
Right triangle situation:
$\cos\theta = \frac{\text{base}}{\text{hypotenuse}}$

Given:
Angle = 45° is equal to $\frac{1}{\sqrt{2}}$
Base = 8 m
Hypotenuse = Ladder length (L)
$cos45^\circ = \frac{8}{L} \\ \frac{1}{\sqrt{2}} = \frac{8}{L} \\ L = 8\sqrt{2}$

✅ Answer: A
👉 Trick:
Quick trick: A $45^\circ$angle with one leg known often means a 45−45−90 triangle, so the hypotenuse is leg $\times \sqrt{2}$​.
The leg means base, which is 8 here: 8 $\times \sqrt{2}$​.

What is the name of the joint military exercise between India and Japan conducted in the Rajasthan desert in March 2026?

A) Dharma Guardian
B) Shinyuu Maitri
C) Veer Guardian
D) Desert Cyclone

Dharma Guardian: This 2026 edition focused on semi-urban and desert warfare tactics.
✅ Answer: A. Dharma Guardian

What should come in place of the question mark?
180, 165, 145, 120, 90, ?

A. 55
B. 60
C. 65
D. 50

Solution
Look at the differences:
180→165 = −15
165→145 = −20
145→120 = −25
120→90 = −30
The differences increase by 5 each time, so the next difference is −35.
90 − 35 = 55
Quick trick: Track the differences, not the numbers themselves.
Correct answer: A. 55

The 14th-century treatise Līlātilakam is associated with which literary dialect?

A. Manipravalam
B. Brahmi
C. Prakrit
D. Pali

Britannica states that the Līlātilakam, a 14th-century treatise on grammar and poetics, describes the literary dialect Manipravalam and discusses the blending of Tamilizing and Sanskritizing trends.
✅ Answer: A. Manipravalam

Which Article of the Indian Constitution provides for a joint sitting of both Houses of Parliament in certain cases?

A. Article 107
B. Article 108
C. Article 109
D. Article 110

The Constitution text and constitutional commentary identify Article 108 as the provision for a joint sitting of both Houses of Parliament in certain cases.
✅ Answer: B. Article 108

If 45% of $60 – \frac{2}{3} \times \sqrt[3]{216} \times \sqrt{9} = y$, then the value of y is:

A. 15
B. 12
C. 18
D. 21

Simplification
$45\%\ of\ 60\ = 27$
Now for roots:
$\sqrt[3]{216} = 6 \\ \sqrt{9} = 3$
Let’s put them:
$y = 27 – \frac{2}{3} \times 6 \times 3 \\ y = 27 – \frac{2 \times 18}{3} \\ y = 27 – 12 \\ y = 15$
✅ Answer: A. 15
👉 Trick: Always simplify roots first.

What should come in place of the question mark?
12, 21, 33, 48, 66, ?

A. 82
B. 84
C. 87
D. 90

Series
12, 21, 33, 48, 66, ?
Differences increase of +3:
+9, +12, +15, +18 → next +21
66 + 21 = 87
✅ Answer: C. 87

In a certain code language:
A ÷ B means A is the daughter of B
A – B means A is the brother of B
A × B means A is the husband of B
A + B means A is the mother of B
How is H related to R if H ÷ V – K × T + R?

A. Cousin
B. Aunt
C. Niece
D. Sister

Solution
From the relations:
H÷V means H is the daughter of V
V−K means V is the brother of K
K×T means K is the husband of T
T+R means T is the mother of R
So V and K are siblings. K is R’s father, and H is V’s daughter. That means H is the cousin of R.
Quick trick: Build the family tree from right to left.
Correct answer: A. Cousin

P, Q, R, S, Y and Z live on six different floors of the same building numbered 1 to 6 from bottom to top.
Only three people live between Y and Z.
Only P lives above Y.
Q lives immediately below Y.
R lives on an odd-numbered floor.
Who lives on floor number 2?

A. S
B. Y
C. P
D. Q

Solution
“Only three people live between Y and Z” means Y and Z are 4 floors apart.
“Only P lives above Y” means Y must be on floor 5 and P on floor 6.
“Q lives immediately below Y” means Q is on floor 4.
Since Y and Z are 4 floors apart, Z must be on floor 1.
Remaining floors are 2 and 3 for R and S.
R is on an odd floor, so R is on 3 and S is on 2.
So the person on floor 2 is S.
Quick trick: Use the “only one above” clue first; it fixes the top end immediately.
Correct answer: A. S

Which city was declared the “UNESCO World Book Capital” for the year 2026?

A) Rio de Janeiro
B) Madrid
C) New Delhi
D) Guadalajara

Rio de Janeiro: UNESCO selected the Brazilian city for its commitment to promoting literature and literacy.
✅ Answer: A. Rio de Janeiro

Read the statements and conclusions carefully.
Statements:
All roses are flowers.
Some flowers are fragrant.
All fragrant things are pleasant.
Conclusions:
(I) Some pleasant things are flowers.
(II) All roses are pleasant.

A. Only conclusion (I) follows
B. Only conclusion (II) follows
C. Both conclusions follow
D. Neither conclusion follows

Solution
From the statements:
All roses are flowers.
Some flowers are fragrant.
All fragrant things are pleasant.

Since some flowers are fragrant, and all fragrant things are pleasant, it follows that some pleasant things are flowers.
But we cannot say all roses are pleasant, because no statement links every rose to fragrant or pleasant.

So only conclusion (I) follows.
Quick trick: “Some” + “all” can create a valid partial overlap, but not a universal statement.
Correct answer: A. Only conclusion (I) follows

Select the triad which follows the same pattern as the pairs given below:
FARM – FAMR – AFMR
TIME – TIEM – ITEM

A. BALD – BADL – ABDL
B. NOTE – NTOE – ONTE
C. GLOW – GOLW – OGWL
D. MINT – MNIT – NMIT

Solution
Look at the pattern:
FARM → FAMR (swap the last two letters)
FAMR → AFMR (swap the first two letters)

So the pattern is:
swap the last two letters
then swap the first two letters

Check option A:
BALD → BADL
BADL → ABDL
That follows the same pattern exactly.
Quick trick: First swap the last two, then the first two.
Correct answer: A. BALD – BADL – ABDL

Which letter-number cluster will replace the question mark in the series?
BDF 10, EGI 13, HJL 16, KMO 19, ?

A. NPR 22
B. NPS 22
C. NQR 22
D. NPR 24

Solution
The pattern is simple:
First letters move forward by 3: B, E, H, K, N
Second letters move forward by 3: D, G, J, M, P
Third letters move forward by 3: F, I, L, O, R
Numbers also increase by 3: 10, 13, 16, 19, 22
So the next term is NPR 22.
Quick trick: Check both the letters and numbers for the same step size.
Correct answer: A. NPR 22

Which of the following letter-number clusters should replace the question mark?
FHJ : DFL :: KMO : ?

A. MOQ
B. NOP
C. NPR
D. OMQ

Series
Letters shift +2 each time:
F → +2 → H → +2 → J
D → +2 → F → +2 → L
Similarly:
K → +2 → M → +2 → O
Check Options: Option A matches
M → +2 → O → +2 → Q
✅ Answer: A. MOQ

What was the primary objective of the ‘Blue Skies 2025’ campaign launched in August 2025?

A. Racing for Air
B. Clean Air, Green Earth
C. Blue Planet Action
D. Air for All, Now

UNEP states that the theme of the International Day of Clean Air for blue skies 2025 was “Racing for Air”.
✅ Answer: A. Racing for Air

Refer to the following number and symbol series and answer the question that follows.
All numbers are single-digit numbers only.
4 @ 7 ! 2 # 5 * 9 $ 1 % 8 & 3
If all symbols are dropped from the series, which number will be seventh from the right?

A. 7
B. 5
C. 9
D. 1

Series
Remove symbols:
(left) 4,7,2,5,9,1,8,3 (right)
7th from right:
Count → 7
✅ Answer: A. 7

The “Vishwa Shanti” (World Peace) statue, inaugurated by the PM in April 2026, is located in which city?

A) Ayodhya
B) Varanasi
C) Ahmedabad
D) Kurukshetra

Kurukshetra: The statue was unveiled as a symbol of universal peace and the teachings of the Bhagavad Gita.
✅ Answer: D. Kurukshetra

If $(a + \frac{1}{a}) = 3$, then what is the value of $(a^4 + \frac{1}{a^4})$ ?

A. 47
B. 45
C. 49
D. 51

You are given:
$a + \frac{1}{a} = 3$
The core idea in these questions is:
👉 You cannot jump to $a^4 + \frac{1}{a^4}$​ directly
👉 You build step by step using identities

First important identity:
$(a + b)^2 = a^2 + b^2 + 2ab \\ a^2 +\frac{1}{a^2} + 2\times a \times \frac{1}{a} \\ a^2 +\frac{1}{a^2} + 2$
Now apply it:
$3^2 = a^2 + \frac{1}{a^2} + 2 \\ 9 – 2 = a^2 + \frac{1}{a^2} \\ a^2 + \frac{1}{a^2} = 7$

Now next concept:
To move from power 2 → power 4, use:
$(a^2 + b^2)^2 = 7^2 \\ a^4 + b^4 + 2a^2b^2 = 49 \\ a^4 +\frac{1}{a^4} + 2\times a^2 \times \frac{1}{a^2} = 49\\ a^4 +\frac{1}{a^4} + 2 = 49$
👉 WHY this works:
Because multiplication combines powers:
$a^2 \times a^2 = a^4$
$\frac{1}{a^2} \times \frac{1}{a^2} = \frac{1}{a^4}$

The good news is that, we have already done power 2 and 4. We input the power result of 2 + 2 = 4.
Let’s finish:
$a^4 +\frac{1}{a^4} + 2 = 49 \\ a^4 +\frac{1}{a^4} = 49 – 2 \\ a^4 +\frac{1}{a^4} = 47$
✅ Answer: A. 47

Which Indian state inaugurated the country’s first “Green Hydrogen Valley” in March 2026?

A) Gujarat
B) Kerala
C) Odisha
D) Rajasthan

Kerala: Located in Kochi, this valley produces green hydrogen using solar and wind power for local industrial use.
✅ Answer: B. Kerala

In a certain code language, PAPA is coded as 2424 and SEAT is coded as 3218. What is the code for P?

A. 4
B. 5
C. 8
D. 6

Pattern
PAPA = 2424
Confusing which is 2 or 4 for P or A.
SEAT = 3218
Do you see the similarities? It is clear that the position don’t matter. So A = 2 and P = 4.
🎯 FINAL ANSWER: A. 4​

If 3 : 24 :: 3.5 : x and 5 : 40 :: 4.5 : y, what is the ratio of x to y?

A. 7:9
B. 9:7
C. 28:36
D. 36:28

Ratio
Pattern:
3 → 24 = ×8
3.5 → 3.5×8 = 28 → x

5 → 40 = ×8
4.5 → 4.5×8 = 36 → y
x:y = 28:36 = 7:9
Quick trick: Same multiplier in both gives the ratio directly.
✅ Answer: A. 7 : 9

Eenaa and Meena start a business by investing in the ratio 5 : 8. If the total profit is ₹52,000, what is the difference between their shares of profit?

A. ₹12,000
B. ₹10,000
C. ₹14,000
D. ₹8,000

Profit Sharing
Ratio = 5:8
Difference: 8 – 5 = 3 parts
$\frac{3}{13} \times 52000 = 12000$
✅ Answer: A. ₹12000

Who was appointed as the Governor of the Reserve Bank of India (RBI) in early 2026?

A) Shaktikanta Das
B) T. Rabi Sankar
C) K.V. Kamath
D) Arindam Bagchi

K.V. Kamath: The veteran banker took over the role, bringing extensive experience from the New Development Bank.
✅ Answer: C. K.V. Kamath

AB is the diameter of a circle. C is a point on the circle such that $\angle{CAB} = 35^\circ$. What is ∠ABC?

A. $55^\circ$
B. $65^\circ$
C. $45^\circ$
D. $35^\circ$

Think in terms of circle angle properties, not raw calculation.
Since AB is a diameter, any angle subtended by AB at the circle is a right angle. So:
∠ACB = 90^∘
Now in triangle ABC:
∠ABC = 180^∘ − 90^∘ − 35^∘ = 55^∘
Quick trick: Angle in a semicircle is always 90^∘.
✅ Answer: A. 55^∘

In a certain code language, ‘BYER’ is coded as ‘3218’ and ‘LYER’ is coded as ‘2178’. What is the code for ‘L’ in the given code language?

A. 7
B. 2
C. 1
D. 3

Pattern
BYER = 3218
LYER = 2178
Do you see the similarities? It is clear that the position don’t matter. So B = 3 and L = 7.
🎯 FINAL ANSWER: A. 7​