Find the length of the ladder if the angle of elevation of the ladder against a wall is 60° and the foot of the ladder is 11.5 m away from the wall.

A. 23 m
B. $\frac{23\sqrt{3}}{2}\ m$
C. $\sqrt{3}\ cm$
D. 11.5 m

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

Given:
Angle = 60°
Base = 11.5 m
Hypotenuse = Ladder length (L)
$$\cos 60° = \frac{11.5}{L} \Rightarrow \frac{1}{2} = \frac{11.5}{L} \Rightarrow L = 23$$
✅ Answer: A. 23 m
👉 Trick:
If angle = 60°, directly use → hypotenuse = 2 × base

In 2025, the 2nd WHO Global Summit on Traditional Medicine officially began on 17 December in which city?

A. Beijing
B. New Delhi
C. Bangkok
D. Geneva

✅ Answer: B. New Delhi

Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in question?
(NOTE – A two/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)
180 – 145 – 125 – 100; 145 – 110 – 90 – 65

A. 165 – 130 – 110 – 85
B. 115 – 80 – 60 – 45
C. 155 – 130 – 110 – 75
D. 130 – 95 – 70 – 50

Number Pattern
Check pattern:
Set 1:
180 → 145 → 125 → 100
-35, -20, -25

Set 2:
145 → 110 → 90 → 65
-35, -20, -25

👉 Same pattern: −35, −20, −25
Check options:
A: 165 → 130 → 110 → 85
-35, -20, -25 ✔
✅ Answer: A
👉 Trick: Differences repeat, not numbers.

According to the Prayaga Prashasti, Samudragupta is compared to which god associated with wealth?

A. Indra
B. Varuna
C. Yama
D. Kubera

✅ Answer: D. Kubera

Who wrote the introductory essay to Sarojini Naidu’s 1905 poetry collection The Golden Threshold?

A. Rabindranath Tagore
B. W. B. Yeats
C. Arthur Symons
D. Edmond Gosse

✅ Answer: C. Arthur Symons

If 45% of $20 – \frac{4}{6} \times \sqrt[3]{729} \times \sqrt{36} = y$, then the value of y is:

A. -27
B. -35
C. -30
D. -21

Simplification
$$45\% × 20 = 9$$$$\sqrt[3]{729}=9,\quad \sqrt{36}=6$$$$\frac{4}{6} × 9 × 6 = 36$$$$y = 9 – 36 = -27$$✅ Answer: A. -27
👉 Trick: Always solve roots first.

What should come in place of ‘?’ in the given series?
33 40 54 75 103 ?

A. 142
B. 140
C. 138
D. 145

Series
33, 40, 54, 75, 103, ?
Differences:
+7, +14, +21, +28 → next +35
103 + 35 = 138
✅ Answer: C. 138

Article _ describes the procedure for joint sitting of both Houses of the Parliament in certain cases.

A. Article 94
B. Article 104
C. Article 115
D. Article 108

✅ Answer: D. Article 108

In a certain code language, A + B means ‘A is the mother 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 daughter of B’ Based on the above, how is H related to R if ‘H – V ÷ K × T + R’?

A. Sister’s son
B. Brother
C. Father’s brother
D. Mother’s brother

Relation Coding
Expression:
H – V ÷ K × T + R

Decode:
H is brother of V
V is daughter of K
K is husband of T
T is mother of R
So:
K–T = parents of R
V = their daughter
H = brother of V → son of K-T
So H = brother of R
✅ Answer: B. Brother

P, Q, R, S, Y, and Z live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor, which is numbered 6. Only three people live between Y and Z. Only P lives above Y. R lives on an odd numbered floor. Q lives immediately below Y. Who lives on floor number 2?

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

Floor Puzzle
Key clues:
Y & Z → 3 people between → positions (1,5) or (2,6)
Only P above Y
Q below Y

Try:
Y = 5 → Z = 1
Q = 4
P = 6
Remaining: R, S
R odd → 3
S → 2
Floor 2 = S
✅ Answer: A. S
👉 Trick: Always fix biggest constraint first.

Which of the following subjects are included in the Union List under the Seventh Schedule of the Indian Constitution?

A. Local government, markets, and fairs
B. Police, public health, and agriculture
C. Education, forests, and marriage
D. Defence, foreign affairs, and citizenship

✅ Answer: D. Defence, foreign affairs, citizenship

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: Some hens are turkeys. Some hens are ostriches. Some turkeys are eagles.
Conclusions: (I) Some hens are eagles. (II) Some turkeys are ostriches.

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

Syllogism
Statements:
Hens–Turkeys
Hens–Ostriches
Turkeys–Eagles
No direct link → hens & eagles ❌
No link → turkeys & ostriches ❌
✅ Answer: D. Neither follows
👉 Trick: No direct connection → no conclusion.

Select the triad which follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.
BALD-BADL-ABLD
EPIC-EPCI-PEIC

A. PART-RTPA-APTR
B. FIRE-IREF-FRIE
C. HIKE-HIEK-IHKE
D. COME-COEM-OEMC

Letter Pattern
BALD → BADL → ABLD
EPIC → EPCI → PEIC
Pattern:
Swap last two → then first two
Check options:
HIKE → HIEK → IHKE ✔
✅ Answer: C. HIKE-HIEK-IHKE

Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?
JHF 3 RPN 5 ZXV 8 HFD 12 ?

A. BJP 15
B. SYV 17
C. KDU 19
D. PNL 17

Series
Letters shift +8 each time:
J → R → Z → H → P
Similarly:
F → N → V → D → L
Numbers:
3,5,8,12 → +2,+3,+4 → next +5 → 17
✅ Answer: D. PNL 17

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

A. Conserve wetlands
B. Reduce urban air pollution
C. Promote solar energy
D. Increase forest cover

✅ Answer: B. Reduce urban air pollution

Refer to the following number and symbol series and answer the question that follows. All numbers are single-digit numbers only.
(Left) 6 8 @ ! 4 5 ^ 5 * 9 & 4 $ # 3 @ 1 + ? 8 (Right)
If all the symbols are dropped from the series, which of the following will be seventh from the right?

A. 5
B. 9
C. 1
D. 6

Series
Remove symbols:
6 8 4 5 5 9 4 3 1 8
7th from right:
Count → 5
✅ Answer: A. 5

The census in India is conducted once in ten years under the legal authority of the Census Act __.

A. 1872
B. 1947
C. 1948
D. 2010

✅ Answer: C. 1948

If $(a + \frac{1}{a}) = 4$, then what is the value of $(a^5 + \frac{1}{a^5})$ ?

A. 724
B. 709
C. 776
D. 770

You are given:$$a + \frac{1}{a} = 4$$
The core idea in these questions is:
👉 You cannot jump to $a^5 + \frac{1}{a^5}$​ 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:$$4^2 = a^2 + \frac{1}{a^2} + 2$$$$16 = a^2 + \frac{1}{a^2} + 2 \Rightarrow a^2 + \frac{1}{a^2} = 14$$
Now next concept:
To move from power 2 → power 3, use:$$(a + \tfrac{1}{a})(a^2 + \tfrac{1}{a^2}) = a^3 + \tfrac{1}{a^3} + (a + \tfrac{1}{a})$$
👉 WHY this works:
Because multiplication combines powers:
$a × a^2 = a^3$
$\frac{1}{a} × \frac{1}{a^2} = \frac{1}{a^3}$
middle terms give back $a + \frac{1}{a}$ and it is equal to 4.
Now apply:$$4 × 14 = a^3 + \frac{1}{a^3} + 4$$$$56 = a^3 + \frac{1}{a^3} + 4 \Rightarrow a^3 + \frac{1}{a^3} = 52$$
Now same concept again for power 5:
But good news is that, we have already done power 2 and 3. For right side, we input the result of 2 + 3.
$$(a^2 + \tfrac{1}{a^2})(a^3 + \tfrac{1}{a^3}) = a^5 + \tfrac{1}{a^5} + (a + \tfrac{1}{a})$$
Apply values:$$14 × 52 = a^5 + \frac{1}{a^5} + 4$$$$728 = a^5 + \frac{1}{a^5} + 4$$$$a^5 + \frac{1}{a^5} = 724$$✅ Answer: A. 724

Which of the following is NOT regarded as an advantage of the LPG reforms in India?

A. Expansion of the private sector
B. Rise in trade restrictions
C. Adoption of advanced technologies
D. Boost in international partnerships

✅ Answer: B. Rise in trade restrictions

In a certain code language, ‘APES’ is coded as ‘4583’ and ‘PEAT’ is coded as ‘6438’. What is the code for ‘S’ in that language?

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

Pattern
APES = 4583
PEAT = 6438
Do you see the similarities? It is clear that the position don’t matter. So S = 5 and T = 6.
🎯 FINAL ANSWER: B. 5​

If 4 : 28 :: 4.1 : x and 4 : 32 :: 3 : y, then what is the ratio of x to y?

A. 287 : 240
B. 285 : 241
C. 288 : 238
D. 291 : 250

Ratio
Pattern:
4 → 28 = ×7
4.1 → 4.1×7 = 28.7 → x
4 → 32 = ×8
3 → 3×8 = 24 = y
x:y = 28.7:24 = 287:240
✅ Answer: A. 287 : 240

Madhu and Madhuri start a business by investing in the ratio 31 : 34. If total profit is ₹44,850, then what is the difference between the shares of profit (in ₹) of Madhu and Madhuri?

A. ₹3,570
B. ₹1,570
C. ₹570
D. ₹2,070

Profit Sharing
Ratio = 31:34
Difference = 3 parts$$\frac{3}{65} × 44850 = 2070$$
✅ Answer: D. ₹2070

Which of the following continents is NOT crossed by the Equator?

A. Europe
B. Asia
C. Africa
D. South America

✅ Answer: A. Europe

AB is the diameter of a circle P. C and D are two points on the circle on either side of AB, such that $\angle{CAB} = 48^\circ$ and $\angle{ABD} = 55^\circ$. What is the difference between the measures of $\angle{CBD}$ and $\angle{CAD}$?

A. $14^\circ$
B. $11^\circ$
C. $18^\circ$
D. $8^\circ$

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:$$\angle ACB = 90^\circ \quad \text{and} \quad \angle ADB = 90^\circ$$
Now use triangle angle sum.
In triangle ABC:$$\angle CAB + \angle CBA + \angle ACB = 180^\circ$$$$48^\circ + \angle CBA + 90^\circ = 180^\circ \Rightarrow \angle CBA = 42^\circ$$So:$$\angle CBD = \angle CBA + \angle ABD = 42^\circ + 55^\circ = 97^\circ$$
Now triangle ABD:$$\angle ABD + \angle BAD + \angle ADB = 180^\circ$$$$55^\circ + \angle BAD + 90^\circ = 180^\circ \Rightarrow \angle BAD = 35^\circ$$
Now:$$\angle CAD = \angle CAB + \angle BAD = 48^\circ + 35^\circ = 83^\circ$$
Finally, difference:$$\angle CBD – \angle CAD = 97^\circ – 83^\circ = 14^\circ$$✅ Answer: A. 14^∘

In a certain code language, ‘TIER’ is coded as ‘2735’ and ‘TIME’ is coded as ‘3475’. What is the code for ‘M’ in the given code language?

A. 5
B. 7
C. 4
D. 3

Pattern
TIER = 2735
TIME = 3475
Do you see the similarities? It is clear that the position don’t matter. So R = 2 and M = 4.
🎯 FINAL ANSWER: C. 4​