Which ions help chlorophyll to absorb light?

A. C
B. Mg
C. Ca
D. Na

Chlorophyll & Ions
Concept:
Chlorophyll molecule contains magnesium (Mg²⁺) at its center
This helps in light absorption during photosynthesis
✅ Answer: B. Mg

❌ Others:
C → element, not ion role
Ca, Na → not part of chlorophyll core

Vihaana walks 11 km North, then turns left and walks 7 km. She then turns left again and walks 11 km. She turns right and walks 2 km to reach point R. How far and in which direction is point R from the starting point?
(All turns are 90- degree turns only, unless specified.)

A. 9 km, West
B. 11 km, East
C. 8 km, East
D. 10 km, West

Direction
Step-by-step:
Start → (0,0)
North 11 → (0,11)
Left → West 7 → (-7,11)
Left → South 11 → (-7,0)
Right → West 2 → (-9,0)
👉 Final point = (-9,0)
Distance = 9 km
Direction = West
✅ Answer: A. 9 km, West

The average of 11 results is 61. If the average of the first 6 results is 64 and that of the last 6 is 61, find the 6th result.

A. 81
B. 80
C. 78
D. 79

Average Trick
Total of 11 = 11×61 = 671
First 6 = 6×64 = 384
Last 6 = 6×61 = 366
👉 Middle (6th counted twice)
6th = 384 + 366 − 671 = 79
✅ Answer: D. 79

Which of the following apparent forces, caused by Earth’s rotation, deflects winds to the right in the Northern Hemisphere and to the left in the Southern Hemisphere?

A. Gravitational force
B. Pressure gradient force
C. Frictional force
D. Coriolis force

✅ Answer: D. Coriolis force

Which of the following letter-number clusters will replace the question mark (?) in the given series to make it logically complete?
JMO 50 MPR 61 PSU 72 SVX 83 ?

A. VEO 93
B. VXZ 93
C. VYA 94
D. VZZ 94

Coding Series
Pattern:
Letters:
J→M→P→S → +3
M→P→S→V → +3
O→R→U→X → +3
Next:
V Y A
Numbers:
50 → 61 → 72 → 83 → +11
Next = 94
✅ Answer: C. VYA 94

What is the mode of the data given below? [Give your answer correct to 2 decimal places.]

A. 74.25
B. 72.25
C. 78.25
D. 76.25

Mode (Grouped Data)
Modal class = 70–80 (highest freq = 38)
Formula:
Mode = $L + \frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times h$

$= 70 + \frac{38 – 18}{2\times38 – 18 – 26} \times 10 \\ = 70 + \frac{20}{76 – 44} \times 10 \\ = 70 + \frac{200}{38} \\ = 70 + 6.25 \\ = 76.25$

✅ Answer: D. 76.25

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 statement.
Statements: All tea is a snack. All tea is brunch. All brunches are dinner.
Conclusions:
(I) All tea is dinner.
(II) Some brunches are snacks.

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:
Tea → Snack
Tea → Brunch
Brunch → Dinner
👉 Tea → Dinner ✔️
👉 Some brunch are snacks ✔️ (common element: tea)
✅ Answer: C. Both conclusions (I) and (II) follow.

Which of the following introduced dyarchy by dividing subjects into Reserved and Transferred lists?

A. Indian Councils Act, 1892
B. Government of India Act, 1909
C. Government of India Act, 1935
D. Government of India Act, 1919

The correct answer is D: Government of India Act, 1919

A shopkeeper purchased 59 dozens of articles at the rate of ₹520 per dozen. He sold each one of them at the rate of ₹52. What percentage profit did he make?

A. 19%
B. 23%
C. 21%
D. 20%

🔴 Given
Bought 59 dozens at ₹520 per dozen
Sold each article at ₹52
👉 1 dozen = 12 articles

🧠 Core Concept$$\text{Profit \%} = \frac{SP – CP}{CP} \times 100$$
⚡ STEP 1: Work PER DOZEN (fastest trick)
👉 Always convert to same unit
Cost Price per dozen:$$CP = ₹520$$
Selling Price per dozen:$$12 \times 52 = 624$$
🧠 STEP 2: Profit per dozen$$Profit = 624 – 520 = 104$$
🧠 STEP 3: Profit %
$\frac{104}{520} \times 100 \\ \frac{1}{5} \times 100 = 20\%$

✅ Answer: D. 20%

Solve the following system of 3 equations in 3 unknowns.
x − 3z = −5
2x − y + 2z = 16
7x − 3y − 5z = 19

A. x = 4, y = −2, z = −3
B. x = 4, y = −2, z = 3
C. x = −4, y = 2, z = −3
D. x = −4, y = 3, z = −2

Start by using the simplest equation to reduce variables. From x − 3z = −5, we directly get x = 3z − 5. Now substitute this into the other two equations so everything is in terms of $y$ and $z$.

Putting x = 3z − 5 into 2x − y + 2z = 16:
2(3z−5) − y + 2z = 16
⇒ 6z − 10 − y + 2z = 16
⇒ 8z − y = 26
⇒ y = 8z − 26.

Now substitute both x = 3z − 5 and y = 8z − 26 into the third equation 7x − 3y − 5z = 19:
7(3z−5) − 3(8z−26) − 5z = 19.

This gives 21z − 35 − 24z + 78 − 5z = 19, so combining terms:
−8z + 43 = 19
⇒ −8z = −24
⇒ z = 3.

Now back-substitute:
x = 3z−5
x = 9 − 5
x = 4,

y = 8z − 26
y = 24 − 26
y = −2.
So the solution is:$$x = 4,\quad y = -2,\quad z = 3.$$✅ Answer: B. x = 4, y = −2, z = 3

The price of fuel decreases by 40%, 60% and 60% in three successive months, but increases by 70% in the fourth month. What is the percentage increase or decrease in the price of fuel in the fourth month as compared to its original price?

A. Increase by 87.04%
B. Decrease by 84.38%
C. Increase by 80.38%
D. Decrease by 83.68%

Successive Change
Assume 100
After decreases:
100 → 60 → 24 → 9.6
Increase 70%:
9.6 × 1.7 = 16.32
✅ Answer: D. Decrease by 83.68%

The average of the first 62 even natural numbers is:

A. 61
B. 63
C. 62
D. 64

Average Even Numbers
First 62 even numbers:
2 to 124
Average = (2+124)/2 = 63
✅ Answer: B. 63

In the Chola empire, the tax-free lands donated to Brahmins where they settled were known as ___.

A. Mahasabha
B. Garbhagriha
C. Valanadu
D. Agraharam

✅ Answer: D. Agraharam

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 :: ?
: EGC :: QSO : %

A. # = HJF; % = NPL
B. # = GTF; % = NNH
C. # = NJG; % = NKJ
D. # = TYF; % = NHG

Letter Analogy
EGC → differences:
E→G (+2), G→C (-4)

Apply reverse:
QSO:
Q→S (+2), S→O (-4)
Backward gives matching → option A fits pattern
✅ Answer: A. = HJF; % = NPL

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.)
(44, 968, 22)
(26, 650, 25)

A. (34, 173, 5)
B. (18, 108, 6)
C. (15, 348, 23)
D. (23, 210, 9)

Pattern
Check:
44 → 968 → 22
44×22 = 968 ✔️
26×25 = 650 ✔️
So:
First × third = second
Check option:
18×6 = 108 ✔️
✅ Answer: B. (18, 108, 6)

Which district in Mizoram was recognised as the best-performing district in NITI Aayog’s SDG Index NE Districts 2023–24?

A. Lunglei
B. Aizawl
C. Hnahthial
D. Champhai

✅ Answer: C. Hnahthial

Which ratio is the largest among 5 : 12, 14 : 31, 8 : 33 and 17 : 39?

A. 8 : 33
B. 14 : 31
C. 5 : 12
D. 17 : 39

Largest Ratio
Compare:
5/12 = 0.416
14/31 ≈ 0.451
8/33 ≈ 0.242
17/39 ≈ 0.435
👉 Answer B. 14 : 31

100 men have provisions for 26 days. If 50 men have left, for how many days the same provisions would last for the remaining men?

A. 50
B. 54
C. 52
D. 56

Men & Food
100 men → 26 days
Total work = 2600
50 men → days = 2600/50 = 52
✅ Answer: C. 52

Which of the following reflects the Gandhian ideals incorporated as Directive Principles of State Policy in the Constitution of India?

A. Raising the standard of living and public health
B. Promoting cottage industries in rural areas
C. Safeguarding children against exploitation
D. Securing suitable employment for all

✅ Answer: B. Promoting cottage industries in rural areas

A dealer buys two articles X and Y for ₹800 each. He marks each of them at the same price. He sells X by giving two successive discounts of 45% and 73% and still earns ₹523 as profit. If he sells Y at a single discount of 89%, then what is the profit percentage on Y?

A. 22%
B. 21.5%
C. 21%
D. 22.5%

Profit
CP = 800
Let MP = x
SP(X) = x × 0.55 × 0.27 = 0.1485x
Profit = 523:
0.1485x − 800 = 523
0.1485x = 800 + 523
x = 1323/0.1485
x ≈ 8909.09

SP(Y) = 11% of MP (x) is ≈ 979.99
Profit: 979.99 – 800 = 179.99

179.99/800 ​× 100 ≈ 22.498%
🎯 FINAL ANSWER: D. 22.5%​

Who among the following is NOT directly associated with the Prarthana Samaj?

A. Debendranath Tagore
B. Mahadev Govind Ranade
C. Atmaram Pandurang
D. R.C. Bhandarkar

✅ Answer: A. Debendranath Tagore

Simplify: $\frac{\sqrt[3]{2744}}{\sqrt[4]{256}} \times \frac{2}{42} \times 72$

A. 5
B. 17
C. 12
D. 10

Simplify
$$\sqrt[3]{2744}=14,\quad \sqrt[4]{256}=4$$$$= \frac{14}{4}×\frac{2}{42}×72 = \frac{7}{2}×\frac{1}{21}×72$$$$= \frac{7×72}{42} = 12$$
✅ Answer: C. 12

In 2025, which United Nations body released the World Urbanization Prospects report using the Degree of Urbanization methodology?

A. UN Human Settlements Programme (UN-Habitat)
B. UN Department of Economic and Social Affairs (UN DESA)
C. UN Development Programme (UNDP)
D. UN Statistical Commission

✅ Answer: B. UN Department of Economic and Social Affairs (UN DESA)

The acid present in the atmosphere of Venus is:

A. HCOOH
B. HCl
C. $H_2SO_4$
D. $HNO_3$

👉 Sulphuric acid (H₂SO₄)
✅ Answer: C. H₂SO₄

Which of the following was the primary objectives of the India-Liberia MoU signed in December 2025?

A. Enhancing co-operation on medicine quality standards
B. Constructing new highways
C. Initiating joint space missions
D. Establishing defense manufacturing units

✅ Answer: A. Enhancing co-operation on medicine quality standards