A boat can row 36 km downstream in the same time as it takes to row 24 km upstream. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

A. 15 km/h
B. 12 km/h
C. 21 km/h
D. 18 km/h

🧠 Core Concept:
Let boat speed = b
👉 Downstream = b + 3
👉 Upstream = b − 3
Time equal:$$\frac{36}{b+3} = \frac{24}{b-3}$$
Cross multiply:
36(b − 3) = 24(b + 3)
36b − 108 = 24b + 72
👉 12b = 180
Divide both sides by 12:
👉 b = 15
✅ Answer: A. 15 km/h

❌ Why others wrong:
12 → ignored stream
18, 21 → wrong cross multiplication

Manoj starts from Point A and drives 25 km towards South. He then takes a left turn, drives 17 km, turns left and drives 28 km. He then takes a left turn and drives 20 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified)

A. 2 km to the west
B. 2 km to the east
C. 3 km to the west
D. 3 km to the east

Trick:
Always draw simple axes 👇
– Start A
– South 25 → (0, -25)
– Left (East) 17 → (17, -25)
– Left (North) 28 → (17, 3)
– Left (West) 20 → (-3, 3)
– Left (South) 3 → (-3, 0)
Final point P = (-3, 0)
👉 A = (0,0)
So distance = 3 km toward East
✅ Answer: D. 3 km toward East

In a certain code language,
A + B means ‘A is the mother of B’
A – B means ‘A is the wife of B’
A × B means ‘A is the sister of B’
A ÷ B means ‘A is the father of B’
Based on the above, how is S related to P if ‘S – K ÷ T × V + P’?

A. Mother’s sister
B. Father’s mother
C. Father’s sister
D. Mother’s mother

Expression:
S – K ÷ T × V + P
Break step-by-step:
S – K → S is wife of K
K ÷ T → K is father of T
👉 S = mother of T
T × V → T is sister of V
👉 S = mother of V
V + P → V is mother of P
👉 S = grandmother of P
✅ Answer: D. Mother’s mother

A tower stands vertically on the ground. From a point on the ground which is 28.6 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45°. Find the height of the tower.

A. 22.6 m
B. 28.6 m
C. 24.6 m
D. 26.6 m

Why we use Tan here: Because there is asked only about height and base, not hypotenuse.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side:
$tan (45\degree) = \frac{opposite}{adjacent}$
It is considered same on both sides. Meaning if opposite is 1 then adjacent is 1 as well.
$tan (45\degree) = \frac{1}{1}$
$tan (45\degree) = 1$
$$Hence if the base is 28.6 then the height will be the same as well.
👉 height = base = 28.6 m
✅ Answer: B. 28.6 m

In a certain code language, ‘BELI’ is coded as ‘6315’ and ‘EVIL’ is coded as ‘9653’. What is the code for ‘V’ in the given code language?

A. 6
B. 3
C. 9
D. 7

BELI → 6315
EVIL → 9653
Common letter = V appears in both? No
Look at E and L
From first word: E = 3, L = 1
From second word: E = 9, L = 3
👉 So mapping is NOT fixed per position
👉 But value must be same
Look both have these but different positions assigned.
BELI → 6315
EVIL → 9653
The question is not about position but what is the value of V. We can see clearly the in first code the only value and number unique is (B = 1). The same way in second code the unique is (V =9).
✅ Answer: C. 9

The mean marks of the following distribution is:

A. 51
B. 60
C. 65
D. 74

Calculation (Shortcut)
Formula:$$\text{Mean} = \frac{\Sigma fx}{\Sigma f}$$
Compute:
81×15 = 1215
35×4 = 140
73×3 = 219
56×16 = 896
Total = 2470
Students = 38
Mean = 2470/38 = 65
✅ Answer: C. 65

Which two neighbors combined have a land border with India longer than China’s border?

A. Bangladesh and Pakistan
B. Bhutan and Afghanistan
C. Nepal and Myanmar
D. Pakistan and Nepal

👉 Bangladesh (~4096 km)
👉 Pakistan (~3323 km)
Combined > China (~3488 km)
✅ Answer: A. Bangladesh and Pakistan

What is the maximum value that must be assigned to A so that the 8-digit number 816A0408 is divisible by 4?

A. 5
B. 7
C. 9
D. 4

The question asked what is the value of A and it must be max digit.
Last 2 digits = 08
👉 Always divisible by 4
So any digit works as long as it is max.
Max one digit = 9
✅ Answer: C. 9

Which major technological advancement characterizes the fourth generation of computers?

A. Microprocessors
B. Transistors
C. Vacuum tubes
D. Integrated circuits

✅ Answer: A. Microprocessors

VASE is related to ZEOA in a certain way based on the English alphabetical order. In the same way, DIKW is related to HMGS. To which of the following is LQCO related, following the same logic?

A. QUXL
B. QVZL
C. OTXJ
D. PUYK

The trick and pattern here is +4, +4, -4, -4.
L (+4) → P
Q (+4) → U
C (-4) → Y
O (-4) → K
✅ Answer: D. PUYK

Based on the English alphabetical order, three of the following four 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 one out is not based on the number of consonants/vowels or their position in the letter cluster.)

A. BXS
B. DZV
C. PLG
D. WSN

Trick:
The last two letters in option A, C, D. Look closely the difference is -5 in next letter.
A. X (-5) = S
B. Z (-4) = V
C. L (-5) = G
D. S (-5) = N
👉 Only option B is -4, so it does not belong here.
✅ Answer: B

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 conclusions logically follow(s) from the statements.
Statements:
– Some canals are rivers.
– Some rivers are oceans.
– Some oceans are ponds.
Conclusions:
(I) All ponds are rivers.
(II) All oceans are canals.

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

The statement is talking about Some, not all, which conlusion does. We cannot assume it ourselves, so:
✅ Answer: A. Neither follows

Which institution released the policy report titled Internationalisation of Higher Education in India: Prospects, Potential, and Policy Recommendations in December 2025?

A. All India Council for Technical Education
B. University Grants Commission
C. Ministry of Education
D. NITI Aayog

✅ Answer: D. NITI Aayog

Evaluate: (-9) – (-56) ÷ (-14) + (-4) × 7

A. -40
B. -41
C. -43
D. -44

Simplification$$-9 – (-56 ÷ -14) + (-4 × 7)$$👉 -56 ÷ -14 = 4
👉 -4 × 7 = -28
= -9 – 4 – 28 = -41
✅ Answer: B. -41

In which language was the Sangam literature of South India, composed between 300 BCE and 300 CE, primarily written?

A. Sanskrit
B. Pali
C. Tamil
D. Prakrit

✅ Answer: C. Tamil

Seven people F, G, H, I, V, W, and X are sitting around a circular table facing the centre of the table. I sits second to the right of W. I sits third to the left of F. V sits third to the left of X. G is an immediate neighbour of both W and F. How many people sit between H and G when counted from the left of H?

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

Key Points:
– “right of” goes clockwise.
– “left of” goes anti-clockwise
– Circular table like a clock: 1,2,3,4,5,6,7.
– There are total 7: F,G,H,I,V,W,X.
– All we have to do is to fit them in position to solve.

Let’s begin.
1 = W
2 = V
3 = I
4 = H
5 = X
6 = F
7 = G
✅ Now Check Conditions (Fast Trick Method):
1. I → W (2nd to right of W)
W → ? → I → ? → ? → ? → ? → W… ✔️ (The circle starts from W to W)

2. I → F (3rd left of F)
W → ? → I → ? → ? → F → ? → W… ✔️

3. V → X (Hard to predict right now, so wait for next)
W → ? → I → ? → ? → F → ? → W… ✔️

4. G → W, F (middle of W and F)
W → ? → I → ? → ? → F → G → W… ✔️

3. V → X (3rd left of X)
W → V → I → ? → X → F → G → W… ✔️

Now only one left which will be H.
W → V → I → H → X → F → G → W … ✔️
The question asked:
👉 How many people have sit Between H and G (left of H)
W → V → I → H → X → F → G → W … ✔️
Left of H:
H → I → V → W → G → F → X → H… ✔️
👉 Answer C: Three

Consider a hypothetical population of rabbits experiencing logistic growth. If the carrying capacity of their environment is 1000 individuals and the current population is 500, what would you expect to happen to the population?

A. The population will decline rapidly due to resource depletion.
B. The population will continue to grow exponentially without any constraints.
C. The population will experience a sudden crash followed by a rapid rebound.
D. The population growth will slow down and eventually stabilize near the carrying capacity.

The question itself says the environment can keep up with 1000 individuals, so it is obvious the rabbits will grow to the level. “Population slows as it reaches carrying capacity”
✅ Answer: D. The population growth will slow down and eventually stabilize near the carrying capacity.

Which postulate of Dalton’s Atomic Theory was proven wrong by the discovery of subatomic particles?

A. Isotopes of the same element have different masses.
B. Atoms retain their identity in chemical reactions.
C. Atoms of different elements have different masses.
D. Matter consists of indivisible atoms.

Wrong postulate:
👉 Atoms indivisible ❌ (electrons discovered)
✅ Answer: D. Matter consists of indivisible atoms.

Three friends X, Y and Z started a business by investing a sum of money in the ratio of 4 : 2 : 5. After 6 months, X withdraws half of his capital. If the sum invested by Z is ₹23,000, then out of a total annual profit of ₹37,000, what is the difference between X’s and Y’s profit?

A. ₹3700
B. ₹5015
C. ₹3065
D. ₹4255

Ratio:
X:Y:Z = 4:2:5
Z = 23000 → unit = 4600
X = 18400
Y = 9200
After 6 months X becomes half
Effective:
X = 4×6 + 2×6 = 36
Y = 2×12 = 24
Ratio = 36:24 = 3:2
Profit difference = ₹3700
✅ Answer: A. 3700

At present, Sharad is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of the ages of these three people 3 years ago was 63 years, then Sharad’s present age (in years) is:

A. 50
B. 55
C. 45
D. 35

Let son = x
Sharad = 3x
Daughter = x−3
3 years ago:
(3x−3)+(x−3)+(x−6)=63
👉 5x−12=63
👉 x=15
Sharad (3x) = 45
🎯 FINAL ANSWER: C. 30.77​

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 operation on the second number results 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.)
7 – 21 – 31 – 62; 9 – 27 – 37 – 74

A. 11-33-43-86
B. 12-36-46-82
C. 8-32-42-84
D. 6-18-28-76

Pattern:
×3, +10, ×2
Let’s check:
7, 21 (7×3), 31 (21+10), 62 (31×2)
9, 27 (9×3), 37 (27+10), 74 (37×2)
Options A: 11, 33 (11×3), 43 (33+10), 86 (43×2)
Check options → only A fits
✅ Answer: A. 11-33-43-86

Find the area of a regular hexagon whose side measures 14√3 cm.

A. 509√3 cm²
B. 294√3 cm²
C. 882√3 cm²
D. 441√3 cm²

Hexagon area: $\frac{3\sqrt{3}}{2} a^2$
We have given: $a = 14\sqrt{3}$
Let’s put in:
$\frac{3\sqrt{3}}{2}\ \times \ (14\sqrt{3})^2 \\ \frac{3\sqrt{3}}{2}\ \times \ ((14)^2(\sqrt{3})^2) \\ \frac{3\sqrt{3}}{2}\ \times \ (196\times3) \\ \frac{3\sqrt{3}}{2}\ \times \ 588 \\ 3\sqrt{3}\ \times \ 294 \\ 294\ \times \ 3\sqrt{3} \\ 882\sqrt{3}$
✅ Answer: C

Which sector uses computers for online transactions, payroll processing, inventory control, and data analysis?

A. Manufacturing Plants
B. Research
C. Service Industry
D. Business and Commerce

Business & commerce uses all listed functions
✅ Answer: D. Business and Commerce

By selling an article at 6/15 of its actual selling price, Hitesh incurs a loss of 28%. If he sells it at 89% of its actual selling price, then the profit percentage is:

A. 59.2%
B. 60.5%
C. 60.2%
D. 60.7%

Let actual SP (Selling Price) = 100
6/15 SP = 40
Loss 28% → CP = 40 / 0.72 = 55.56
New SP = 89
Profit = (89−55.56)/55.56 ×100 ≈ 60.2%
✅ Answer: C. 60.2%

If both the roots of the quadratic equation $A(8x^2 + 4) + Bx + 4x^2 − 8 = 0$ and $3A(2x^2 + 1) + Kx + 3x^2 − 6 = 0$ are common, then what is the value of $9B^2 − 16K^2$ ?

A. -1
B. 1
C. 2
D. 0

The fastest trick:
Make equation standard.
👉 Expression like:$$9B^2 – 16K^2$$👉 Recognize:$$(3B)^2 – (4K)^2$$
Compare ratios → get: $$B : K = 4 : 3$$Direct observe: (put values of ration in B and K)$$9B^2 = 16K^2 \Rightarrow \text{difference = 0}$$
⏱️ Time: 20–25 sec

Want to learn Math then look:
🔴 Given
Two quadratic equations:
(1)$$A(8x^2 + 4) + Bx + 4x^2 – 8 = 0$$(2)$$3A(2x^2 + 1) + Kx + 3x^2 – 6 = 0$$👉 Both have same roots

🧠 Core Concept (VERY IMPORTANT)
👉 If two quadratic equations have same roots, then:$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

👉 (Coefficients are proportional)

Equation (1):$$A(8x^2 + 4) + Bx + 4x^2 – 8$$Expand:$$8Ax^2 + 4A + Bx + 4x^2 – 8$$Group terms:$$(8A + 4)x^2 + Bx + (4A – 8) = 0$$
Equation (2):$$3A(2x^2 + 1) + Kx + 3x^2 – 6$$Expand:$$6Ax^2 + 3A + Kx + 3x^2 – 6$$Group terms:$$(6A + 3)x^2 + Kx + (3A – 6) = 0$$
Step 2: Apply proportionality
Compare coefficients:$$\frac{8A + 4}{6A + 3} = \frac{B}{K} = \frac{4A – 8}{3A – 6}$$
Step 3: Solve ratio (first = third)$$\frac{8A + 4}{6A + 3} = \frac{4A – 8}{3A – 6}$$
Simplify both:
Left:$$8A + 4 = 4(2A + 1), \quad 6A + 3 = 3(2A + 1)$$$$= \frac{4(2A+1)}{3(2A+1)} = \frac{4}{3}$$Right:$$4A – 8 = 4(A – 2), \quad 3A – 6 = 3(A – 2)$$$$= \frac{4(A-2)}{3(A-2)} = \frac{4}{3}$$👉 Both sides equal automatically ✔️
👉 So condition satisfied for all valid A

Step 4: Use middle ratio$$\frac{B}{K} = \frac{4}{3}$$$$B : K = 4 : 3$$
Step 5: Put values
Let:$$B = 4t,\quad K = 3t$$
Step 6: Find required value$$9B^2 – 16K^2$$Substitute:$$= 9(4t)^2 – 16(3t)^2$$$$= 9 \cdot 16t^2 – 16 \cdot 9t^2$$$$= 144t^2 – 144t^2$$$$= 0$$✅ Answer: D. 0