Mental Ability — Pack 01

Question 1

12 men complete in 10 days. 15 men in:

Accepted Answer

8 days — M1D1=M2D2. 120=15×D → 8.

Answer

12

Answer

6

Answer

10

Question 2

Ratio 2:3. Each increased by 5. New ratio 3:4. Original numbers:

Accepted Answer

10,15 — (2x+5):(3x+5)=3:4 → 8x+20=9x+15 → x=5. So 10, 15.

Answer

8,12

Answer

6,9

Answer

20,30

Question 3

d/dx (x^n) =

Accepted Answer

nx^(n-1) — Power rule. d/dx(x²) = 2x; d/dx(x³) = 3x².

Answer

x^n

Answer

x^(n-1)

Answer

n!

Question 4

cos 30° equals:

Accepted Answer

√3/2 — cos 30° = sin 60° = √3/2.

Answer

1/2

Answer

√2/2

Answer

1

Question 5

If x% of y = y% of z, then:

Accepted Answer

x = z — x/100 · y = y/100 · z → x = z.

Answer

x = y

Answer

y = z

Answer

Not necessarily

Question 6

Which letter is 5th to the right of 12th letter from left in English alphabet?

Accepted Answer

Q — 12th = L. 5th to right = Q (17th letter).

Answer

P

Answer

R

Answer

S

Question 7

Blood: A is son of B, B is daughter of C. C to A:

Accepted Answer

Grandmother — C female → grandmother.

Answer

Father

Answer

Grandfather

Answer

Uncle

Question 8

Number of subsets of a set with n elements:

Accepted Answer

2^n — Each element is in or out → 2 choices. Empty set counts. Number of proper subsets: 2^n - 1.

Answer

n

Answer

n²

Answer

n!

Question 9

Surface area of a sphere of radius 14 cm (π=22/7):

Accepted Answer

2464 cm² — SA = 4πr² = 4·22/7·196 = 2464 cm².

Answer

616 cm²

Answer

1232 cm²

Answer

4928 cm²

Question 10

The ratio of areas of two squares with sides in ratio 2:3 is:

Accepted Answer

4:9 — Area ∝ side² → ratio = 4:9.

Answer

2:3

Answer

8:27

Answer

16:81

Question 11

Digit in tens place of 9876:

Accepted Answer

7 — 7.

Answer

8

Answer

9

Answer

6

Question 12

Equilateral triangle angles:

Accepted Answer

60° each — All 60°.

Answer

90°

Answer

120°

Answer

Different

Question 13

Direction: North + 180° = ?

Accepted Answer

South — Opposite.

Answer

East

Answer

West

Answer

North

Question 14

2⁵ equals:

Accepted Answer

32 — 2·2·2·2·2 = 32.

Answer

10

Answer

16

Answer

25

Question 15

Total surface area of a cone = πr(r + l). For r=3, l=5:

Accepted Answer

24π — TSA = πr(r+l) = π·3·(3+5) = 24π.

Answer

15π

Answer

27π

Answer

45π

Question 16

Vector dot product a·b =

Accepted Answer

|a||b| cos θ — Scalar. If perpendicular, a·b = 0. Also = a₁b₁ + a₂b₂ + a₃b₃.

Answer

|a||b| sin θ

Answer

|a|+|b|

Answer

Always zero

Question 17

2, 6, 12, 20, 30, ?

Accepted Answer

42 — Differences: 4,6,8,10,12. Next = 30+12 = 42.

Answer

40

Answer

36

Answer

38

Question 18

Factorial 0!:

Accepted Answer

1 — By convention 1.

Answer

0

Answer

Undefined

Answer

Infinite

Question 19

Series: 5, 6, 9, 14, 21, ?

Accepted Answer

30 — Diff 1,3,5,7,9; 21+9=30.

Answer

28

Answer

32

Answer

35

Question 20

0.1 × 0.01:

Accepted Answer

0.001 — 0.1×0.01=0.001.

Answer

0.01

Answer

0.1

Answer

0.0001

Question 21

A can do a piece of work in 6 days and B in 4 days. How long will they take together?

Accepted Answer

2 2/5 days — Combined rate = 1/6 + 1/4 = 5/12 per day → 12/5 = 2 2/5 days.

Answer

2 1/2 days

Answer

1 1/2 days

Answer

None of these

Question 22

A train 520 m long is running with a speed of 90 km/hr. In what time will it cross a bridge 130 m long?

Accepted Answer

26 second — Total distance = 520+130 = 650 m. Speed = 90 km/h = 25 m/s. Time = 650/25 = 26 seconds.

Answer

25 second

Answer

32 second

Answer

30 second

Question 23

Mean Value Theorem (Lagrange) guarantees c with:

Accepted Answer

f'(c) = (f(b)-f(a))/(b-a) — At some c in (a,b), instantaneous rate equals average rate. Basis for many proofs.

Answer

f'(c) = 0

Answer

f(c) = 0

Answer

c = (a+b)/2

Question 24

CI on 1000 at 10% for 3 years:

Accepted Answer

₹331 — 1000(1.1³-1)=331.

Answer

₹300

Answer

₹300

Answer

₹310

Question 25

Analogy: Hunger : Food :: Thirst : ?

Accepted Answer

Water — Thirst quenched by water.

Answer

Drink

Answer

Bottle

Answer

Glass

Mental Ability — Pack 01