Mental Ability — Pack 05

Question 1

The radius of a circle of area 154 cm² (π=22/7) is:

Accepted Answer

7 cm — πr² = 154 → r² = 154×7/22 = 49 → r = 7.

Answer

14 cm

Answer

21 cm

Answer

28 cm

Question 2

A and B together can do a piece of work in 12 days; A alone in 18 days. How long will B alone take?

Accepted Answer

36 days — 1/B = 1/12 - 1/18 = (3-2)/36 = 1/36. B alone = 36 days.

Answer

6 days

Answer

30 days

Answer

21 days

Question 3

Walk 5m N, 5m E, 5m S: resultant:

Accepted Answer

5m E — Nets 5m East.

Answer

0

Answer

5m N

Answer

10m

Question 4

Complete: Z, Y, X, W, ?

Accepted Answer

V — Reverse alphabet.

Answer

U

Answer

T

Answer

R

Question 5

Next: 1, 2, 6, 24, 120, ?

Accepted Answer

720 — Factorials ×n: 720.

Answer

600

Answer

240

Answer

500

Question 6

Out of 5 numbers, average of first 4 is 15, average of last 4 is 12. The last number is 18. What is the first number?

Accepted Answer

30 — Sum of first 4 = 60. Sum of last 4 = 48. (Sum of all 5) = first + 48 = first + 48. Also = 60 + last = 60 + 18 = 78. So first = 78 - 48 = 30.

Answer

48

Answer

27

Answer

33

Question 7

Volume of a cuboid with dimensions 4×3×5 cm is:

Accepted Answer

60 cm³ — V = l×b×h = 4×3×5 = 60 cm³.

Answer

12 cm³

Answer

15 cm³

Answer

80 cm³

Question 8

The largest four-digit number that is a perfect square of a whole number is:

Accepted Answer

9801 — 99² = 9801, the largest 4-digit perfect square.

Answer

9604

Answer

9216

Answer

9025

Question 9

√2 approximately:

Accepted Answer

1.414 — 1.414.

Answer

1.732

Answer

2

Answer

1.5

Question 10

Number series: 5, 11, 19, 29, 41, ?

Accepted Answer

55 — Differences: 6,8,10,12,14. 41+14=55.

Answer

51

Answer

53

Answer

50

Question 11

If a cube has volume 216 cm³, each edge is:

Accepted Answer

6 cm — ∛216 = 6 cm; surface area = 6·36 = 216 cm².

Answer

4 cm

Answer

5 cm

Answer

8 cm

Question 12

Solution of dy/dx = ky:

Accepted Answer

y = C·e^(kx) — Exponential growth/decay. Population, radioactivity, Newton cooling.

Answer

y = kx

Answer

y = x^k

Answer

y = ln(kx)

Question 13

Surface area of a cylinder open at top (base + curved) of radius r, height h:

Accepted Answer

2πrh + πr² — Open cylinder surface = curved (2πrh) + one circular base (πr²).

Answer

πr²

Answer

2πrh

Answer

πr(r+h)

Question 14

Plane equation in normal form:

Accepted Answer

ax+by+cz+d=0 — (a,b,c) is normal vector. Distance from origin: |d|/√(a²+b²+c²).

Answer

ax+by+c=0

Answer

x+y+z=1

Answer

Only 2D

Question 15

Which of these is an irrational number?

Accepted Answer

√2 — √2 is irrational (non-terminating non-repeating decimal). √9=3, √16=4, √25=5 are rational.

Answer

√9

Answer

√16

Answer

√25

Question 16

Probability of drawing a red card from a standard deck:

Accepted Answer

1/2 — 26 red (hearts + diamonds) out of 52 = 1/2.

Answer

1/4

Answer

1/13

Answer

2/13

Question 17

Expand (x − 2)²:

Accepted Answer

x² − 4x + 4 — (a−b)² = a² − 2ab + b².

Answer

x² − 4

Answer

x² + 4x + 4

Answer

x² − 4x

Question 18

The next number in the Fibonacci series 1, 1, 2, 3, 5, 8, ... is:

Accepted Answer

13 — Each term is sum of previous two: 5+8 = 13.

Answer

10

Answer

11

Answer

12

Question 19

tan 90° =

Accepted Answer

Undefined (∞) — tan 90° = sin 90°/cos 90° = 1/0 → undefined.

Answer

0

Answer

1

Answer

−1

Question 20

If x+1/x = 2, x² + 1/x² =?

Accepted Answer

2 — (x+1/x)² = x²+2+1/x². 4 = x²+2+1/x². So 2.

Answer

4

Answer

1

Answer

3

Question 21

Convert 5/8 to decimal:

Accepted Answer

0.625 — 5 ÷ 8 = 0.625.

Answer

0.425

Answer

0.825

Answer

0.125

Question 22

Batsman avg 27 runs in 25 innings. To raise avg to 30, runs needed in 26th:

Accepted Answer

105 — 25×27=675. (675+x)/26=30. x=105.

Answer

95

Answer

90

Answer

100

Question 23

The sum of the first 50 natural numbers is:

Accepted Answer

1275 — Sum = n(n+1)/2 = 50·51/2 = 1275.

Answer

1225

Answer

1500

Answer

2550

Question 24

Point-slope form: y-y1=

Accepted Answer

m(x-x1) — Standard.

Answer

(x-x1)

Answer

m×x

Answer

mx+c

Question 25

Boat problem: upstream 12 km in 4 hrs, downstream in 2. Stream speed:

Accepted Answer

1.5 — Up=3, down=6. Still=4.5, stream=1.5.

Answer

2

Answer

1

Answer

3

Mental Ability — Pack 05