Mental Ability — Pack 02

Question 1

A number is increased by 20% and then decreased by 20%. The net change is:

Accepted Answer

4% decrease — Net = 100 → 120 → 96; 4% net decrease.

Answer

No change

Answer

4% increase

Answer

20% decrease

Question 2

Slope of horizontal line:

Accepted Answer

0 — 0.

Answer

1

Answer

∞

Answer

-1

Question 3

Eye : See :: Ear : ?

Accepted Answer

Hear — Eye → see, Ear → hear.

Answer

Listen

Answer

Sound

Answer

Touch

Question 4

Ratio of present ages A:B = 3:5. After 5 years 2:3. A's present age:

Accepted Answer

15 — 3x+5 : 5x+5 = 2:3. 9x+15 = 10x+10. x=5. A=15.

Answer

10

Answer

12

Answer

20

Question 5

Simplify: 3a + 5a − 2a:

Accepted Answer

6a — 3a + 5a − 2a = 6a (combine like terms).

Answer

4a

Answer

8a

Answer

10a

Question 6

The area of a parallelogram with base 12 cm and height 8 cm is:

Accepted Answer

96 cm² — Area = base × height = 12 × 8 = 96 cm².

Answer

48 cm²

Answer

72 cm²

Answer

192 cm²

Question 7

If x²+ 5x + 6 = 0, product of roots is:

Accepted Answer

6 — Product = c/a = 6/1 = 6. (Roots are 2 and 3 → 2·3 = 6.)

Answer

5

Answer

−5

Answer

−6

Question 8

If x, y, z are in AP, then y is called the:

Accepted Answer

Arithmetic mean — y = (x+z)/2 — arithmetic mean of x and z when in AP.

Answer

Geometric mean

Answer

Median

Answer

Mode

Question 9

The area of a rhombus with diagonals d₁ and d₂ is:

Accepted Answer

(1/2)d₁·d₂ — Rhombus area = ½ × product of diagonals.

Answer

d₁·d₂

Answer

(1/4)d₁·d₂

Answer

(d₁+d₂)²

Question 10

Speed 72 km/h = ___ m/s:

Accepted Answer

20 — 72 × 5/18 = 20 m/s.

Answer

10

Answer

15

Answer

25

Question 11

HCF of 48 and 72 is:

Accepted Answer

24 — 48 = 2⁴·3; 72 = 2³·3²; HCF = 2³·3 = 24.

Answer

8

Answer

12

Answer

16

Question 12

2, 5, 10, 17, 26, ?

Accepted Answer

37 — n²+1: 1,4,9,16,25,36 → +1 each. 36+1 = 37.

Answer

35

Answer

40

Answer

38

Question 13

Kiran walked 78 meters towards North. Then turned left and walked 35 meters. Then turned left, walked 30 meters; turned right and walked 5 meters. Next, turned left and walked 48 meters and stopped. How far and in which direction is Kiran from his starting point?

Accepted Answer

40 meters, West — Net displacement: Net East-West = -35-5 = -40 (West). Net North-South = 78-30-48 = 0. So 40 meters West.

Answer

12 meters, North

Answer

70 meters, East

Answer

78 meters, East

Question 14

The area of a triangle is 216 cm² and its sides are in the ratio 3:4:5. The perimeter of the triangle is:

Accepted Answer

72 cm — 3-4-5 right triangle. Sides 3k, 4k, 5k. Area = (1/2)(3k)(4k) = 6k² = 216 → k²=36 → k=6. Perimeter = 12k = 72 cm.

Answer

60 cm

Answer

100 cm

Answer

56 cm

Question 15

Number of permutations of word 'MATHS':

Accepted Answer

120 — 5 distinct letters → 5! = 120. With repetition, divide by factorial of repeat counts.

Answer

24

Answer

720

Answer

60

Question 16

A train 120 m long passes a pole in 6 seconds. Its speed is:

Accepted Answer

72 km/h — Speed = 120/6 = 20 m/s = 20 × 18/5 = 72 km/h.

Answer

36 km/h

Answer

54 km/h

Answer

60 km/h

Question 17

Area of a triangle using Heron's formula requires:

Accepted Answer

All three sides (a, b, c) — Heron: A = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2.

Answer

Only base

Answer

Two sides

Answer

Angles

Question 18

Prob of even on dice:

Accepted Answer

1/2 — 3 out of 6 = 1/2.

Answer

1/3

Answer

1/6

Answer

2/3

Question 19

LCM × HCF of two numbers equals:

Accepted Answer

Product of numbers — For any two positive integers, LCM(a,b) × HCF(a,b) = a × b.

Answer

Sum

Answer

Difference

Answer

Quotient

Question 20

Factorise: x² − 9:

Accepted Answer

(x−3)(x+3) — Difference of squares: a² − b² = (a−b)(a+b).

Answer

(x−9)(x+9)

Answer

(x−3)²

Answer

(x+3)²

Question 21

Cube of 11:

Accepted Answer

1331 — 11³=1331.

Answer

1221

Answer

1100

Answer

1210

Question 22

If PROSE is coded as PPOQE, how is LIGHT coded?

Accepted Answer

LGGFT — Pattern: each letter shifted by -2 except first and last unchanged. P-P, R-2=P, O-O, S-2=Q, E-E. Apply to LIGHT: L,I-2=G,G,H-2=F,T → LGGFT.

Answer

LIGFT

Answer

JIEHR

Answer

LLGFE

Question 23

Lengths of two tangents drawn from an external point to a circle are:

Accepted Answer

Equal — Tangents from an external point are equal in length.

Answer

Unequal

Answer

Random

Answer

Always 0

Question 24

Area of parallelogram:

Accepted Answer

base×height — bh.

Answer

(1/2)bh

Answer

b+h

Answer

s²

Question 25

In trigonometry, sin²θ + cos²θ =

Accepted Answer

1 — Fundamental Pythagorean identity.

Answer

0

Answer

2

Answer

tan²θ

Mental Ability — Pack 02