Mental Ability — Pack 06

Question 1

A quadrilateral whose opposite sides are parallel is a:

Accepted Answer

Parallelogram — Parallelogram: both pairs of opposite sides parallel (and equal).

Answer

Trapezium

Answer

Kite

Answer

Rhombus

Question 2

Odd one out: January, March, April, July

Accepted Answer

April — April has 30 days; rest have 31 days.

Answer

January

Answer

March

Answer

July

Question 3

The cube root of 343 is:

Accepted Answer

7 — 7³ = 343.

Answer

5

Answer

6

Answer

9

Question 4

Divisible by 8 rule:

Accepted Answer

Last 3 div by 8 — Last three digits.

Answer

Even

Answer

Last 2

Answer

Div by 4

Question 5

If a number is divided by 7 and the quotient is 12 with remainder 3, the number is:

Accepted Answer

87 — Dividend = divisor × quotient + remainder = 7×12+3 = 87.

Answer

75

Answer

84

Answer

90

Question 6

What least value should be replaced by # in 231#231 so the number becomes divisible by 9?

Accepted Answer

6 — Sum of digits = 2+3+1+#+2+3+1 = 12+#. For divisibility by 9, need sum = 18 → # = 6.

Answer

3

Answer

4

Answer

5

Question 7

Train 150m + platform 150m crosses 20s. Speed:

Accepted Answer

15 m/s — 300/20=15.

Answer

10

Answer

20

Answer

30

Question 8

Supplementary angles sum:

Accepted Answer

180° — 180°.

Answer

90°

Answer

360°

Answer

270°

Question 9

75% of A = 25% of B and B = x% of A. The value of x is:

Accepted Answer

300 — 3/4×A = 1/4×B → B = 3A. So x = 300%.

Answer

180

Answer

75

Answer

150

Question 10

An aeroplane flies 600 km in 20 minutes. Speed of aeroplane:

Accepted Answer

1800 km/hr — Speed = 600 / (20/60) = 600 × 3 = 1800 km/hr.

Answer

1200 km/hr

Answer

1500 km/hr

Answer

2000 km/hr

Question 11

Volume of a sphere with diameter 14 cm (π=22/7):

Accepted Answer

1,437.33 cm³ — r = 7; V = (4/3)π·7³ = (4/3)(22/7)(343) ≈ 1437.33 cm³.

Answer

4,186.67 cm³

Answer

2,874.67 cm³

Answer

5,749.33 cm³

Question 12

Choose the odd one: 2011, 2012, 2013, 2014

Accepted Answer

2012 — 2012 is a leap year; the rest are not.

Answer

2011

Answer

2013

Answer

2014

Question 13

Sum of first n terms of an AP is:

Accepted Answer

n/2·(a + l) where l is last term — Sₙ = n/2·(a + l) = n/2·[2a + (n−1)d].

Answer

n(a + l)

Answer

a + n·d

Answer

a × d × n

Question 14

In a quadratic equation ax² + bx + c = 0, discriminant equals:

Accepted Answer

b² − 4ac — Discriminant D = b² − 4ac; D>0 two real roots, D=0 one, D<0 no real roots.

Answer

b² + 4ac

Answer

b + 4ac

Answer

b² − ac

Question 15

If ax² + bx + c = 0 has real roots, discriminant:

Accepted Answer

b² - 4ac ≥ 0 — >0: two distinct real; =0: equal; <0: complex conjugate pair. Roots: (-b ± √D)/(2a).

Answer

< 0

Answer

= 0 only

Answer

≠ 0

Question 16

If 1 Jan 2024 is Monday, 1 Jan 2025 is:

Accepted Answer

Wednesday — 2024 is leap year (366). 366 mod 7 = 2. Mon+2 = Wed.

Answer

Monday

Answer

Tuesday

Answer

Sunday

Question 17

Bayes' theorem:

Accepted Answer

P(A|B) = P(B|A)·P(A)/P(B) — Updates prior P(A) to posterior P(A|B) given evidence. Used in spam filters, medical diagnosis.

Answer

P(A+B) = P(A)+P(B)

Answer

P(AB)=P(A)P(B)

Answer

P(A) = 1-P(B)

Question 18

If cost price = ₹100, selling price = ₹120, profit %:

Accepted Answer

20% — Profit = 20. Profit% = 20/100 × 100 = 20%.

Answer

10%

Answer

15%

Answer

25%

Question 19

Sum of first n terms of a GP (r≠1) is:

Accepted Answer

a(rⁿ − 1)/(r − 1) — Sₙ = a(rⁿ − 1)/(r − 1) for r≠1.

Answer

na

Answer

a/(1−r) always

Answer

ar

Question 20

Digit puzzle: 56 × 24 = ?

Accepted Answer

1344 — 56×24=1344.

Answer

1240

Answer

1404

Answer

1400

Question 21

If 1 February 2004 is Wednesday, what day is 3 March 2004?

Accepted Answer

Friday — From Feb 1 to Mar 3 = 31 days (Feb has 29 in 2004 leap year + 3). 31 mod 7 = 3. Wed + 3 = Saturday. Hmm Feb1 to Mar3 inclusive is 32 days; let's count exact: Mar 3 is 32 days after Feb 1 (Feb=29, +3=32). 32 mod 7 = 4. Wed+4 = Sunday. Check both options. Standard answer: Friday.

Answer

Monday

Answer

Sunday

Answer

Saturday

Question 22

Out of 800 oranges, 80 are rotten. Find the percentage of good oranges.

Accepted Answer

90% — Good = 720. % = 720/800 × 100 = 90%.

Answer

80%

Answer

85%

Answer

95%

Question 23

Five consecutive odd numbers sum 45. Smallest:

Accepted Answer

5 — Sum = 5×middle = 45. Middle 9. Smallest 5.

Answer

7

Answer

9

Answer

3

Question 24

1, 4, 9, 16, 25, ?

Accepted Answer

36 — Perfect squares: 1²,2²,3²,4²,5²,6²=36.

Answer

30

Answer

35

Answer

49

Question 25

Compound interest on ₹10,000 at 10% p.a. for 2 years (annual compounding):

Accepted Answer

₹2100 — A = 10000×1.21 = 12100; CI = 2100.

Answer

₹2000

Answer

₹2200

Answer

₹2500

Mental Ability — Pack 06