Common Admission Test (CAT) Questions and Answers with Explanation

Q:

The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is

A) 20	B) 25
C) 30	D) 35

Answer & Explanation Answer: C) 30

Explanation:

Let breadth = x m

Then, length = (x+5)m

Area of a rectangle = Length x Breadth

x(x+5) = 750

x² + 5x - 750= 0

(x+30)(x-25)= 0

x = 25 or x = -30

Hence, breadth x = 25m

=> Length = x + 5 = 25 + 5 = 30m.

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Q:

If $a^{2} = 12, t h e n a^{4} = ?$

A) 144	B) 72
C) 36	D) 24

Answer & Explanation Answer: A) 144

Explanation:

Given a x a = 12

asked to find a x a x a x a = (a x a) x (a x a)

a⁴ = a² x a²

= 12 x 12

= 144.

More :: Mathematical operations questions and answers.

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Q:

Hydrogen bomb is based on the principle of

A) nuclear fission	B) nuclear fusion
C) natural radioactivity	D) artificial radioactivity

Answer & Explanation Answer: B) nuclear fusion

Explanation:

Hydrogen Bomb is based on the principle of Nuclear Fusion.

Hydrogen_bomb_is_based_on_the_principle_of1552385714.jpg image

Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles.

The difference in mass between the reactants and products is manifested as either the release or absorption of energy.

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Q:

Find the area of the rectangle or square with the given dimensions L = 5 inches, W= 3 inches?

A) 13	B) 14
C) 15	D) 16

Answer & Explanation Answer: C) 15

Explanation:

We know that,

Area of rectangle A = L x W = 5 x 3 = 15 sq.inches.

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Q:

Find the perimeter of the rectangle or square with the given dimensions l = 5 feet, w = 2 feet?

A) 11ft	B) 13ft
C) 14ft	D) 15ft

Answer & Explanation Answer: C) 14ft

Explanation:

We know that,

Perimeter of rectangle = 2(L+W) = 2(5 + 2) = 2 (7) = 14 fts.

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Q:

A sector of 120, cut out from a circle, has an area of $\frac{66}{7} c m^{2}$ . Find the radius of the circle ?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Let the radius of the circle be r cm. Then,

$\frac{120}{360} {πr}^{2} = \frac{66}{7}$

$r^{2} = \frac{66}{7} * \frac{7}{22} * 3$

r=3.

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Q:

Two concentric circles form a ring. The inner and outer circumferences of ring are $\frac{518}{7}$ m and $\frac{352}{7}$ m respectively. Find the width of the ring.

A) 4	B) 5
C) 6	D) 7

Answer & Explanation Answer: A) 4

Explanation:

Let the inner and outer radii be r and R metres.

Then $2 πR = \frac{352}{7} = > R = \frac{352}{7} * \frac{7}{22} * \frac{1}{2} = 8 m$

$2 πR = \frac{528}{7} = > R = \frac{528}{7} * \frac{7}{22} * \frac{1}{2} = 12 m$

=> Width of the ring = (R - r) = (12 - 8) m = 4 m.

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Q:

Find the length of the altitude of an equilateral triangle of side $3 \sqrt{3}$ cm.

A) 4.5	B) 3.5
C) 2.5	D) 6.5

Answer & Explanation Answer: A) 4.5

Explanation:

Let the length of the altitude be h.
Then, h = $a \frac{\sqrt{3}}{2}$ = $3 \sqrt{3} \times \frac{\sqrt{3}}{2}$ = 4.5

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