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Q:

If tan x = 1, 0 < x < 90, then what is the value of 2 sin x cos x?

A) 1/2	B) 1
C) √3/2	D) √3

Answer & Explanation Answer: B) 1

Explanation:

tan x = 1

then x = 45

2sin x. cos x = 2× 1/√2 x 1/√2 = 1

an x = 1

then

x = 45

o

2sin x. cos x =

2

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

For the inequation x^2–7x + 12 > 0, which one of the following is correct ?

A) 3 < x < 4	B) –∞ < x < 3 only
C) 4 < x < ∞ only	D) –∞ < x < 3 or 4 < x < ∞

Answer & Explanation Answer: D) –∞ < x < 3 or 4 < x < ∞

Explanation:

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Filed Under: Simplification
Exam Prep: Bank Exams

Q:

If p and q are the roots of the equation x2 –15x + r = 0 and p –q = 1, then what is the value of r ?

A) 55	B) 56
C) 60	D) 64

Answer & Explanation Answer: B) 56

Explanation:

In the below equation,

x2–15x + r = 0

sum of roots = p + q = -(-15)/1 = 15 (sum of roots for equation ax2+ bx + c is -b/a)

product of roots = pq = r/1 = r (product of roots for equation ax2+ bx + c is c/a)

given p –q = 1

also we know that p+q = 15

subtracting the squares of both

(p+q)2 + (p-q)2 = 15^2–1

p2 + q2 + 2pq –p2 –q2 +2pq = 225 -1

4pq = 224

4r = 224

r = 56

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Q:

If $a^{x} = b^{y} = c^{z}$ and $b^{2} = ac$ , then what is $\frac{1}{x} + \frac{1}{z}$ equal to ?

A) 1/y	B) -1/y
C) 2/y	D) -2/y

Answer & Explanation Answer: C) 2/y

Explanation:

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Filed Under: Simplification
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Q:

What is $\frac{{(x - y)}^{3} + {(y - 2)}^{3} + {(z - x)}^{3}}{3 (x - y) (y - z) (z - x)}$ =?

A) 1	B) 0
C) 1/3	D) 3

Answer & Explanation Answer: A) 1

Explanation:

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Filed Under: Simplification
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Q:

Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?

A) a2π+12	B) a
C) a2π2-1	D) πa/2

Answer & Explanation Answer: C) a2π2-1

Explanation:

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm	B) 2 cm or 14 cm
C) 3 cm or 21 cm	D) 4 cm or 28 cm

Answer & Explanation Answer: B) 2 cm or 14 cm

Explanation:

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

Q:

The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area?

A) 300%	B) 400%
C) 450%	D) 500%

Answer & Explanation Answer: A) 300%

Explanation:

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

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