Aptitude and Reasoning Questions

Q:

If (1/cos θ) – (1/cot θ) = 1/P, then what is the value of cos θ?

A) (P + 1)/(P – 1) B)  (P2+ 1)/2P
C) 2(P2+ 1)/P D)  2P/(P2+ 1)
 
Answer & Explanation Answer: D)  2P/(P2+ 1)

Explanation:
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Q:

If cot A = n/(n + 1) and cot B = 1/(2n + 1), then what is the value of cot (A + B)?

A) -1 B) 0
C) 1 D) 2
 
Answer & Explanation Answer: A) -1

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Q:

What approximate value should come in place of the question mark (?) in the following equation (Note: You are not expected to calculate the exact value)?

[(7.99)2–(13.001)2+(4.01)3]2=?

A) -1800 B) 1450
C) -1660 D) 1660
 
Answer & Explanation Answer: D) 1660

Explanation:

[(7.99)^2–(13.001)^2+(4.01)^3]^2= X X= [8^2-13^2+4^3]^2 X= [64-169+64]^2 X= [-41]^2 X=1681

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Q:

In a triangle PQR, ∠Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circum circle of the triangle?

A) 5 B) 6
C) 6.5 D) 6√2
 
Answer & Explanation Answer: C) 6.5

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Q:

P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle?

A) 1.5 B) 2
C) 2.5 D) 3
 
Answer & Explanation Answer: C) 2.5

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Q:

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A) 12/π+4 B) 6/π+4
C) 3/π+4 D) 6/π+2√2
 
Answer & Explanation Answer: B) 6/π+4

Explanation:
As it is clear that 2r = a where a is the side of the square and
R is the radius of circle
It is given that 2πr + 4a = 12
a = 12/(π+4)
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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 < ∞

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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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