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Q:

If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

A) 3√2 B) 3/√2
C) 1/√2 D) √2
 
Answer & Explanation Answer: D) √2

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Filed Under: Simplification
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Q:

What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?

A) tan 2θ B) cot 2θ
C) cot θ D) cot 3θ
 
Answer & Explanation Answer: B) cot 2θ

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Q:

What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?

A) 0 B) tan2x
C) 1 D) 2 tan x
 
Answer & Explanation Answer: B) tan2x

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Q:

What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]?

A) cos x sin y B) (sin y)/(sin x)
C) sin z D) sin x tan y
 
Answer & Explanation Answer: B) (sin y)/(sin x)

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Q:

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

A) 493 B) 7
C) 14 D) 983
 
Answer & Explanation Answer: B) 7

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Q:

A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm2) of each part?

A) 96 + 64√2 B) 80 + 64√2
C) 96 + 48√2 D) 80 + 48√2
 
Answer & Explanation Answer: A) 96 + 64√2

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Q:

A hemisphere is kept on top of a cube. Its front view is shown in the given figure. The total weight of the figure is 21 cm. The ratio of curved surface area of hemisphere and total surface area of cube is 11 : 42. What is the total volume (in cub.cm) of figure?

A) 3318.33 B) 3462.67
C) 3154.67 D) 3248.33
 
Answer & Explanation Answer: B) 3462.67

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Q:

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A) 31276 B) 36194
C) 25182 D) 33264
 
Answer & Explanation Answer: D) 33264

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