Q. What is the number of signals that can be sent by 6 flags of different colours taking one or more at a time?
1) 21
2) 63
3) 720
4) 1956
Q. What is the area bounded by the curve y = x2 and the line y = 16?
1) 32/3
2) 64/3
3) 256/3
4) 128/3
Q. From the top of a lighthouse 120 m above the sea, the angle of depression of a boat is 15°. What is the distance of the boat from the lighthouse?
1) 400 m
2) 421 m
3) 444 m
4) 460 m
Q. What is the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points?
1) 2
2) 4
3) 6
4) 12
Q. If ω is a complex cube root of unity, then what is ω10 + ω-10equal to ?
1) 2
2) -1
3) -2
4) 1
Q. If the equations x2 + kx + 64 = 0 and x2 - 8x + k = 0 have real roots, then what is the value of k?
1) 4
2) 8
3) 12
4) 16
Q. What is the value of sin15° sin75°?
1) 1/4
2) 1/8
3) 1/16
4) 1
Q. If y = sec2 θ + cos2 θ, where 0 < θ < π/2, then which one of the following is correct?
1) y = 0
2) 0≤ y ≤ 2
3) y ≥ 2
4) None of the above
Q. If α and β are positive angles such α + β = π/4, then what is (1 + tan α) (1 + tan β) equal to?
1) 0
2) 1
3) 2
4) 3
Q. Two poles are 10m and 20m high. The line joining their tops makes an angle of 15° with the horizontal. What is the approximate distance between the poles?
1) 35.3 m
2) 37.3 m
3) 41 m
4) 44 m
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