The function f(x) = tan^-1 (sinx + cosx) is an increasing function in

• (π/4, π /2)

• (–π/2, π /4)

• (0, π /2)

• (0, π /2)

Let A =    If |A²| = 25, then |α| equals

• 5²

• 1

• 1/5

• 1/5

Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true ?

• f(x) ≥ 1 for all x ∈ R

• f(x) is not differentiable at x = 1

• f(x) is differentiable everywhere

• f(x) is differentiable everywhere

The function f: R ~ {0} → R given by

can be made continuous at x = 0 by defining f(0) as

• 2

• -1

• 1

• 1

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

• 1/729

• 8/9

• 8/729

• 8/729

Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle α with the positive x-axis, then cos α equals-

• 

• 1/2

• 1

• 1

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of the 3 N force were reversed, the resultant would be N. The value of P is

• 5N

• 6N

• 4N

• 4N

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

• 0.06

• 0.14

• 0.2

• 0.2

If a line makes an angle of π/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

• π/6

• π/3

• π/4

• π/4

30.

If are unit vectors and θ is the acute angle between them, then  is a unit vector for 

• Exactly two values of θ

• More than two values of θ

• No value of θ

• No value of θ