If `P(0,1,2),\ Q(4,-2,1)a n d\ O(0,0,0)` are three points then `angle P O Q=` a. `pi/6` b. `pi/4` c. `pi/3` d. `pi/2`

The amplitude of 1/i is equal to a. 0 b. pi/2 c. -pi/2 d. pi

int_0^(pi//2)xsinx\ dx is equal to a. pi//2 b. pi//4 c. pi d. 1

If tanA=a/(a+1) and tanB=1/(2a+1) then the value of A+B is: (a). 0 (b). pi/2 (c). pi/3 (d). pi/4

Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec axx vec b)xx( vec cxx vec d)=0. Let P_1a n dP_2 be planes determined by the pair of vectors vec a , vec b ,a n d vec c , vec d , respectively. Then the angle between P_1a n dP_2 is a. 0 b. pi//4 c. pi//3 d. pi//2

If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2pi , then theta is a. pi \ b. pi/2 \ c. pi/3 \ d. pi/6

The value of int_0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi//8

If int_0^a1/(1+4x^2)dx=\ pi/8 , then a equals a. pi/2 b. pi/4 c. 1/2 d. 1

The amplitude of 1/i is equal to 0 b. pi/2 c. -pi/2 d. pi

int_0^(pi//2)sin2xlogtanx\ dx\ is equal to a. pi//2 b. pi c. 0 d. 2pi

P and Q are points on the ellipse x^2/a^2+y^2/b^2 =1 whose center is C . The eccentric angles of P and Q differ by a right angle. If /_PCQ minimum, the eccentric angle of P can be (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/12