`prod_(i=1)^89 tan i^@=`
(a) 0
(b) 1
(c) `oo`
(d) none of these

tan^(-1)(1/(11))+tan^(-1)(2/(11)) is equal to (a) 0 (b) 1//2 (c) -1 (d) none of these

If sum_(i=1)^10 sin^-1 x_i = 5pi then sum_(i=1)^10 x_i^2 = (A) 0 (B) 5 (C) 10 (D) none of these

The smallest positive integer n for which ((1+i)/(1-i))^n=1 is (a) 8 (b) 16 (c) 12 (d) None of these

Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these

If A=[[1, 2, x], [0 ,1 ,0],[ 0, 0, 1]] and B=[[1,-2,y],[0, 1, 0 ],[0, 0, 1]] and A B=I_3 , then x+y equals (a) 0 (b) -1 (c) 2 (d) none of these

The value of lim_(x->0)(sqrt(1/2(1-cos2x)))/x i s (a)1 (b) -1 (c) 0 (d) none of these

The value of tan1otan2otan3oddottan89o is (a) 1 (b) -1 (c) 0 (d) None of these

If for the matrix A ,\ A^3=I , then A^(-1)= (a) A^2 (b) A^3 (c) A (d) none of these

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these

The smallest natural number is (a) 0 (b) 1 (c) -1 (d) None of these