4.If `|x|=1`then x is
(a) {1} (b) {-1} (c) {-1,1} (d) {-1,-1}

If tan^(-1)(x+1)/(x-1)+tan^(-1)(x-1)/x=tan^(-1)(-7) , then the value of x is (a) 0 (b) -2 (c) 1 (d) 2

The solution set of the equation sin^(-1)sqrt(1-x^(2))+cos^(-1)x=(cot^(-1)(sqrt(1-x^(2))))/(x)-sin^(-1)x is (a) [-1,1]-{0}(b)(0,1)uu{-1}(c)(-1,0)uu{1} (d) [-1,1]

If y = sin^(-1) x then x belongs to the interval: (a) (0,pi) (b) (-1,1) (c) [-1,1] (d) [0,pi]

If (x+(1)/(x))=2, then (x-(1)/(x)) is equal to (a) 0 (b) 1 (c) 2 (d) 5

If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is independent of ' x ' then (a)x in (-1,1) (b) x in (-oo,-1) (c)x in [1,oo) (d) x in (0,1)

If f(x)=|\(1,x,x+1),(2x,x(x-1),(x+1)x,3x(x-1),x(x-1)(x-2),(x+1)x(x-1))| then f(100) is equal to (A) 0 (B) 1 (C) 100 (D) -100

The roots of the equation |[1,1,1],[a,x,a],[b,b,x]|=0 are (a) 1,1, (b) 1,a (c) 1,b, (d) a,b

Let f(x)={ax^(2)+1,x>1x+(1)/(2),x<=1. then ,f(x) is derivable at x=1, if a=2( b) a=1( c) a=0 (d) a=(1)/(2)

The derivative of y=(1-x)(2-x)...(n-x) at x=1 is (a) 0( b) (-1)(n-1)!(c)n!-1(d)(-1)^(n-1)(n-1)!

If (x-1)/(x)=3, then the value of 1+(1)/(x^(2)) is (a) 9(b) 10(c)11 (d) None of these