If `n-1C_r=(k^2-3)^nC_(r+1),` then (a) `(-oo,-2]` (b) `[2,oo)` (c) `[-sqrt3, sqrt3]` (d) `(sqrt3,2]`

If cos^-1((x^2 -1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)

Simplify (1)/(sqrt3+sqrt2)+(1)/(sqrt3-sqrt2)

If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)1/x=tan^(-1)1/3, then x is equal to 1 (b) 2 (c) 3 (d) sqrt(2)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The exhaustive set of values of a for which inequation (a -1)x^2- (a+1)x+ a -1>=0 is true AA x >2 (a) (-oo,1) (b)[7/3,oo) (c) [3/7,oo) (d) none of these

Let A B C be a triangle such that /_A C B=pi/6 and let a , ba n dc denote the lengths of the side opposite to A , B ,a n dC respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,a n dc=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) 2+sqrt(3) (d) 4sqrt(3)

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (a) (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r (c) ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

If C_(r ) = (n!)/(r!(n - r)!) , then prove that sqrt(C_(1)) + sqrt(C_(2)) + …. + sqrt(C_(n)) sqrt(n(2^(n) - 1))

Which of the following is not the solution of (log)_3(x^2-2)<(log)_3(3/2|x|-1) is (a) (sqrt(2),2) (b) (-2,-sqrt(2)) (c) (-sqrt(2),2 (d) none of these