Sum of roots of the equation `x^4-2x^2sin^2(pix/2)+1=0` is `0` (b) 2 (c) 1 (d) 3

The sum of square of roots of the equation 2x^4+x^2+x+2=0 is :

The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi] is 2 (b) 3 (c) 4 (d) 0

The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi/2 is 2 (b) 3 (c) 1 (d) 0

The sum of real roots of the equation |x-2|^2+|x-2|-2=0 is (A) 4 (B) 1 (C) 2 (D) -2

The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Three (B) Four (C) One (D) Two

The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x is 0 (b) 1 (c) 2 (d) 3

The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=-sqrt(3) is 4 (b) 5 (c) 6 (d) none of these

Let f(x)=x^3-3(a-2)x^2+3ax+7 and f(x) is increasing in (0,1] and decreasing is [1,5) , then roots of the equation (f(x)-14)/((x-1)^2)=0 is (A) 1 (B) 3 (C) 7 (D) -2

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x^2-5x+3)=-3/2 is (a) 4 b. 0 c. 1 d. 2