If `sin^-1 (x+ x^2/2+x^3/4+x^4/8+…) = pi/6,` where `|x|lt2` then the value of x is (A) `2/5` (B) `3/2` (C) `-2/3` (D) `-3/2`

If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) 0 (b) 2 (c) 1 (d) 3

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

If x^2+x+1 is a factor of the polynomial 3x^3+8x^2+8x+3+5k , then the value of k is (a) 0 (b) 2/5 (c) 5/2 (d) -1

If the sum of the zeros of the polynomial f(x)=2x^3-3k x^2+4x-5 is 6 , then the value of k is (a) 2 (b) 4 (c) -2 (d) -4

If the maximum and minimum values of y=(x^2-3x+c)/(x^2+3x+c) are 7 and 1/7 respectively then the value of c is equal to (A) 3 (B) 4 (C) 5 (D) 6

If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a) 3 b. 2 c. 1 d. -2

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n the value of sin^(-1)sin2x is (a) 6-2pi (b) 2pi-6 (c) pi-3 (d) 3-pi

If 2^x - 4^(2x-1) = 0 then x = ? (a) 2/3 (b) -2/3 (c) 3/2 (d) -3/2

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n the value of sin^(-1)2x is 6-2pi (b) 2pi-6 pi-3 (d) 3-pi

If 2x-3/2=5x+3/4, then x= (a) 3/4 (b) -3/4 (c) 4/3 (d) -4/3