If `2^(2x-1)+4^x=2^(x-1/2)+2^(x+1/2)`, then `x` equals
a. `1/2`
b. `2/3`
c. `1`
d. `3/2`

If y = tan^(-1) ((2x-1)/(1+ x- x^2) ) , then (dy)/(dx) at x = 1 is equal to a) 1/2 b) 2/3 c) 1 d) 3/2

If g(x) = x^2 +x -2 and 1/2 (gof) (x) = 2x^2 - 5x +2 , then f(x) is equal to a) 2x -3 b) 2x+3 c) 2x^2 +3x +1 d) 2x^2 -3x -1

If x/((2x-1)(x+2)(x-3))=A+B/(2x-1)+C/(x+2)+D/(x-3) then A=

If (x-2)/3=(2x-1)/3-1, then x= (a) 2 (b) 4 (c) 6 (d) 8

If 8^(x) = (4)/(2^(x)) then find x A)1 B)2 C) (1)/(2) D) (2)/(3)

If A= [(2x,0),(x,x)] and A^(-1)= [(1,0),(-1,2)] , then x=a)2 b) (1)/(2) c)1 d)3

If f(x)=(1+x)(3+x^(2))^(1/2)(9+x^(3))^(1/3) then f'(-1) is equal to 0( b) 2sqrt(2)(c)4(d)6

If x^2+y^2=t -1/t and x^4+y^4=t^2+1/t^2 then (dy)/ (dx) is equal to a) 1/(x^2y^3) b) 1/(xy^3) c) 1/(x^2y^2) d) 1/(x^3y)

If y=tan^(-1)((4x)/(1+5x^(2)))+tan^(-1)((2+3x)/(3-2x)) , then (dy)/(dx) is equal to a) (5)/(1+25x^(2)) b) (1)/(1+25x^(2)) c)0 d) (5)/(1-25x^(2))

If int(2x^2+3)/((x^2-1)(x^2+4))dx=alog((x-1)/(x+1))+btan^(- 1) (x/2)+C then the values of a and b are respectively (A) 1/2,1/2 (B) 1,1 (C) 1/2,1 (D) None