If `S={x in N :2+(log)_2sqrt(x+1)>1-(log)_(1/2)sqrt(4-x^2)}` , then (a)`S={1}` (b) `S=Z` (d) `S=N` (d) none of these

Solve log_(5)sqrt(7x-4)-1/2=log_5sqrt(x+2)

Solve log_(2)(2sqrt(17-2x))=1 - log_(1//2)(x-1) .

Solve: 1/4x^(log_2sqrt(x))=(2. x^((log)_2x))^(1/4)

The value of lim_(x->0)(sqrt(1/2(1-cos2x)))/x i s (a)1 (b) -1 (c) 0 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If S=(1/2)^2+((1/2)^2 1)/3+((1/2)^3 1)/4+((1/2)^4 1)/5+...... ,t h e n (a) S=ln8-2 (b) S=ln(4/e) (c) S=ln4+1 (d) none of these

Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" (a)4 (b) log 8 (c) log 4 (d) none of these

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

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these