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

If S_n=1^2-2^2+3^2-4^2+5^2-6^2+...... ,t h e n

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

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (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

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dxi s 0 (b) log 7 (c) 5 log 13 (d) none of these

Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal to a. 3 b. 6/5 c. 3/2 d. none of these

T h ev a l u eofint_1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi s (a) pi/8(log)_e2 (b) pi/2(log)_e2 (c) -pi/2(log)_e2 (d) none of these

If (log)_(10)5=aa n d(log)_(10)3=b ,t h e n (A) (log)_(30)8=(3(1-a))/(b+1) (B) (log)_(40)15=(a+b)/(3-2a) (C) (log)_(243)32=(1-a)/b (d) none of these

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3-(log)_3 2 log(3/2) (d) none of these