The equation `int_0^x (t^2-8t+13)dt=xsin(a/x)` has a solution if `sin(a/6)` is
(A) zero (B) `-1` (C) `1` (D) none of these

The number of solution of equation |x-1|=e^x is (A) 0 (B) 1 (C) 2 (D) none of these

The number of solution of equation |x-1|= e^x is (A) 0 (B) 1 (C) 2 (D) none of these

Cosider the equation int_(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) If x takes the values for which the equation has a solution, then the number of values of a in [0, 100] is

If f(x)=int_0^sinx cos^-1t dt+int_0^cosx sin^-1t dt, 0ltxltpi/2 , then f(pi/4)= (A) 0 (B) pi/sqrt(2) (C) 1 (D) none of these

If f(x)=1+1/x int_1^x f(t)dt , then the value of f(e^(-1)) is (a) 1 (b) 0 (c) -1 (d) none of these

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these

Cosider the equation int_(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) The number of real values of x for which the equation has solution is

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these