Let `A=sinx+tanx` and `B=2x` in the interval `0ltxltpi/2` then (A) `AgtB` (B) `A=B` (C) `AltB` (D) none of these

Let a=int_0^(pi/2) sinx/xdx , then (A) 0ltalt1 (B) agt2 (C) 1ltaltpi/2 (D) none of these

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

The number of solutions of the equation tanx.tan4x=1 for 0ltxltpi is (A) 2 (B) 4 (C) 6 (D) none of these

If a!=0 and log_x (a^2+1)lt0 then x lies in the interval (A) (0,oo) (B) (0,1) (C) (0,a) (D) none of these

Let [x] denote the greatest integer less than or equal to x , then int_0^(pi/4) sinx d(x-[x])= (A) 1/2 (B) 1-1/sqrt(2) (C) 1 (D) none of these

The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (0,1/e) (d) none of these

For the equation |x^2|+|x|-6=0 , the sum of the real roots is (a) 1 (b) 0 (c) 2 (d) none of these

If x lies in the interval [0,\ 1] , then the least value of x^2+x+1 is (a) 3 (b) 3//4 (c) 1 (d) none of these

Let a= cos((2pi)/7)+i sin((2pi)/7), A=a+a^2+a^4 and B=a^3+a^5+a^6, then A and B are the roots of the equation (A) x^2-x+2=0 (B) x^2-x-2=0 (C) x^2+x+2=0 (D) none of these

If [x] denotes the integral part of x and a=int_(-1)^0 (sin^2x)/([x/pi]+1/2)dx, b=int_0^1 (sin^2x)/([x/pi]+1/2)d (x-[x]) , then (A) a=b (B) a=-b (C) a=2b (D) none of these