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

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

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

int_0^oo (xlogx)/(1+x^2)^2dx= (A) e (B) 1 (C) 0 (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

If A and B are square matices of the same order such that A^2=A,B^2=B,AB=BA=0 then (A) AB^2=0 (B) (A+B)^2=A+B (C) (A-B)^2=A+B (D) none of these

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

If a, b,c be the sides foi a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal then sin^2 A/2, sin^2, B/2, sin^2 C/2 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is continuous and differentiable at any point, then (A) a=1/2, b=-3/2 (B) a=-1/2, b=3/2 (C) a=1,b=-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