If `(sinalpha)x^2-2x+bgeq2,` for all real values of `xlt=1a n dalpha in (0,pi/2)uu(pi//2,pi),` then possible real value of `b` is /are `a2` b. `3` c. `4` d. `5`

The maximum value of 1+sin((pi)/(4) +theta) +2cos((pi)/(4) - theta) for all real values of theta is :

If the equation x^(2)+4+3sin(ax+b)-2x=0 has at least one real solution, where a,b in [0,2pi] then one possible value of (a+b) can be equal to

The value of the integral int_(pi//2)^(pi//2)(x^2ln(pi+x)/(pi-x))cosx\ dx is a. 0 b. (pi^2)/2-4 c. (pi^2)/2+4 d. (pi^2)/2

If (x^(2)+ax+3)/(x^(2)+x+a) takes all real values for possible real values of x, then a.4a^(2)+39 0 c.a>=(1)/(4) d.a<(1)/(4)

If a.3^(tan x)+a*3^(-tan x)-2=0 has real solutions,x!=(pi)/(2),0<=x<=pi, then find the set of all possible values of parameter 'a'.

If cos(x+pi/3)+cos x=a has real solutions, then (a) number of integral values of a are 3 (b) sum of number of integral values of a is 0 (c) when a=1 , number of solutions for x in [0,2pi] are 3 (d) when a=1, number of solutions for x in [0,2pi] are 2

The value of int_(pi//2)^(pi//2)(x^3+x\ cos x+tan^5x+1)dx , is 2 b. pi c. 0 d. 1

The value of (lim)_(x->pi/2)(int t\ dt)/(sin(2x-pi)) integral from pi/2 to x is oo b. pi/2 c. pi/4 d. pi/8