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)/(6)+theta)+2cos((pi)/(3)-theta) for real values of theta is

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

If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible values of n is (a)3 (b) 2 (c) 4 (d) 8

If the equation x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)

If (x^2+a x+3)//(x^2+x+a) takes all real values for possible real values of x , then a. 4a^2+39 -0 c. ageq1/4 d. a<1/4

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real values of x and non-real values for non-real values of x , then a=0 b. b=0 c. c=0 d. nothing can be said about a ,b ,cdot

The value of int_(-pi//2)^(pi//2)(x^(2)cosx)/(1+e^(x)) d x is equal to

The value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi

If 0lt=xlt=2pia n d|cosx|lt=sinx , then then (a) set of all values of x is [pi/4,(3pi)/4] (b) the number of solutions that are integral nultiple of pi/4 is one (c) the number of the largest and the smallest solution is pi (d) the set of all values of x is x in [pi/4,pi/2]uu[pi/2,(3pi)/4]