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`

Find the maximum value of 1+sin(pi/4+theta)+2cos(pi/4-theta) for all real values of theta

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

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2

If (x^2+a x+3)/(x^2+x+a) takes all real values for possible real values of x , then a. a^3-9a+12<=0 b. 4a^3+39 < 0 c. ageq1/4 d. a<1/4

The number of real values of x satisfying tan^-1(x/(1-x^2))+tan^-1 (1/x^3) = (3pi)/(4)

If x is real and (x^2+2x+c)/(x^2+4x+3c) can take all real values, of then show that 0lt=clt=1.

If (3-tan^2(pi/7))/(1-tan^2(pi/7))=kcos(pi/7) then the value of k is (a)1 (b) 2 (c) 3 (d) 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

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(pi)/2 (b) (pi)/2-11 (c) (5pi)/2-11 (d) none of these

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