If `f(x)=(ab-b^2-2)x+int_0^x(cos^4theta+sin^4theta)d theta` is a decreasing function of `x` for all `x in R` and `b in R`, b being independent of `x,` then

If f(x)= (ab+b^2+1)x+int_(0)^(x)(cos^4theta+sin^4theta)" d"theta is an incrasing function of x for all x in R and b in R , b being independent of x then

Let f(x) be a funtion defined by f(x)=(ab-a^(2)-2)x-int_(0)^(x)(cos^(4)t+sin^(2)t-2)dt If f(x) is a decreasing function for all x in R and for all a in R where a is independent of x then b belongs to

Let f(x)={b^(2)+(a-1)b-(1)/(4)}x+int_(0)^(x)(sin^(4)theta+cos^(4)theta)d theta If f(x) be a non- decreasing function AA x in R and AA b in R then "a" can belong to

Let f(x)={b^(2)+(a-1)b-(1)/(4)}x+int_(0)^(x)(sin^(4)theta+cos^(4)theta)d theta If f(x) be a non- decreasing function AA x in R and AA b in R then "a" can belong to

If f(x)=int_0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 then :

If f(x)=int_(0)^((pi)/(2))(ln(1+x sin^(2)theta))/(sin^(2)theta)d theta,x>=0 then :

If x=sin^(16)theta+cos^(20)theta, then for all theta in R

8sin theta cos theta cos2 theta cos4 theta=sin x the x=

8sin theta cos theta cos2 theta cos4 theta=sin x rArr x=

8sin theta cos theta*cos2 theta cos4 theta=sin x rArr x=