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)=(ab-b^(2)-2)x+int_(0)^(x)(cos^(4)theta+sin^(4)theta)d theta is a decreasing 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

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

f(x)=[-c^(2)+(b-1)c-2)]x+int(sin^(2)x+cos^(4)x)dx If f(x) be an increasing function of x AA x in R then all possible values of b if (c in R)

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

Let f be a differentiable function AA x in R where f(1)=1&f(3)=4&f'(x)>=1 AA x in R then f(2) can be equal to

Let |f (x)| le sin ^(2) x, AA x in R, then

Let |f (x)| le sin ^(2) x, AA x in R, then

Let f(a)>0, and let f(x) be a non- decreasing continuous function in [a,b]. Then,(1)/(b-a)int_(a)^(b)f(x)dx has the