Let `f(x)=(1+b^2)x^2+2b x+1` and let `m(b)` the minimum value of `f(x)dot` As `b` varies, the range of `m(b)` is `[0,1]` (b) `(0,1/2]` `[1/2,1]` (d) `(0,1]`

Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1] (B) (0,1/2] (C) [1/2,1] (D) (0,1]

The minimum value of e^(2x^2-2x+1)sin^2x is e (b) 1/e (c) 1 (d) 0

Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0 . Then the minimum value of ("det.(A)")/(b) is

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

Let A={1, 2, 3, 4} and B=N , Let f:A to B be defined by f(x)=x^(3) then, Find the range of f.

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (-1, e) (b) (1, e) (-e ,-1) (d) (-e ,1)

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

Let f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1 Find the values of b for which f(x) has the greatest value at x=1.

Let f: R to R be defined by f(x)=(x)/(1+x^(2)), x in R. Then, the range of f is (A) [-(1)/(2),(1)/(2)] (B) (-1,1)-{0} (C) R-[-(1)/(2),(1)/(2)] (D) R-[-1,1]

Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these