Mathematics Tes...

If f(x) is a function whose domain is symmetric about the origin, then f(x) + f(–x) is

If \(f(9)=9, f^{\prime}(9)=4,\) then \(\lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}\) equals

If \(f(x)=\sqrt{x}, g(x)=e^{x-1},\) and \(\int f o g(x) d x=A f o g(x)+B t a n^{-1}(f o g(x))+C,\) then

\(A+B\) is equal to

If \(x=\sin \left(2 \tan ^{-1} 2\right), y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)\) then

In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is

\(\lim _{x \rightarrow-\infty}\left\{\frac{x^{4} \sin \left(\frac{1}{x}\right)+x^{2}}{1+|x|^{3}}\right\}\) is equal to

The distance moved by the particle in time \(t\) is given by \(x=t^{3}-12 t^{2}+6 t+8 .\) At

the instant when its acceleration is zero, then the velocity is

The value of \(\sin \left[2 \tan ^{-1}\left(\frac{1}{3}\right)\right]+\cos \left[\tan ^{-1}(2 \sqrt{2})\right]=\)

If \(\sin x+\operatorname{cosec} x=2,\) then \(\sin ^{n} x+\operatorname{cosec}^{n} x\) is equal to