KVPY Sample Paper KVPY Stream-SX Model Paper-18

The number of points in \[(-\,\infty ,\infty )\] for which \[{{x}^{2}}-x\sin x-\cos x=0\]is

A) 6

B) 4

C) 2

D) 0

Correct Answer: C

Solution :

We have,

\[{{x}^{2}}-x\sin x-\cos x=0\]

Let \[f(x)={{x}^{2}}-x\sin x-\cos x\]

\[f'(x)=2x-x\cos x\]

\[\underset{x\to \infty }{\mathop{\lim }}\,f(x)=\infty \]

\[\underset{x\to -\,\infty }{\mathop{\lim }}\,f(x)=\infty \]

\[f(0)=-1\]

Hence, 2 solutions exists.