Question
$\mathop {\lim }\limits_{x \to \infty } (\sqrt {{x^2} + 8x + 3} - \sqrt {{x^2} + 4x + 3} ) = $
$ = \mathop {\lim }\limits_{x \to \infty } \,\frac{4}{{\left( {\sqrt {1 + \frac{8}{x} + \frac{3}{{{x^2}}}} + \sqrt {1 + \frac{4}{x} + \frac{3}{{{x^2}}}} } \right)}} = 2$
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| List $I$ | List $II$ |
| $P$ $\quad\left(\frac{1}{y^2}\left(\frac{\cos \left(\tan ^{-1} y\right)+y \sin \left(\tan ^{-1} y\right)}{\cot \left(\sin ^{-1} y\right)+\tan \left(\sin ^{-1} y\right)}\right)^2+y^4\right)^{1 / 2}$ का मान है | $1.\quad$ $\frac{1}{2} \sqrt{\frac{5}{3}}$ |
| $Q.\quad$ यदि $\cos x+\cos y+\cos z=0=\sin x+\sin y+\sin z$ तब $\cos \frac{x-y}{2}$ का सम्भावित मान है | $2.\quad$ $\sqrt{2}$ |
| $R.\quad$ यदि $\cos \left(\frac{\pi}{4}-x\right) \cos 2 x+\sin x \sin 2 x \sec x=\cos x \sin 2 x \sec x+$ $\cos \left(\frac{\pi}{4}+x\right) \cos 2 x$ तब $\sec x$ का सम्भावित मान है- | $3.\quad$ $\frac{1}{2}$ |
| $S.\quad$ यदि $\cot \left(\sin ^{-1} \sqrt{1-x^2}\right)=\sin \left(\tan ^{-1}(x \sqrt{6})\right), x \neq 0$, तब $x$ का स्मभावित मान है- | $4.\quad$ $1$ |
Codes: $ \quad P \quad Q \quad R \quad S $