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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 5701. |
\[\frac{{{d}^{2}}}{d{{x}^{2}}}(2\cos x\,\cos 3x)=\] [RPET 2003] |
| A. | \[{{2}^{2}}(\cos 2x+{{2}^{2}}\cos 4x)\] |
| B. | \[{{2}^{2}}(\cos 2x-{{2}^{2}}\cos 4x)\] |
| C. | \[{{2}^{2}}(-\cos 2x+{{2}^{2}}\cos 4x)\] |
| D. | \[-{{2}^{2}}(\cos 2x+{{2}^{2}}\cos 4x)\] |
| Answer» E. | |
| 5702. |
\[\frac{{{d}^{n}}}{d{{x}^{n}}}(\log x)\]= [RPET 2002] |
| A. | \[\frac{(n-1)!}{{{x}^{n}}}\] |
| B. | \[\frac{n\,!}{{{x}^{n}}}\] |
| C. | \[\frac{(n-2)!}{{{x}^{n}}}\] |
| D. | \[{{(-1)}^{n-1}}\frac{(n-1)!}{{{x}^{n}}}\] |
| Answer» E. | |
| 5703. |
If \[y=a\cos \,(\log x)+b\sin \,(\log x)\] where \[a,\,b\] are parameters then \[{{x}^{2}}{y}''\,+\,x{y}'\,=\] [EAMCET 2002] |
| A. | \[y\] |
| B. | \[-y\] |
| C. | \[2y\] |
| D. | \[-2y\] |
| Answer» C. \[2y\] | |
| 5704. |
\[\frac{d}{dx}{{\tan }^{-1}}\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}=\] |
| A. | \[\frac{a}{{{a}^{2}}+{{x}^{2}}}\] |
| B. | \[\frac{-a}{{{a}^{2}}+{{x}^{2}}}\] |
| C. | \[\frac{1}{a\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| D. | \[\frac{1}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| Answer» E. | |
| 5705. |
If \[y=a{{e}^{x}}+b{{e}^{-x}}+c\] where \[a,b,c\] are parameters then \[{{y}''}'=\] [EAMCET 2002] |
| A. | \[y\] |
| B. | \[y'\] |
| C. | 0 |
| D. | \[y''\] |
| Answer» C. 0 | |
| 5706. |
If \[y={{\left( x+\sqrt{1+{{x}^{2}}} \right)}^{n}},\] then \[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\] is [AIEEE 2002] |
| A. | \[{{n}^{2}}y\] |
| B. | \[-{{n}^{2}}y\] |
| C. | \[-y\] |
| D. | \[2{{x}^{2}}y\] |
| Answer» B. \[-{{n}^{2}}y\] | |
| 5707. |
A curve is given by the equations \[x=a\cos \theta +\frac{1}{2}b\cos 2\theta ,\] \[y=a\sin \theta +\frac{1}{2}b\,\sin \,2\theta \], then the points for which \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0,\] is given by [Kurukshetra CEE 2002] |
| A. | \[\sin \theta =\frac{2{{a}^{2}}+{{b}^{2}}}{5ab}\] |
| B. | \[\tan \theta =\frac{3{{a}^{2}}+2{{b}^{2}}}{4ab}\] |
| C. | \[\cos \theta =\frac{-\left( {{a}^{2}}+2{{b}^{2}} \right)}{3ab}\] |
| D. | \[\cos \theta =\frac{\left( {{a}^{2}}-2{{b}^{2}} \right)}{3ab}\] |
| Answer» D. \[\cos \theta =\frac{\left( {{a}^{2}}-2{{b}^{2}} \right)}{3ab}\] | |
| 5708. |
\[\frac{{{d}^{2}}x}{d{{y}^{2}}}\] is equal to [AMU 2001] |
| A. | \[\frac{1}{{{(dy/dx)}^{2}}}\] |
| B. | \[\frac{\left( {{d}^{2}}y/d{{x}^{2}} \right)}{{{\left( dy/dx \right)}^{2}}}\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] |
| D. | \[\frac{\left( -{{d}^{2}}y/d{{x}^{2}} \right)}{{{\left( dy/dx \right)}^{2}}}\] |
| Answer» E. | |
| 5709. |
If \[y={{x}^{3}}\log {{\log }_{e}}(1+x)\], then \[{y}''\,(0)\] equals [AMU 1999] |
| A. | 0 |
| B. | ? 1 |
| C. | \[6\,\,\log {{}_{e}}\,2\] |
| D. | 6 |
| Answer» B. ? 1 | |
| 5710. |
If \[y=\sin x+{{e}^{x}},\]then \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=\] [Karnataka CET 1999; UPSEAT 2001; Kurukshetra CEE 2002] |
| A. | \[{{(-\sin x+{{e}^{x}})}^{-1}}\] |
| B. | \[\frac{\sin x-{{e}^{x}}}{{{(\cos x+{{e}^{x}})}^{2}}}\] |
| C. | \[\frac{\sin x-{{e}^{x}}}{{{(\cos x+{{e}^{x}})}^{3}}}\] |
| D. | \[\frac{\sin x+{{e}^{x}}}{{{(\cos x+{{e}^{x}})}^{3}}}\] |
| Answer» D. \[\frac{\sin x+{{e}^{x}}}{{{(\cos x+{{e}^{x}})}^{3}}}\] | |
| 5711. |
If f be a polynomial, then the second derivative of \[f({{e}^{x}})\] is [Karnataka CET 1999] |
| A. | \[{f}'({{e}^{x}})\] |
| B. | \[{f}''\,({{e}^{x}})\,{{e}^{x}}+{f}'({{e}^{x}})\] |
| C. | \[{f}''\,({{e}^{x}}){{e}^{2x}}+{f}''({{e}^{x}})\] |
| D. | \[{f}''\,({{e}^{x}}){{e}^{2x}}+{f}'\,({{e}^{x}})\,{{e}^{x}}\] |
| Answer» E. | |
| 5712. |
If \[{{e}^{y}}+xy=e\], then the value of \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]for \[x=0\], is [Kurukshetra CEE 2002] |
| A. | \[\frac{1}{e}\] |
| B. | \[\frac{1}{{{e}^{2}}}\] |
| C. | \[\frac{1}{{{e}^{3}}}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{{{e}^{3}}}\] | |
| 5713. |
If \[y=x\log \left( \frac{x}{a+bx} \right)\], then \[{{x}^{3}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] [WB JEE 1991; Roorkee 1976] |
| A. | \[x\frac{dy}{dx}-y\] |
| B. | \[{{\left( x\frac{dy}{dx}-y \right)}^{2}}\] |
| C. | \[y\frac{dy}{dx}-x\] |
| D. | \[{{\left( y\frac{dy}{dx}-x \right)}^{2}}\] |
| Answer» C. \[y\frac{dy}{dx}-x\] | |
| 5714. |
If \[y={{\sin }^{2}}\alpha +{{\cos }^{2}}(\alpha +\beta )+2\sin \alpha \sin \beta \cos (\alpha +\beta )\], then \[\frac{{{d}^{3}}y}{d{{\alpha }^{3}}}\] is, (keeping \[\beta \]as constant) |
| A. | \[\frac{{{\sin }^{3}}(\alpha +\beta )}{\cos \alpha }\] |
| B. | \[\cos (\alpha +3\beta )\] |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 5715. |
\[\frac{{{d}^{20}}y}{d{{x}^{20}}}(2\cos x\cos 3x)\]= [EAMCET 1994] |
| A. | \[{{2}^{20}}(\cos 2x-{{2}^{20}}\cos 4x)\] |
| B. | \[{{2}^{20}}(\cos 2x+{{2}^{20}}\cos 4x)\] |
| C. | \[{{2}^{20}}(\sin 2x+{{2}^{20}}\sin 4x)\] |
| D. | \[{{2}^{20}}(\sin 2x-{{2}^{20}}\sin 4x)\] |
| Answer» C. \[{{2}^{20}}(\sin 2x+{{2}^{20}}\sin 4x)\] | |
| 5716. |
If \[y=a+b{{x}^{2}};a,b\] arbitrary constants, then [EAMCET 1994] |
| A. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=2xy\] |
| B. | \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}=\frac{dy}{dx}\] |
| C. | \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\] |
| D. | \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}=2xy\] |
| Answer» C. \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\] | |
| 5717. |
If \[y=a{{x}^{n+1}}+b{{x}^{-n}}\], then \[{{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] [Karnataka CET 1993] |
| A. | \[n\,(n-1)y\] |
| B. | \[n\,(n+1)y\] |
| C. | ny |
| D. | \[{{n}^{2}}y\] |
| Answer» C. ny | |
| 5718. |
If \[y=a{{e}^{mx}}+b{{e}^{-mx}}\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{m}^{2}}y=\] [MP PET 1987] |
| A. | \[{{m}^{2}}(a{{e}^{mx}}-b{{e}^{-mx}})\] |
| B. | 1 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 5719. |
If \[y={{({{x}^{2}}-1)}^{m}}\], then the \[{{(2m)}^{th}}\]differential coefficient of y is [MP PET 1987] |
| A. | m |
| B. | \[(2m)!\] |
| C. | 2m |
| D. | m! |
| Answer» C. 2m | |
| 5720. |
If \[y={{x}^{2}}{{e}^{mx}}\], where m is a constant, then \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=\] [MP PET 1987] |
| A. | \[m{{e}^{mx}}({{m}^{2}}{{x}^{2}}+6mx+6)\] |
| B. | \[2{{m}^{3}}x{{e}^{mx}}\] |
| C. | \[m{{e}^{mx}}({{m}^{2}}{{x}^{2}}+2mx+2)\] |
| D. | None of these |
| Answer» B. \[2{{m}^{3}}x{{e}^{mx}}\] | |
| 5721. |
If \[y={{e}^{{{\tan }^{-1}}x}}\], then \[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] |
| A. | \[(1-2x)\frac{dy}{dx}\] |
| B. | \[-2x\frac{dy}{dx}\] |
| C. | \[-x\frac{dy}{dx}\] |
| D. | 0 |
| Answer» B. \[-2x\frac{dy}{dx}\] | |
| 5722. |
If \[f(x)=a\sin (\log x)\], then \[{{x}^{2}}f''(x)+xf'(x)=\] |
| A. | \[f(x)\] |
| B. | \[-f(x)\] |
| C. | 0 |
| D. | 1 |
| Answer» C. 0 | |
| 5723. |
\[\frac{{{d}^{n}}}{d{{x}^{n}}}({{e}^{2x}}+{{e}^{-2x}})=\] |
| A. | \[{{e}^{2x}}+{{(-1)}^{n}}{{e}^{-2x}}\] |
| B. | \[{{2}^{n}}({{e}^{2x}}-{{e}^{-2x}})\] |
| C. | \[{{2}^{n}}[{{e}^{2x}}+{{(-1)}^{n}}{{e}^{-2x}}]\] |
| D. | None of these |
| Answer» D. None of these | |
| 5724. |
If \[y=A\cos nx+B\sin nx,\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] [Karnataka CET 1996] |
| A. | \[{{n}^{2}}y\] |
| B. | \[-y\] |
| C. | \[-{{n}^{2}}y\] |
| D. | None of these |
| Answer» D. None of these | |
| 5725. |
\[{{n}^{th}}\]derivative of \[{{x}^{n+1}}\]is |
| A. | \[(n+1)!x\] |
| B. | \[(n+1)!\] |
| C. | \[n!x\] |
| D. | \[n!\] |
| Answer» B. \[(n+1)!\] | |
| 5726. |
If \[y=\sin x\sin 3x,\]then \[{{y}_{n}}=\] |
| A. | \[\frac{1}{2}\left[ \cos \left( 2x+n\frac{\pi }{2} \right)-\cos \left( 4x+n\frac{\pi }{2} \right) \right]\] |
| B. | \[\frac{1}{2}\left[ {{2}^{n\,\,}}\cos \left( 2x+n\frac{\pi }{2} \right)-{{4}^{n}}\cos \left( 4x+n\frac{\pi }{2} \right) \right]\] |
| C. | \[\frac{1}{2}\left[ {{4}^{n}}\cos \left( 4x+n\frac{\pi }{2} \right)-{{2}^{n}}\cos \left( 2x+n\frac{\pi }{2} \right) \right]\] |
| D. | None of these |
| Answer» C. \[\frac{1}{2}\left[ {{4}^{n}}\cos \left( 4x+n\frac{\pi }{2} \right)-{{2}^{n}}\cos \left( 2x+n\frac{\pi }{2} \right) \right]\] | |
| 5727. |
The differential coefficient of \[f(\sin x)\] with respect to x, where \[f(x)=\log x\], is [Karnataka CET 2004] |
| A. | \[\tan x\] |
| B. | \[\cot x\] |
| C. | \[f(\cos x)\] |
| D. | \[1/x\] |
| Answer» C. \[f(\cos x)\] | |
| 5728. |
The 2nd derivative of \[a{{\sin }^{3}}t\] with respect to \[a{{\cos }^{3}}t\,\,\text{at}\,\,t=\frac{\pi }{4}\] is [Kerala (Engg.) 2002] |
| A. | \[\frac{4\sqrt{2}}{3a}\] |
| B. | 2 |
| C. | \[\frac{1}{12a}\] |
| D. | None of these |
| Answer» B. 2 | |
| 5729. |
The derivative of \[{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\] w.r.t. \[{{\cot }^{-1}}\left( \frac{1-3{{x}^{2}}}{3x-{{x}^{2}}} \right)\] is [Karnataka CET 2003] |
| A. | 1 |
| B. | \[\frac{3}{2}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 5730. |
Differential coefficient of \[{{\tan }^{-1}}\left( \frac{x}{1+\sqrt{1-{{x}^{2}}}} \right)\] w.r.t \[{{\sin }^{-1}}x,\] is [Kurukshetra CEE 2002] |
| A. | \[\frac{1}{2}\] |
| B. | 1 |
| C. | 2 |
| D. | \[\frac{3}{2}\] |
| Answer» B. 1 | |
| 5731. |
If \[y={{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}}+{{\sec }^{-1}}\frac{1+{{x}^{2}}}{1-{{x}^{2}}}\], then \[\frac{dy}{dx}\]= [RPET 1996] |
| A. | \[\frac{4}{1-{{x}^{2}}}\] |
| B. | \[\frac{1}{1+{{x}^{2}}}\] |
| C. | \[\frac{4}{1-{{x}^{2}}}\] |
| D. | \[\frac{-4}{1+{{x}^{2}}}\] |
| Answer» D. \[\frac{-4}{1+{{x}^{2}}}\] | |
| 5732. |
The derivative of \[{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,\]w.r.t. \[{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\] is [Karnataka CET 2000; Pb. CET 2004] |
| A. | ?1 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 5733. |
The derivative of \[{{\sin }^{2}}x\]with respect to \[{{\cos }^{2}}x\] is [DCE 2002] |
| A. | \[{{\tan }^{2}}x\] |
| B. | \[\tan x\] |
| C. | \[-\tan x\] |
| D. | None of these |
| Answer» E. | |
| 5734. |
If \[u={{\tan }^{-1}}\left\{ \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right\}\] and \[v=2{{\tan }^{-1}}x\], then \[\frac{du}{dv}\] is equal to [RPET 1997] |
| A. | 4 |
| B. | 1 |
| C. | ¼ |
| D. | ?1/4 |
| Answer» D. ?1/4 | |
| 5735. |
Derivative of \[{{\sec }^{-1}}\left\{ \frac{1}{2{{x}^{2}}-1} \right\}\]w.r.t \[\sqrt{1+3x}\]at \[x=-\frac{1}{3}\] is [EAMCET 1991] |
| A. | 0 |
| B. | 1/2 |
| C. | 1/3 |
| D. | None of these |
| Answer» B. 1/2 | |
| 5736. |
Differential coefficient of \[{{\tan }^{-1}}\sqrt{\frac{1-{{x}^{2}}}{1+{{x}^{2}}}}\] w.r.t. \[{{\cos }^{-1}}({{x}^{2}})\] is [RPET 1996] |
| A. | \[\frac{1}{2}\] |
| B. | \[-\frac{1}{2}\] |
| C. | 1 |
| D. | 0 |
| Answer» B. \[-\frac{1}{2}\] | |
| 5737. |
Differential coefficient of \[{{x}^{3}}\] with respect to \[{{x}^{2}}\] is [RPET 1995] |
| A. | \[\]\[\frac{3{{x}^{2}}}{2}\] |
| B. | \[\frac{3x}{2}\] |
| C. | \[\frac{3{{x}^{3}}}{2}\] |
| D. | \[\frac{3}{2x}\] |
| Answer» C. \[\frac{3{{x}^{3}}}{2}\] | |
| 5738. |
The differential coefficient of \[{{x}^{6}}\] with respect to \[{{x}^{3}}\] is [EAMCET 1988; UPSEAT 2000] |
| A. | \[5{{x}^{2}}\] |
| B. | \[3{{x}^{3}}\] |
| C. | \[5{{x}^{5}}\] |
| D. | \[2{{x}^{3}}\] |
| Answer» E. | |
| 5739. |
The differential coefficient of \[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\] with respect to \[{{\tan }^{-1}}\]x is [Kurukshetra CEE 1998; RPET 1999] |
| A. | \[\frac{1}{2}\] |
| B. | \[-\frac{1}{2}\] |
| C. | 1 |
| D. | None of these |
| Answer» B. \[-\frac{1}{2}\] | |
| 5740. |
The differential coefficient of \[{{\tan }^{-1}}\sqrt{x}\] with respect to \[\sqrt{x}\] is [MP PET 1987] |
| A. | \[\frac{1}{\sqrt{1+x}}\] |
| B. | \[\frac{1}{2x\sqrt{1+x}}\] |
| C. | \[\frac{1}{2\sqrt{x(1+x)}}\] |
| D. | \[\frac{1}{1+x}\] |
| Answer» E. | |
| 5741. |
Differential coefficient of \[\frac{{{\tan }^{-1}}x}{1+{{\tan }^{-1}}x}\] w.r.t. \[{{\tan }^{-1}}x\] is |
| A. | \[\frac{1}{1+{{\tan }^{-1}}x}\] |
| B. | \[\frac{-1}{1+{{\tan }^{-1}}x}\] |
| C. | \[\frac{1}{{{(1+{{\tan }^{-1}}x)}^{^{2}}}}\] |
| D. | \[\frac{-1}{2\,{{(1+{{\tan }^{-1}}x)}^{2}}}\] |
| Answer» D. \[\frac{-1}{2\,{{(1+{{\tan }^{-1}}x)}^{2}}}\] | |
| 5742. |
Differential coefficient of\[{{\sin }^{-1}}x\] w.r.t \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] is [MNR 1983; AMU 2002] |
| A. | 1 |
| B. | \[\frac{1}{1+{{x}^{2}}}\] |
| C. | 2 |
| D. | None of these |
| Answer» B. \[\frac{1}{1+{{x}^{2}}}\] | |
| 5743. |
\[\frac{d}{dx}{{\cos }^{-1}}\frac{x-{{x}^{-1}}}{x+{{x}^{-1}}}\]= [DSSE 1985; Rookee 1963] |
| A. | \[\frac{1}{1+{{x}^{2}}}\] |
| B. | \[\frac{-1}{1+{{x}^{2}}}\] |
| C. | \[\frac{2}{1+{{x}^{2}}}\] |
| D. | \[\]\[\frac{-2}{1+{{x}^{2}}}\] |
| Answer» E. | |
| 5744. |
The differential coefficient of \[{{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}\] w.r.t. \[{{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}}\] is [Roorkee 1966; BIT Ranchi 1996; Karnataka CET 1994; MP PET 1999; UPSEAT 1999, 2001] |
| A. | 1 |
| B. | ? 1 |
| C. | 0 |
| D. | None of these |
| Answer» B. ? 1 | |
| 5745. |
\[\frac{d}{dx}\left( {{\tan }^{-1}}\frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\] is equal to [MP PET 2004] |
| A. | \[\frac{1}{1+{{x}^{2}}}\] |
| B. | \[\frac{1}{2(1+{{x}^{2}})}\] |
| C. | \[\frac{{{x}^{2}}}{2\sqrt{1+{{x}^{2}}}(\sqrt{1+{{x}^{2}}}-1)}\] |
| D. | \[\frac{2}{1+{{x}^{2}}}\] |
| Answer» C. \[\frac{{{x}^{2}}}{2\sqrt{1+{{x}^{2}}}(\sqrt{1+{{x}^{2}}}-1)}\] | |
| 5746. |
Differential coefficient of \[{{\sin }^{-1}}\frac{1-x}{1+x}w.r.t\]\[\sqrt{x}\]is [Roorkee 1984] |
| A. | \[\frac{1}{2\sqrt{x}}\] |
| B. | \[\frac{\sqrt{x}}{\sqrt{1-x}}\] |
| C. | 1 |
| D. | None of these |
| Answer» E. | |
| 5747. |
The differential coefficient of \[{{\tan }^{-1}}\left( \frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}} \right)\] is [MP PET 2003] |
| A. | \[\sqrt{1-{{x}^{2}}}\] |
| B. | \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| C. | \[\frac{1}{2\sqrt{1-{{x}^{2}}}}\] |
| D. | x |
| Answer» D. x | |
| 5748. |
If \[y={{\sin }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\], then \[\frac{dy}{dx}\] equals [EAMCET 1991; RPET 1996] |
| A. | \[\frac{2}{1-{{x}^{2}}}\] |
| B. | \[\frac{1}{1+{{x}^{2}}}\] |
| C. | \[\pm \frac{2}{1+{{x}^{2}}}\] |
| D. | \[-\frac{2}{1+{{x}^{2}}}\] |
| Answer» D. \[-\frac{2}{1+{{x}^{2}}}\] | |
| 5749. |
If \[y={{\tan }^{-1}}\left( \frac{x}{\sqrt{1-{{x}^{2}}}} \right)\], then \[\frac{dy}{dx}=\] [MP PET 1999] |
| A. | \[-\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| B. | \[\frac{x}{\sqrt{1-{{x}^{2}}}}\] |
| C. | \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| D. | \[\frac{\sqrt{1-{{x}^{2}}}}{x}\] |
| Answer» D. \[\frac{\sqrt{1-{{x}^{2}}}}{x}\] | |
| 5750. |
Differential coefficient of \[{{\cos }^{-1}}(\sqrt{x})\]with respect to \[\sqrt{(1-x)}\] is [MP PET 1997] |
| A. | \[\sqrt{x}\] |
| B. | \[-\sqrt{x}\] |
| C. | \[\frac{1}{\sqrt{x}}\] |
| D. | \[-\frac{1}{\sqrt{x}}\] |
| Answer» D. \[-\frac{1}{\sqrt{x}}\] | |