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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.
| 5801. |
The function defined by \[f(x)=\left\{ \begin{align} & |x-3|\,;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ge 1 \\ & \frac{1}{4}{{x}^{2}}-\frac{3}{2}x+\frac{13}{4};\,x |
| A. | Continuous at \[x=1\] |
| B. | Continuous at \[x=3\] |
| C. | Differentiable at \[x=1\] |
| D. | All the above |
| Answer» E. | |
| 5802. |
At the point \[x=1\], the given function \[f(x)=\left\{ \begin{align} & {{x}^{3}}-1;\,\,1 |
| A. | Continuous and differentiable |
| B. | Continuous and not differentiable |
| C. | Discontinuous and differentiable |
| D. | Discontinuous and not differentiable |
| Answer» C. Discontinuous and differentiable | |
| 5803. |
Let \[[x]\]denotes the greatest integer less than or equal to x. If \[f(x)=[x\sin \pi x]\], then \[f(x)\]is [IIT 1986] |
| A. | Continuous at \[x=0\] |
| B. | Continuous in \[(-1,0)\] |
| C. | Differentiable in (?1,1) |
| D. | All the above |
| Answer» E. | |
| 5804. |
If \[y={{\sin }^{-1}}\left( \frac{19}{20}x \right)+{{\cos }^{-1}}\left( \frac{19}{20}x \right)\], then \[\frac{dy}{dx}=\] |
| A. | 0 |
| B. | 1 |
| C. | ? 1 |
| D. | None of these |
| Answer» B. 1 | |
| 5805. |
If \[y=\log \log x\], then \[{{e}^{y}}\frac{dy}{dx}=\] [MP PET 1994, 95] |
| A. | \[\frac{1}{x\log x}\] |
| B. | \[\frac{1}{x}\] |
| C. | \[\frac{1}{\log x}\] |
| D. | \[{{e}^{y}}\] |
| Answer» C. \[\frac{1}{\log x}\] | |
| 5806. |
\[\frac{d}{dx}[{{e}^{ax}}\cos (bx+c)]\]= [AISSE 1989] |
| A. | \[{{e}^{ax}}[a\cos (bx+c)-b\sin (bx+c)]\] |
| B. | \[{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]\] |
| C. | \[{{e}^{ax}}[\cos (bx+c)-\sin (bx+c)]\] |
| D. | None of these |
| Answer» B. \[{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]\] | |
| 5807. |
\[\frac{d}{dx}[{{\tan }^{-1}}(\cot x)+{{\cot }^{-1}}(\tan x)]=\] |
| A. | 0 |
| B. | 1 |
| C. | ? 1 |
| D. | ? 2 |
| Answer» E. | |
| 5808. |
At \[x=\sqrt{\frac{\pi }{2}},\frac{d}{dx}\cos (\sin {{x}^{2}})\]= |
| A. | ?1 |
| B. | 1 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 5809. |
If \[f(x)=\,|x|,\]then \[f'(0)=\] [MNR 1982] |
| A. | 0 |
| B. | 1 |
| C. | x |
| D. | None of these |
| Answer» E. | |
| 5810. |
\[\frac{d}{dx}\left[ \log \sqrt{\sin \sqrt{{{e}^{x}}}} \right]\]= |
| A. | \[\frac{1}{4}{{e}^{x/2}}\cot ({{e}^{x/2}})\] |
| B. | \[{{e}^{x/2}}\cot ({{e}^{x/2}})\] |
| C. | \[\frac{1}{4}{{e}^{x}}\cot \,({{e}^{x}})\] |
| D. | \[\frac{1}{2}{{e}^{x/2}}\cot \,({{e}^{x/2}})\] |
| Answer» B. \[{{e}^{x/2}}\cot ({{e}^{x/2}})\] | |
| 5811. |
\[\frac{d}{dx}\left[ \frac{2}{\pi }\sin {{x}^{0}} \right]=\] |
| A. | \[\frac{\pi }{180}\cos {{x}^{0}}\] |
| B. | \[\frac{1}{90}\cos {{x}^{0}}\] |
| C. | \[\frac{\pi }{90}\cos {{x}^{0}}\] |
| D. | \[\frac{2}{90}\cos {{x}^{0}}\] |
| Answer» C. \[\frac{\pi }{90}\cos {{x}^{0}}\] | |
| 5812. |
If \[y=x\sin x,\]then |
| A. | \[\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}+\cot x\] |
| B. | \[\frac{dy}{dx}=\frac{1}{x}+\cot x\] |
| C. | \[\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}-\cot x\] |
| D. | None of these |
| Answer» B. \[\frac{dy}{dx}=\frac{1}{x}+\cot x\] | |
| 5813. |
If \[y={{\sec }^{-1}}\left( \frac{x+1}{x-1} \right)+{{\sin }^{-1}}\left( \frac{x-1}{x+1} \right)\], then \[\frac{dy}{dx}=\] [MNR 1984] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 5814. |
If \[y={{\tan }^{-1}}\left( \frac{\sqrt{a}-\sqrt{x}}{1+\sqrt{ax}} \right)\], then \[\frac{dy}{dx}=\] [AI CBSE 1988] |
| A. | \[\frac{1}{2(1+x)\sqrt{x}}\] |
| B. | \[\frac{1}{(1+x)\sqrt{x}}\] |
| C. | \[-\frac{1}{2(1+x)\sqrt{x}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5815. |
If \[y=\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}\], then \[\frac{dy}{dx}=\] [Roorkee 1971] |
| A. | \[\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{1-\sin x}-\frac{1}{2x} \right]\] |
| B. | \[\frac{2{{(x-\sin x)}^{3/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\] |
| C. | \[\frac{2{{(x-\sin x)}^{1/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\] |
| D. | None of these |
| Answer» C. \[\frac{2{{(x-\sin x)}^{1/2}}}{\sqrt{x}}\left[ \frac{3}{2}.\frac{1-\cos x}{x-\sin x}-\frac{1}{2x} \right]\] | |
| 5816. |
If \[y=\frac{{{e}^{2x}}+{{e}^{-2x}}}{{{e}^{2x}}-{{e}^{-2x}}}\], then \[\frac{dy}{dx}=\] [AI CBSE 1988] |
| A. | \[\frac{-8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] |
| B. | \[\frac{8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] |
| C. | \[\frac{-4}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] |
| D. | \[\frac{4}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] |
| Answer» B. \[\frac{8}{{{({{e}^{2x}}-{{e}^{-2x}})}^{2}}}\] | |
| 5817. |
\[\frac{d}{dx}\left\{ {{e}^{x}}\log (1+{{x}^{2}}) \right\}=\] [AI CBSE 1987] |
| A. | \[{{e}^{x}}\left[ \log (1+{{x}^{2}})+\frac{2x}{1+{{x}^{2}}} \right]\] |
| B. | \[{{e}^{x}}\left[ \log (1+{{x}^{2}})-\frac{2x}{1+{{x}^{2}}} \right]\] |
| C. | \[{{e}^{x}}\left[ \log (1+{{x}^{2}})+\frac{x}{1+{{x}^{2}}} \right]\] |
| D. | \[{{e}^{x}}\left[ \log (1+{{x}^{2}})-\frac{x}{1+{{x}^{2}}} \right]\] |
| Answer» B. \[{{e}^{x}}\left[ \log (1+{{x}^{2}})-\frac{2x}{1+{{x}^{2}}} \right]\] | |
| 5818. |
If \[y=\sqrt{\frac{1+{{e}^{x}}}{1-{{e}^{x}}}}\], then \[\frac{dy}{dx}=\] [AI CBSE 1986] |
| A. | \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{2x}}}}\] |
| B. | \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{x}}}}\] |
| C. | \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1+{{e}^{2x}}}}\] |
| D. | \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{2x}}}}\] |
| Answer» B. \[\frac{{{e}^{x}}}{(1-{{e}^{x}})\sqrt{1-{{e}^{x}}}}\] | |
| 5819. |
\[\frac{d}{dx}\{{{e}^{-a{{x}^{2}}}}\log (\sin x)\}=\] [AI CBSE 1984] |
| A. | \[{{e}^{-a{{x}^{2}}}}(\cot x+2ax\log \sin x)\] |
| B. | \[{{e}^{-a{{x}^{2}}}}(\cot x+ax\log \sin x)\] |
| C. | \[{{e}^{-a{{x}^{2}}}}(\cot x-2ax\log \sin x)\] |
| D. | None of these |
| Answer» D. None of these | |
| 5820. |
If \[y=\frac{{{e}^{2x}}\cos x}{x\sin x},\]then \[\frac{dy}{dx}=\] [AI CBSE 1982] |
| A. | \[\frac{{{e}^{2x}}[(2x-1)\cot x-x\,\text{cose}{{\text{c}}^{2}}x]}{{{x}^{2}}}\] |
| B. | \[\frac{{{e}^{2x}}[(2x+1)\cot x-x\,\text{cose}{{\text{c}}^{2}}x]}{{{x}^{2}}}\] |
| C. | \[\frac{{{e}^{2x}}[(2x-1)\cot x+x\,\text{cose}{{\text{c}}^{2}}x]}{{{x}^{2}}}\] |
| D. | None of these |
| Answer» B. \[\frac{{{e}^{2x}}[(2x+1)\cot x-x\,\text{cose}{{\text{c}}^{2}}x]}{{{x}^{2}}}\] | |
| 5821. |
If \[y=\frac{{{e}^{x}}\log x}{{{x}^{2}}}\], then \[\frac{dy}{dx}=\] [AI CBSE 1982] |
| A. | \[\frac{{{e}^{x}}[1+(x+2)\log x]}{{{x}^{3}}}\] |
| B. | \[\frac{{{e}^{x}}[1-(x-2)\log x]}{{{x}^{4}}}\] |
| C. | \[\frac{{{e}^{x}}[1-(x-2)\log x]}{{{x}^{3}}}\] |
| D. | \[\frac{{{e}^{x}}[1+(x-2)\log x]}{{{x}^{3}}}\] |
| Answer» E. | |
| 5822. |
\[\frac{d}{dx}\left[ \frac{{{e}^{ax}}}{\sin (bx+c)} \right]=\] [AI CBSE 1983] |
| A. | \[\frac{{{e}^{ax}}[a\sin (bx+c)+b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\] |
| B. | \[\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{\sin (bx+c)}\] |
| C. | \[\frac{{{e}^{ax}}[a\sin (bx+c)-b\cos (bx+c)]}{{{\sin }^{2}}(bx+c)}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5823. |
\[\frac{d}{dx}(x{{e}^{{{x}^{2}}}})=\] [DSSE 1981] |
| A. | \[2{{x}^{2}}{{e}^{x}}^{2}+{{e}^{x}}^{2}\] |
| B. | \[{{x}^{2}}{{e}^{x}}^{2}+{{e}^{x}}^{2}\] |
| C. | \[{{e}^{x}}.2{{x}^{2}}+{{e}^{x}}^{2}\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}{{e}^{x}}^{2}+{{e}^{x}}^{2}\] | |
| 5824. |
\[\frac{d}{dx}\{\log (\sec x+\tan x)\}=\] [AISSE 1982] |
| A. | \[\cos x\] |
| B. | \[\sec x\] |
| C. | \[\tan x\] |
| D. | \[\cot x\] |
| Answer» C. \[\tan x\] | |
| 5825. |
\[\frac{d}{dx}{{e}^{x\sin x}}=\] [DSSE 1979] |
| A. | \[{{e}^{x\sin x}}(x\cos x+\sin x)\] |
| B. | \[{{e}^{x\sin x}}(\cos x+x\sin x)\] |
| C. | \[{{e}^{x\sin x}}(\cos x+\sin x)\] |
| D. | None of these |
| Answer» B. \[{{e}^{x\sin x}}(\cos x+x\sin x)\] | |
| 5826. |
\[\frac{d}{dx}\left[ {{\tan }^{-1}}\sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\] [BIT Ranchi 1989; Roorkee 1989; RPET 1996] |
| A. | \[-\frac{1}{2}\] |
| B. | 0 |
| C. | \[\frac{1}{2}\] |
| D. | 1 |
| Answer» D. 1 | |
| 5827. |
\[\frac{d}{dx}\left[ \log \sqrt{\frac{1-\cos x}{1+\cos x}} \right]=\] [BIT Ranchi 1990] |
| A. | \[\sec x\] |
| B. | \[\cos \text{ec}\,x\] |
| C. | \[\cos \text{ec}\frac{x}{2}\] |
| D. | \[\sec \frac{x}{2}\] |
| Answer» C. \[\cos \text{ec}\frac{x}{2}\] | |
| 5828. |
The differential coefficient of the given function \[{{\log }_{e}}\left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right)\] with respect to x is [MP PET 1993] |
| A. | \[\cos \text{ec}\,x\] |
| B. | \[\tan x\] |
| C. | \[\cos x\] |
| D. | \[\sec x\] |
| Answer» E. | |
| 5829. |
If \[y={{\cot }^{-1}}\left( \frac{1+x}{1-x} \right)\], then \[\frac{dy}{dx}=\] [DSSE 1984] |
| 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» C. \[\frac{2}{1+{{x}^{2}}}\] | |
| 5830. |
If \[y=1+x+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}+.....\infty ,\]then \[\frac{dy}{dx}=\] [Karnataka CET 1999] |
| A. | y |
| B. | \[y-1\] |
| C. | \[y+1\] |
| D. | None of these |
| Answer» B. \[y-1\] | |
| 5831. |
If \[y={{\tan }^{-1}}\left( \frac{{{x}^{1/3}}+{{a}^{1/3}}}{1-{{x}^{1/3}}{{a}^{1/3}}} \right)\], then \[\frac{dy}{dx}=\] [DSSE 1986] |
| A. | \[\frac{1}{3{{x}^{2/3}}(1+{{x}^{2/3}})}\] |
| B. | \[\frac{1}{3{{x}^{2/3}}(1+{{x}^{2/3}})}\] |
| C. | \[-\frac{1}{3{{x}^{2/3}}(1+{{x}^{2/3}})}\] |
| D. | \[-\frac{a}{3{{x}^{2/3}}(1+{{x}^{2/3}})}\] |
| Answer» B. \[\frac{1}{3{{x}^{2/3}}(1+{{x}^{2/3}})}\] | |
| 5832. |
\[\frac{d}{dx}\left( {{x}^{3}}{{\tan }^{2}}\frac{x}{2} \right)\]= [AISSE 1979] |
| A. | \[{{x}^{3}}\tan \frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3x{{\tan }^{2}}\frac{x}{2}\] |
| B. | \[{{x}^{3}}\tan \frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3{{x}^{2}}{{\tan }^{2}}\frac{x}{2}\] |
| C. | \[{{x}^{3}}{{\tan }^{2}}\frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3{{x}^{2}}{{\tan }^{2}}\frac{x}{2}\] |
| D. | None of these |
| Answer» C. \[{{x}^{3}}{{\tan }^{2}}\frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3{{x}^{2}}{{\tan }^{2}}\frac{x}{2}\] | |
| 5833. |
\[\frac{d}{dx}\left( \frac{\sec x+\tan x}{\sec x-\tan x} \right)=\] [DSSE 1979, 81; CBSE 1981] |
| A. | \[\frac{2\cos x}{{{(1-\sin x)}^{2}}}\] |
| B. | \[\frac{\cos x}{{{(1-\sin x)}^{2}}}\] |
| C. | \[\frac{2\cos x}{1-\sin x}\] |
| D. | None of these |
| Answer» B. \[\frac{\cos x}{{{(1-\sin x)}^{2}}}\] | |
| 5834. |
\[\frac{d}{dx}\sqrt{{{\sec }^{2}}x+\text{cose}{{\text{c}}^{2}}x}=\] [DSSE 1981] |
| A. | \[4\cos \text{ec 2}x.\cot 2x\] |
| B. | \[-4\cos \text{ec 2}x.\cot 2x\] |
| C. | \[-4\cos \text{ec }x.\cot 2x\] |
| D. | None of these |
| Answer» C. \[-4\cos \text{ec }x.\cot 2x\] | |
| 5835. |
\[\frac{d}{dx}\sqrt{x\sin x}=\] [AISSE 1985] |
| A. | \[\frac{\sin x+x\cos x}{2\sqrt{x\sin x}}\] |
| B. | \[\frac{\sin x+x\cos x}{\sqrt{x\sin x}}\] |
| C. | \[\frac{x\sin x+\cos x}{\sqrt{2\sin x}}\] |
| D. | \[\frac{\sin x+x\cos x}{2\sqrt{x\sin x}}\] |
| Answer» B. \[\frac{\sin x+x\cos x}{\sqrt{x\sin x}}\] | |
| 5836. |
\[\frac{d}{dx}{{({{x}^{2}}+\cos x)}^{4}}=\] [DSSE 1979] |
| A. | \[4({{x}^{2}}+\cos x)(2x-\sin x)\] |
| B. | \[4{{({{x}^{2}}-\cos x)}^{3}}(2x-\sin x)\] |
| C. | \[4{{({{x}^{2}}+\cos x)}^{3}}(2x-\sin x)\] |
| D. | \[4{{({{x}^{2}}+\cos x)}^{3}}(2x+\sin x)\] |
| Answer» D. \[4{{({{x}^{2}}+\cos x)}^{3}}(2x+\sin x)\] | |
| 5837. |
If \[y=\sqrt{\frac{1+\tan x}{1-\tan x}}\], then \[\frac{dy}{dx}=\] [AISSE 1981, 83, 84, 85; DSSE 1985; AI CBSE 1981, 83] |
| A. | \[\frac{1}{2}\sqrt{\frac{1-\tan x}{1+\tan x}}.{{\sec }^{2}}\left( \frac{\pi }{4}+x \right)\] |
| B. | \[\sqrt{\frac{1-\tan x}{1+\tan x}}.{{\sec }^{2}}\left( \frac{\pi }{4}+x \right)\] |
| C. | \[\frac{1}{2}\sqrt{\frac{1-\tan x}{1+\tan x}}.\sec \left( \frac{\pi }{4}+x \right)\] |
| D. | None of these |
| Answer» B. \[\sqrt{\frac{1-\tan x}{1+\tan x}}.{{\sec }^{2}}\left( \frac{\pi }{4}+x \right)\] | |
| 5838. |
If \[y=\sin \left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\], then \[\frac{dy}{dx}=\] [AISSE 1987] |
| A. | \[\frac{4x}{1-{{x}^{2}}}.\cos \left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\] |
| B. | \[\frac{x}{{{(1-{{x}^{2}})}^{2}}}.\cos \left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\] |
| C. | \[\frac{x}{(1-{{x}^{2}})}.\cos \left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\] |
| D. | \[\frac{4x}{{{(1-{{x}^{2}})}^{2}}}.\cos \left( \frac{1+{{x}^{2}}}{1-{{x}^{2}}} \right)\] |
| Answer» E. | |
| 5839. |
\[\frac{d}{dx}\{\cos (\sin {{x}^{2}})\}=\] [DSSE 1979] |
| A. | \[\sin (\sin {{x}^{2}}).\cos {{x}^{2}}.2x\] |
| B. | \[-\sin (\sin {{x}^{2}}).\cos {{x}^{2}}.2x\] |
| C. | \[-\sin (\sin {{x}^{2}}).{{\cos }^{2}}x.2x\] |
| D. | None of these |
| Answer» C. \[-\sin (\sin {{x}^{2}}).{{\cos }^{2}}x.2x\] | |
| 5840. |
If \[y=1+x+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{3}}}{3\,!}+.....+\frac{{{x}^{n}}}{n\,!}\], then \[\frac{dy}{dx}=\] |
| A. | y |
| B. | \[y+\frac{{{x}^{n}}}{n!}\] |
| C. | \[y-\frac{{{x}^{n}}}{n!}\] |
| D. | \[y-1-\frac{{{x}^{n}}}{n!}\] |
| Answer» D. \[y-1-\frac{{{x}^{n}}}{n!}\] | |
| 5841. |
If \[y={{(x{{\cot }^{3}}x)}^{3/2}},\]then \[dy/dx=\] |
| A. | \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{3}}x-3x{{\cot }^{2}}x\cos \text{e}{{\text{c}}^{2}}x]\] |
| B. | \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{2}}x-3x{{\cot }^{2}}x\,\text{cose}{{\text{c}}^{2}}x]\] |
| C. | \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/3}}[{{\cot }^{3}}x-3x\,\text{cos}\text{e}{{\text{c}}^{2}}x]\] |
| D. | \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{3/2}}[{{\cot }^{3}}x-3x\,\text{cos}\text{e}{{\text{c}}^{2}}x]\] |
| Answer» B. \[\frac{3}{2}{{(x{{\cot }^{3}}x)}^{1/2}}[{{\cot }^{2}}x-3x{{\cot }^{2}}x\,\text{cose}{{\text{c}}^{2}}x]\] | |
| 5842. |
If \[y=\frac{\sqrt{a+x}-\sqrt{a-x}}{\sqrt{a+x}+\sqrt{a-x}}\], then \[\frac{dy}{dx}=\] [AISSE 1986] |
| A. | \[\frac{ay}{x\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| B. | \[\frac{ay}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] |
| C. | \[\frac{ay}{x\sqrt{{{x}^{2}}-{{a}^{2}}}}\] |
| D. | None of these |
| Answer» B. \[\frac{ay}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] | |
| 5843. |
If \[y=\frac{\sqrt{{{x}^{2}}+1}+\sqrt{{{x}^{2}}-1}}{\sqrt{{{x}^{2}}+1}-\sqrt{{{x}^{2}}-1}}\], then \[\frac{dy}{dx}=\] |
| A. | \[2x+\frac{2{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\] |
| B. | \[2x+\frac{{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\] |
| C. | \[x+\frac{2{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\] |
| D. | None of these |
| Answer» B. \[2x+\frac{{{x}^{3}}}{\sqrt{{{x}^{4}}-1}}\] | |
| 5844. |
If \[A=\frac{{{2}^{x}}\cot x}{\sqrt{x}},\]then \[\frac{dA}{dx}=\] |
| A. | \[\frac{{{2}^{x-1}}\left\{ -2x\,\text{cos}\text{e}{{\text{c}}^{2}}x+\cot x.\log \left( \frac{{{4}^{x}}}{e} \right) \right\}}{{{x}^{3/2}}}\] |
| B. | \[\frac{{{2}^{x-1}}\left\{ -2x\cos \text{e}{{\text{c}}^{2}}x+\cot x.\log \left( \frac{{{4}^{x}}}{e} \right) \right\}}{x}\] |
| C. | \[\frac{2x\left\{ -2x\text{cose}{{\text{c}}^{2}}x+\cot x.\log \left( \frac{{{4}^{x}}}{e} \right) \right\}}{{{x}^{\text{3/2}}}}\] |
| D. | None of these |
| Answer» B. \[\frac{{{2}^{x-1}}\left\{ -2x\cos \text{e}{{\text{c}}^{2}}x+\cot x.\log \left( \frac{{{4}^{x}}}{e} \right) \right\}}{x}\] | |
| 5845. |
\[\frac{d}{dx}\left( \frac{\log x}{\sin x} \right)=\] |
| A. | \[\frac{\frac{\sin x}{x}-\log x.\cos x}{\sin x}\] |
| B. | \[\frac{\frac{\sin x}{x}-\log x.\cos x}{{{\sin }^{2}}x}\] |
| C. | \[\frac{\sin x-\log x.\cos x}{{{\sin }^{2}}x}\] |
| D. | \[\frac{\frac{\sin x}{x}-\log x}{{{\sin }^{2}}x}\] |
| Answer» C. \[\frac{\sin x-\log x.\cos x}{{{\sin }^{2}}x}\] | |
| 5846. |
If \[y=\frac{\tan x+\cot x}{\tan x-\cot x},\]then \[\frac{dy}{dx}=\] |
| A. | \[2\tan 2x\sec 2x\] |
| B. | \[\tan 2x\sec 2x\] |
| C. | \[-\tan 2x\sec 2x\] |
| D. | \[-2\tan 2x\sec 2x\] |
| Answer» E. | |
| 5847. |
If \[y={{x}^{2}}\log x+\frac{2}{\sqrt{x}},\] then \[\frac{dy}{dx}=\] |
| A. | \[x+2x\log x-\frac{1}{\sqrt{x}}\] |
| B. | \[x+2x\log x-\frac{1}{{{x}^{3/2}}}\] |
| C. | \[x+2x\log x-\frac{2}{{{x}^{3/2}}}\] |
| D. | None of these |
| Answer» C. \[x+2x\log x-\frac{2}{{{x}^{3/2}}}\] | |
| 5848. |
If \[y={{t}^{4/3}}-3{{t}^{-2/3}}\], then \[dy/dt\]= |
| A. | \[\frac{2{{t}^{2}}+3}{3{{t}^{5/3}}}\] |
| B. | \[\frac{2{{t}^{2}}+3}{{{t}^{5/3}}}\] |
| C. | \[\frac{2(2{{t}^{2}}+3)}{{{t}^{5/3}}}\] |
| D. | \[\frac{2(2{{t}^{2}}+3)}{3{{t}^{5/3}}}\] |
| Answer» E. | |
| 5849. |
\[\frac{d}{dx}{{\sin }^{-1}}(3x-4{{x}^{3}})=\] [RPET 2003] |
| A. | \[\frac{3}{\sqrt{1-{{x}^{2}}}}\] |
| B. | \[\frac{-3}{\sqrt{1-{{x}^{2}}}}\] |
| C. | \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| D. | \[\frac{-1}{\sqrt{1-{{x}^{2}}}}\] |
| Answer» B. \[\frac{-3}{\sqrt{1-{{x}^{2}}}}\] | |
| 5850. |
\[\frac{d}{dx}\left( \frac{1}{{{x}^{4}}\sec x} \right)=\] |
| A. | \[\frac{x\sin x+4\cos x}{{{x}^{5}}}\] |
| B. | \[\frac{-(x\sin x+4\cos x)}{{{x}^{5}}}\] |
| C. | \[\frac{4\cos x-x\sin x}{{{x}^{5}}}\] |
| D. | None of these |
| Answer» C. \[\frac{4\cos x-x\sin x}{{{x}^{5}}}\] | |