MCQOPTIONS
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MCQOPTIONS
This section includes 53 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If \[y=\sqrt{x+\sqrt{x+\sqrt{x+........\text{to}}}}\infty \,,\,\text{then}\frac{dy}{dx}=\] [RPET 2002] |
| A. | \[\frac{x}{2y-1}\] |
| B. | \[\frac{2}{2y-1}\] |
| C. | \[\frac{-1}{2y-1}\] |
| D. | \[\frac{1}{2y-1}\] |
| Answer» E. | |
| 2. |
If \[y={{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+......\infty }}},\]then \[\frac{dy}{dx}=\] |
| A. | \[\frac{2xy}{2y-{{x}^{2}}}\] |
| B. | \[\frac{xy}{y+{{x}^{2}}}\] |
| C. | \[\frac{xy}{y-{{x}^{2}}}\] |
| D. | \[\frac{2xy}{2+\frac{{{x}^{2}}}{y}}\] |
| Answer» B. \[\frac{xy}{y+{{x}^{2}}}\] | |
| 3. |
\[\frac{d}{dx}\{{{(\sin x)}^{x}}\}\]=[DSSE 1985, 87; AISSE 1983] |
| A. | \[\left[ \frac{x\cos x+\sin x\log \sin x}{\sin x} \right]\] |
| B. | \[{{(\sin x)}^{x}}\left[ \frac{x\cos x+\sin x\log \sin x}{\sin x} \right]\] |
| C. | \[{{(\sin x)}^{x}}\left[ \frac{x\sin x+\sin x\log \sin x}{\sin x} \right]\] |
| D. | None of these |
| Answer» C. \[{{(\sin x)}^{x}}\left[ \frac{x\sin x+\sin x\log \sin x}{\sin x} \right]\] | |
| 4. |
If \[y={{(\sin x)}^{{{(\sin x)}^{(\sin x)......\infty }}}}\], then \[\frac{dy}{dx}=\] |
| A. | \[\frac{{{y}^{2}}\cot x}{1-y\log \sin x}\] |
| B. | \[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\] |
| C. | \[\frac{y\cot x}{1-y\log \sin x}\] |
| D. | \[\frac{y\cot x}{1+y\log \sin x}\] |
| Answer» B. \[\frac{{{y}^{2}}\cot x}{1+y\log \sin x}\] | |
| 5. |
If \[x=a{{t}^{2}},y=2at\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=\] [Karnataka CET 1993] |
| A. | \[-\frac{1}{{{t}^{2}}}\] |
| B. | \[\frac{1}{2a{{t}^{3}}}\] |
| C. | \[-\frac{1}{{{t}^{3}}}\] |
| D. | \[-\frac{1}{2a{{t}^{3}}}\] |
| Answer» E. | |
| 6. |
If \[y={{(1+x)}^{x}},\]then \[\frac{dy}{dx}=\] |
| A. | \[{{(1+x)}^{x}}\left[ \frac{x}{1+x}+\log ex \right]\] |
| B. | \[\frac{x}{1+x}+\log (1+x)\] |
| C. | \[{{(1+x)}^{x}}\left[ \frac{x}{1+x}+\log (1+x) \right]\] |
| D. | None of these |
| Answer» D. None of these | |
| 7. |
If \[x=a\left( t-\frac{1}{t} \right)\,,y=a\] \[\left( t+\frac{1}{t} \right)\]then \[\frac{dy}{dx}=\] [Karnataka CET 2004] |
| A. | \[\frac{y}{x}\] |
| B. | \[\frac{-y}{x}\] |
| C. | \[\frac{x}{y}\] |
| D. | \[\frac{-x}{y}\] |
| Answer» D. \[\frac{-x}{y}\] | |
| 8. |
If \[{{x}^{3}}+{{y}^{3}}-3axy=0\], then \[\frac{dy}{dx}\] equals[RPET 1996] |
| A. | \[\frac{ay-{{x}^{2}}}{{{y}^{2}}-ax}\] |
| B. | \[\frac{ay-{{x}^{2}}}{ay-{{y}^{2}}}\] |
| C. | \[\frac{{{x}^{2}}+ay}{{{y}^{2}}+ax}\] |
| D. | \[\frac{{{x}^{2}}+ay}{ax-{{y}^{2}}}\] |
| Answer» B. \[\frac{ay-{{x}^{2}}}{ay-{{y}^{2}}}\] | |
| 9. |
If \[x=a\sin \theta \] and \[y=b\]\[\cos \theta ,\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is [UPSEAT 2002] |
| A. | \[\frac{a}{{{b}^{2}}}{{\sec }^{2}}\theta \] |
| B. | \[\frac{-b}{a}{{\sec }^{2}}\theta \] |
| C. | \[\frac{-b}{{{a}^{2}}}{{\sec }^{3}}\theta \] |
| D. | \[\frac{-b}{{{a}^{2}}}{{\sec }^{3}}\theta \] |
| Answer» D. \[\frac{-b}{{{a}^{2}}}{{\sec }^{3}}\theta \] | |
| 10. |
If \[x=\frac{3at}{1+{{t}^{3}}},y=\frac{3a{{t}^{2}}}{1+{{t}^{3}}},\]then \[\frac{dy}{dx}\]= |
| A. | \[\frac{t(2+{{t}^{3}})}{1-2{{t}^{3}}}\] |
| B. | \[\frac{t(2-{{t}^{3}})}{1-2{{t}^{3}}}\] |
| C. | \[\frac{t(2+{{t}^{3}})}{1+2{{t}^{3}}}\] |
| D. | \[\frac{t(2-{{t}^{3}})}{1+2{{t}^{3}}}\] |
| Answer» C. \[\frac{t(2+{{t}^{3}})}{1+2{{t}^{3}}}\] | |
| 11. |
If \[{{x}^{3}}+8xy+{{y}^{3}}=64\],then \[\frac{dy}{dx}=\] [AI CBSE 1979] |
| A. | \[-\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\] |
| B. | \[\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\] |
| C. | \[\frac{3x+8{{y}^{2}}}{8{{x}^{2}}+3y}\] |
| D. | None of these |
| Answer» B. \[\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\] | |
| 12. |
If \[\sin y=x\sin (a+y),\]then \[\frac{dy}{dx}=\] [Karnataka CET 2000; UPSEAT 2001; Pb. CET 2001; Kerala (Engg.) 2005] |
| A. | \[\frac{{{\sin }^{2}}(a+y)}{\sin (a+2y)}\] |
| B. | \[\frac{{{\sin }^{2}}(a+y)}{\sin (a+2y)}\] |
| C. | \[\frac{{{\sin }^{2}}(a+y)}{\sin a}\] |
| D. | \[\frac{{{\sin }^{2}}(a+y)}{\cos a}\] |
| Answer» D. \[\frac{{{\sin }^{2}}(a+y)}{\cos a}\] | |
| 13. |
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. \[\frac{\sin x+{{e}^{x}}}{{{(\cos x+{{e}^{x}})}^{3}}}\] | |
| 14. |
If \[y={{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}},\]where \[0 |
| A. | \[\frac{2}{1+{{x}^{2}}}\] |
| B. | \[\frac{2x}{1+{{x}^{2}}}\] |
| C. | \[\frac{-2}{1+{{x}^{2}}}\] |
| D. | \[\frac{-x}{1+{{x}^{2}}}\] |
| Answer» B. \[\frac{2x}{1+{{x}^{2}}}\] | |
| 15. |
If \[x=\log p\]and \[y=\frac{1}{p}\], then |
| A. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2p=0\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\] |
| C. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}=0\] |
| D. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}=0\] |
| Answer» D. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}=0\] | |
| 16. |
\[\frac{d}{dx}\left( {{\tan }^{-1}}\frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\] 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. \[\frac{{{x}^{2}}}{2\sqrt{1+{{x}^{2}}}(\sqrt{1+{{x}^{2}}}-1)}\] | |
| 17. |
If \[y=\sin (2{{\sin }^{-1}}x),\]then \[\frac{dy}{dx}=\] [AI CBSE 1983] |
| A. | \[\frac{2-4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\] |
| B. | \[\frac{2+4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\] |
| C. | \[\frac{2-4{{x}^{2}}}{\sqrt{1+{{x}^{2}}}}\] |
| D. | \[\frac{2+4{{x}^{2}}}{\sqrt{1+{{x}^{2}}}}\] |
| Answer» B. \[\frac{2+4{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}\] | |
| 18. |
\[\frac{d}{dx}\left\{ \log \left( \frac{{{e}^{x}}}{1+{{e}^{x}}} \right) \right\}=\] |
| A. | \[\frac{1}{1-{{e}^{x}}}\] |
| B. | \[-\frac{1}{1+{{e}^{x}}}\] |
| C. | \[-\frac{1}{1-{{e}^{x}}}\] |
| D. | None of these |
| Answer» E. | |
| 19. |
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 | |
| 20. |
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. | |
| 21. |
\[\frac{d}{dx}{{e}^{x\sin x}}=\] [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. \[{{e}^{x\sin x}}(\cos x+x\sin x)\] | |
| 22. |
\[\frac{d}{dx}\sqrt{{{\sec }^{2}}x+\text{cose}{{\text{c}}^{2}}x}=\][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. \[-4\cos \text{ec }x.\cot 2x\] | |
| 23. |
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. | |
| 24. |
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. \[\frac{ay}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\] | |
| 25. |
\[\frac{d}{dx}\left( \frac{{{e}^{x}}}{1+{{x}^{2}}} \right)=\] |
| A. | \[\frac{{{e}^{x}}(1+x)}{{{(1+{{x}^{2}})}^{2}}}\] |
| B. | \[\frac{{{e}^{x}}{{(1-x)}^{2}}}{{{(1+{{x}^{2}})}^{2}}}\] |
| C. | \[\frac{{{e}^{x}}{{(1+x)}^{2}}}{(1+{{x}^{2}})}\] |
| D. | \[\frac{{{e}^{x}}{{(1-x)}^{2}}}{(1+{{x}^{2}})}\] |
| Answer» C. \[\frac{{{e}^{x}}{{(1+x)}^{2}}}{(1+{{x}^{2}})}\] | |
| 26. |
\[\frac{d}{dx}{{e}^{x+3\log x}}=\] |
| A. | \[{{e}^{x}}.{{x}^{2}}(x+3)\] |
| B. | \[{{e}^{x}}.x(x+3)\] |
| C. | \[{{e}^{x}}+\frac{3}{x}\] |
| D. | None of these |
| Answer» B. \[{{e}^{x}}.x(x+3)\] | |
| 27. |
If \[y=x+\frac{1}{x}\], then |
| A. | \[{{x}^{2}}\frac{dy}{dx}+xy=0\] |
| B. | \[{{x}^{2}}\frac{dy}{dx}+xy+2=0\] |
| C. | \[{{x}^{2}}\frac{dy}{dx}-xy+2=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 28. |
If \[{{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}\], then \[\frac{dy}{dx}=\] |
| A. | \[{{\left( \frac{y}{x} \right)}^{1/3}}\] |
| B. | \[-{{\left( \frac{y}{x} \right)}^{1/3}}\] |
| C. | \[{{\left( \frac{x}{y} \right)}^{1/3}}\] |
| D. | \[-{{\left( \frac{x}{y} \right)}^{1/3}}\] |
| Answer» C. \[{{\left( \frac{x}{y} \right)}^{1/3}}\] | |
| 29. |
If \[y={{\log }_{10}}x+{{\log }_{x}}10+{{\log }_{x}}x+{{\log }_{10}}10,\]then \[\frac{dy}{dx}=\] |
| A. | \[\frac{1}{x{{\log }_{e}}10}-\frac{{{\log }_{e}}10}{x{{({{\log }_{e}}x)}^{2}}}\] |
| B. | \[\frac{1}{x{{\log }_{e}}10}-\frac{1}{x{{\log }_{10}}e}\] |
| C. | \[\frac{1}{x{{\log }_{e}}10}-\frac{{{\log }_{e}}10}{x{{({{\log }_{e}}x)}^{2}}}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{x{{\log }_{e}}10}-\frac{1}{x{{\log }_{10}}e}\] | |
| 30. |
\[\frac{d}{dx}\left( {{\tan }^{-1}}\sqrt{\frac{1+\cos \frac{x}{2}}{1-\cos \frac{x}{2}}} \right)\]is equal to [MP PET 2004] |
| A. | \[-\frac{1}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[-\frac{1}{2}\] |
| D. | \[\frac{1}{4}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 31. |
If \[y={{(\cos {{x}^{2}})}^{2}}\]then \[\frac{dy}{dx}\]is equal to [Pb. CET 2004] |
| A. | \[-4x\sin 2{{x}^{2}}\] |
| B. | \[-x\sin {{x}^{2}}\] |
| C. | \[-2x\sin 2{{x}^{2}}\] |
| D. | \[-x\cos 2{{x}^{2}}\] |
| Answer» D. \[-x\cos 2{{x}^{2}}\] | |
| 32. |
\[\frac{d}{dx}\log |x|\text{ }=......,(x\ne 0)\] |
| A. | \[\frac{1}{x}\] |
| B. | \[-\frac{1}{x}\] |
| C. | x |
| D. | \[-x\] |
| Answer» B. \[-\frac{1}{x}\] | |
| 33. |
The value of \[\frac{d}{dx}[|x-1|+|x-5|]\] at \[x=3\] is [MP PET 2000] |
| A. | ? 2 |
| B. | 0 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 34. |
If \[y=\frac{{{(1-x)}^{2}}}{{{x}^{2}}}\], then \[\frac{dy}{dx}\]is[MP PET 1999] |
| A. | \[\frac{2}{{{x}^{2}}}+\frac{2}{{{x}^{3}}}\] |
| B. | \[-\frac{2}{{{x}^{2}}}+\frac{2}{{{x}^{3}}}\] |
| C. | \[-\frac{2}{{{x}^{2}}}-\frac{2}{{{x}^{3}}}\] |
| D. | \[-\frac{2}{{{x}^{3}}}+\frac{2}{{{x}^{2}}}\] |
| Answer» E. | |
| 35. |
If \[y={{e}^{x}}\log x\], then \[\frac{dy}{dx}\]is[SCRA 1996] |
| A. | \[\frac{{{e}^{x}}}{x}\] |
| B. | \[{{e}^{x}}\left( \frac{1}{x}+x\log x \right)\] |
| C. | \[{{e}^{x}}\left( \frac{1}{x}+\log x \right)\] |
| D. | \[\frac{{{e}^{x}}}{\log x}\] |
| Answer» D. \[\frac{{{e}^{x}}}{\log x}\] | |
| 36. |
If \[f(x)=3{{e}^{{{x}^{2}}}}\],then \[f'(x)-2xf(x)+\frac{1}{3}f(0)-f'(0)=\] |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{7}{3}{{e}^{{{x}^{2}}}}\] |
| D. | None of these |
| Answer» C. \[\frac{7}{3}{{e}^{{{x}^{2}}}}\] | |
| 37. |
For the curve \[\sqrt{x}+\sqrt{y}=1,\frac{dy}{dx}\]at \[\left( \frac{1}{4},\frac{1}{4} \right)\]is [Karnataka CET 1993] |
| A. | ½ |
| B. | 1 |
| C. | ?1 |
| D. | 2 |
| Answer» D. 2 | |
| 38. |
If \[y={{\sin }^{-1}}\sqrt{(1-x)}+{{\cos }^{-1}}\sqrt{x}\], then \[\frac{dy}{dx}=\] |
| A. | \[\frac{1}{\sqrt{x(1-x)}}\] |
| B. | \[\frac{-1}{\sqrt{x(1-x)}}\] |
| C. | \[\frac{1}{\sqrt{x(1+x)}}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{\sqrt{x(1+x)}}\] | |
| 39. |
\[\frac{d}{dx}\left( {{\tan }^{-1}}\frac{\cos x}{1+\sin x} \right)=\] [AISSE 1984, 85; MNR 1983; RPET 1997] |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[-1\] |
| D. | 1 |
| Answer» B. \[\frac{1}{2}\] | |
| 40. |
\[\frac{d}{dx}({{e}^{{{x}^{3}}}})\] is equal to [RPET 1995] |
| A. | \[3x{{e}^{{{x}^{3}}}}\] |
| B. | \[3{{x}^{2}}{{e}^{{{x}^{3}}}}\] |
| C. | \[3x{{\left( {{e}^{{{x}^{3}}}} \right)}^{2}}\] |
| D. | \[2{{x}^{2}}{{e}^{{{x}^{3}}}}\] |
| Answer» C. \[3x{{\left( {{e}^{{{x}^{3}}}} \right)}^{2}}\] | |
| 41. |
If \[y=(1+{{x}^{1/4}})(1+{{x}^{1/2}})(1-{{x}^{1/4}})\], then \[\frac{dy}{dx}\]= [MP PET 1994] |
| A. | 1 |
| B. | ? 1 |
| C. | x |
| D. | \[\sqrt{x}\] |
| Answer» C. x | |
| 42. |
If \[y={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}},\]then \[{{y}_{n}}=\] |
| A. | \[n!\] |
| B. | \[n!{{a}_{n}}x\] |
| C. | \[n!{{a}_{n}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 43. |
The derivative of \[F[f\{\varphi (x)\}]\] is [AMU 2001] |
| A. | \[{F}'\,[f\,\{\varphi \,(x)\}]\] |
| B. | \[F\,[f\,\{\varphi \,(x)\}\,]\,{f}'\{\varphi (x)\}\] |
| C. | \[{F}'[f\,\{\varphi \,(x)\}]\,{f}'\{\varphi (x)\}\] |
| D. | \[{F}'\,[f\,\{\varphi \,(x)\}]\,{f}'\{\varphi (x)\}\,{\varphi }'\,(x)\] |
| Answer» E. | |
| 44. |
\[f(x)\] and \[g(x)\] are two differentiable function on \[[0,\,2]\] such that \[f''(x)-g''(x)=0,f'(1)=2,g'(1)=4\], \[f(2)=3\], \[g(2)=9,\] then \[f(x)-g(x)\] at \[x=3/2\] is [AIEEE 2002] |
| A. | 0 |
| B. | 2 |
| C. | 10 |
| D. | ? 5 |
| Answer» E. | |
| 45. |
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 | |
| 46. |
The differential of \[{{e}^{{{x}^{3}}}}\]with respect to \[\log x\] is [Karnataka CET 2002] |
| A. | \[{{e}^{{{x}^{3}}}}\] |
| B. | \[3{{x}^{2}}{{e}^{{{x}^{3}}}}\] |
| C. | \[3{{x}^{3}}{{e}^{{{x}^{3}}}}\] |
| D. | \[3{{x}^{2}}{{e}^{{{x}^{3}}}}+3{{x}^{2}}\] |
| Answer» D. \[3{{x}^{2}}{{e}^{{{x}^{3}}}}+3{{x}^{2}}\] | |
| 47. |
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. | |
| 48. |
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. | |
| 49. |
If \[y={{\sin }^{-1}}\sqrt{1-{{x}^{2}}}\], then \[dy/dx=\] [AISSE 1987] |
| A. | \[\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| B. | \[\frac{1}{\sqrt{1+{{x}^{2}}}}\] |
| C. | \[-\frac{1}{\sqrt{1-{{x}^{2}}}}\] |
| D. | \[-\frac{1}{\sqrt{{{x}^{2}}-1}}\] |
| Answer» D. \[-\frac{1}{\sqrt{{{x}^{2}}-1}}\] | |
| 50. |
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. \[\frac{dy}{dx}=\frac{1}{x}+\cot x\] | |