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.
| 51. |
If \[f(x)={{\log }_{x}}(\log x),\]then \[f'(x)\]at \[x=e\]is [IIT 1985; RPET 2000; MP PET 2000; Karnataka CET 2002; Pb. CET 2002] |
| A. | e |
| B. | \[\frac{1}{e}\] |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 52. |
If \[r={{[2\varphi +{{\cos }^{2}}(2\varphi +\pi /4)]}^{1/2}}\] then what is the value of the derivative of \[dr/d\varphi \] at \[\varphi =\pi /4\] [Orissa JEE 2005] |
| A. | \[2\,{{\left( \frac{1}{\pi +1} \right)}^{1/2}}\] |
| B. | \[2\,{{\left( \frac{2}{\pi +1} \right)}^{-1/2}}\] |
| C. | \[2\,{{\left( \frac{1}{\pi +1} \right)}^{-1/2}}\] |
| D. | \[2\,{{\left( \frac{2}{\pi +1} \right)}^{1/2}}\] |
| Answer» E. | |
| 53. |
The derivative of \[f(x)=x|x|\] is [SCRA 1996] |
| A. | \[2x\] |
| B. | ? 2x |
| C. | \[2{{x}^{2}}\] |
| D. | \[2|x|\] |
| Answer» E. | |