Explore topic-wise MCQs in Mathematics.

This section includes 6 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

\[\sum\limits_{m=1}^{n}{{{\tan }^{-1}}}\left( \frac{2m}{{{m}^{4}}+{{m}^{2}}+2} \right)\]is equal to

A. \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n}{{{n}^{2}}+n+2} \right)\]
B. \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}-n}{{{n}^{2}}-n+2} \right)\]
C. \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}+n+2}{{{n}^{2}}+n} \right)\]
D. None of these
Answer» B. \[{{\tan }^{-1}}\left( \frac{{{n}^{2}}-n}{{{n}^{2}}-n+2} \right)\]
Discussion
2.

\[{{\tan }^{-1}}\,\left[ \frac{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}} \right]=\]

A. \[\frac{\pi }{4}+\frac{1}{2}{{\cos }^{-1}}{{x}^{2}}\]
B. \[\frac{\pi }{4}+{{\cos }^{-1}}{{x}^{2}}\]
C. \[\frac{\pi }{4}+\frac{1}{2}{{\cos }^{-1}}x\]
D. \[\frac{\pi }{4}-\frac{1}{2}{{\cos }^{-1}}{{x}^{2}}\]
Answer» B. \[\frac{\pi }{4}+{{\cos }^{-1}}{{x}^{2}}\]
Discussion
3.

The equation \[{{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]has

A. No solution
B. Unique solution
C. Infinite number of solutions
D. None of these
Answer» C. Infinite number of solutions
Discussion
4.

If \[{{\sin }^{-1}}x=\frac{\pi }{5}\] for some \[x\in (-1,\,1)\], then the value of \[{{\cos }^{-1}}x\] is[IIT 1992]

A. \[\frac{3\pi }{10}\]
B. \[\frac{5\pi }{10}\]
C. \[\frac{7\pi }{10}\]
D. \[\frac{9\pi }{10}\]
Answer» B. \[\frac{5\pi }{10}\]
Discussion
5.

If \[\tan ({{\cos }^{-1}}x)=\sin \left( {{\cot }^{-1}}\frac{1}{2} \right)\], then x =

A. \[\pm \frac{5}{3}\]
B. \[\pm \frac{\sqrt{5}}{3}\]
C. \[\pm \frac{5}{\sqrt{3}}\]
D. None of these
Answer» C. \[\pm \frac{5}{\sqrt{3}}\]
Discussion
6.

If \[\theta ={{\tan }^{-1}}a,\varphi ={{\tan }^{-1}}b\] and \[ab=-1,\] then \[\theta -\varphi =\]

A. 0
B. \[\frac{\pi }{4}\]
C. \[\frac{\pi }{2}\]
D. None of these
Answer» D. None of these
Discussion