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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.
| 3851. |
If \[{{\sin }^{-1}}\frac{1}{2}={{\tan }^{-1}}x,\]then x = |
| A. | \[\sqrt{3}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{\sqrt{2}}\] | |
| 3852. |
If \[{{\tan }^{-1}}2x+{{\tan }^{-1}}3x=\frac{\pi }{4}\], then x = [Roorkee 1978, 80; MNR 1986; Pb. CET 2001; Karnataka CET 2002] |
| A. | -1 |
| B. | \[\frac{1}{6}\] |
| C. | \[-1,\,\frac{1}{6}\] |
| D. | None of these |
| Answer» C. \[-1,\,\frac{1}{6}\] | |
| 3853. |
\[\cos \left[ 2{{\cos }^{-1}}\frac{1}{5}+{{\sin }^{-1}}\frac{1}{5} \right]=\] [IIT 1981] |
| A. | \[\frac{2\sqrt{6}}{5}\] |
| B. | \[-\frac{2\sqrt{6}}{5}\] |
| C. | \[\frac{1}{5}\] |
| D. | \[-\frac{1}{5}\] |
| Answer» C. \[\frac{1}{5}\] | |
| 3854. |
\[{{\cos }^{-1}}\sqrt{1-x}+{{\sin }^{-1}}\sqrt{1-x}=\] |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 3855. |
If \[{{\tan }^{-1}}\frac{x-1}{x+2}+{{\tan }^{-1}}\frac{x+1}{x+2}=\frac{\pi }{4}\], then x = |
| A. | \[\frac{1}{\sqrt{2}}\] |
| B. | \[-\frac{1}{\sqrt{2}}\] |
| C. | \[\pm \sqrt{\frac{5}{2}}\] |
| D. | \[\pm \frac{1}{2}\] |
| Answer» D. \[\pm \frac{1}{2}\] | |
| 3856. |
If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\frac{\pi }{2},\]then [Karnataka CET 1996] |
| A. | \[x+y+z-xyz=0\] |
| B. | \[x+y+z+xyz=0\] |
| C. | \[xy+yz+zx+1=0\] |
| D. | \[xy+yz+zx-1=0\] |
| Answer» E. | |
| 3857. |
If \[{{\tan }^{-1}}x-{{\tan }^{-1}}y={{\tan }^{-1}}A,\]then A = [MP PET 1988] |
| A. | \[x-y\] |
| B. | \[x+y\] |
| C. | \[\frac{x-y}{1+xy}\] |
| D. | \[\frac{x+y}{1-xy}\] |
| Answer» D. \[\frac{x+y}{1-xy}\] | |
| 3858. |
If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=\pi \], then [Roorkee 1994] |
| A. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+xyz=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+xyz=1\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz=1\] |
| Answer» E. | |
| 3859. |
\[{{\cot }^{-1}}\frac{3}{4}+{{\sin }^{-1}}\frac{5}{13}=\] |
| A. | \[{{\sin }^{-1}}\frac{63}{65}\] |
| B. | \[{{\sin }^{-1}}\frac{12}{13}\] |
| C. | \[{{\sin }^{-1}}\frac{65}{68}\] |
| D. | \[{{\sin }^{-1}}\frac{5}{12}\] |
| Answer» B. \[{{\sin }^{-1}}\frac{12}{13}\] | |
| 3860. |
\[{{\tan }^{-1}}1+{{\tan }^{-1}}2+{{\tan }^{-1}}3=\] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | 0 |
| D. | None of these |
| Answer» E. | |
| 3861. |
\[\tan \left[ {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right]\]= [IIT 1983; EAMCET 1988; MP PET 1990; MNR 1992] |
| A. | 42887 |
| B. | 44364 |
| C. | 42552 |
| D. | 44393 |
| Answer» C. 42552 | |
| 3862. |
\[\tan \left( {{90}^{o}}-{{\cot }^{-1}}\frac{1}{3} \right)=\] |
| A. | 3 |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{1}{\sqrt{10}}\] |
| Answer» D. \[\frac{1}{\sqrt{10}}\] | |
| 3863. |
\[2{{\tan }^{-1}}\frac{1}{3}+{{\tan }^{-1}}\frac{1}{2}=\] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{\tan }^{-1}}2\] |
| Answer» E. | |
| 3864. |
\[{{\sin }^{-1}}x+{{\sin }^{-1}}\frac{1}{x}+{{\cos }^{-1}}x+{{\cos }^{-1}}\frac{1}{x}=\] |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{3\pi }{2}\] |
| D. | None of these |
| Answer» B. \[\frac{\pi }{2}\] | |
| 3865. |
\[{{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{3}{5}=\] |
| A. | \[{{\tan }^{-1}}\frac{27}{11}\] |
| B. | \[{{\sin }^{-1}}\frac{11}{27}\] |
| C. | \[{{\cos }^{-1}}\frac{11}{27}\] |
| D. | None of these |
| Answer» B. \[{{\sin }^{-1}}\frac{11}{27}\] | |
| 3866. |
If \[\sin ({{\cot }^{-1}}(x+1)=\cos ({{\tan }^{-1}}x)\], then x = [IIT Screening 2004] |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | 0 |
| D. | \[\frac{9}{4}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 3867. |
\[\sin [{{\cot }^{-1}}(\cos {{\tan }^{-1}}x)]\]= |
| A. | \[\frac{x}{\sqrt{{{x}^{2}}+2}}\] |
| B. | \[\frac{x}{\sqrt{{{x}^{2}}+1}}\] |
| C. | \[\frac{1}{\sqrt{{{x}^{2}}+2}}\] |
| D. | \[\sqrt{\frac{{{x}^{2}}+1}{{{x}^{2}}+2}}\] |
| Answer» E. | |
| 3868. |
\[\sin \left[ \frac{\pi }{2}-{{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right) \right]=\] |
| A. | \[\frac{\sqrt{3}}{2}\] |
| B. | \[-\frac{\sqrt{3}}{2}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[-\frac{1}{2}\] |
| Answer» D. \[-\frac{1}{2}\] | |
| 3869. |
If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y+{{\sin }^{-1}}z=\frac{\pi }{2}\], then the value of \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2xyz\]is equal to [Pb. CET 2002] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 3870. |
The value of \[\cos ({{\tan }^{-1}}(\tan 2))\]is [AMU 2002] |
| A. | \[\frac{1}{\sqrt{5}}\] |
| B. | \[-\frac{1}{\sqrt{5}}\] |
| C. | \[\cos \,2\] |
| D. | \[-\cos 2\] |
| Answer» D. \[-\cos 2\] | |
| 3871. |
\[{{\cot }^{-1}}(-\sqrt{3})\]= |
| A. | \[-\frac{\pi }{6}\] |
| B. | \[\frac{5\pi }{6}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | \[\frac{2\pi }{3}\] |
| Answer» C. \[\frac{\pi }{3}\] | |
| 3872. |
The solution set of the equation \[{{\sin }^{-1}}x=2{{\tan }^{-1}}x\] is [AMU 2002] |
| A. | {1, 2} |
| B. | {-1, 2} |
| C. | {-1, 1, 0} |
| D. | {1, 1/2, 0} |
| Answer» D. {1, 1/2, 0} | |
| 3873. |
If \[\theta ={{\sin }^{-1}}[\sin (-{{600}^{o}})]\], then one of the possible value of \[\theta \]is [Kerala (Engg.) 2002] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{2\pi }{3}\] |
| D. | \[\frac{-2\pi }{3}\] |
| Answer» B. \[\frac{\pi }{2}\] | |
| 3874. |
The range of \[{{\tan }^{-1}}\]x is [DCE 2002] |
| A. | \[\left( \pi ,\frac{\pi }{2} \right)\] |
| B. | \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] |
| C. | \[(-\pi ,\,\,\pi )\] |
| D. | \[(0,\pi )\] |
| Answer» C. \[(-\pi ,\,\,\pi )\] | |
| 3875. |
\[\sec (\text{cose}{{\text{c}}^{-1}}x)\] is equal to [Kurukshetra CEE 2001] |
| A. | \[\text{cosec}({{\sec }^{-1}}x)\] |
| B. | \[\cot x\] |
| C. | \[\pi \] |
| D. | None of these |
| Answer» B. \[\cot x\] | |
| 3876. |
The value of x which satisfies the equation \[{{\tan }^{-1}}x=\] \[{{\sin }^{-1}}\left( \frac{3}{\sqrt{10}} \right)\] is [Pb. CET 1999] |
| A. | 3 |
| B. | -3 |
| C. | \[\frac{1}{3}\] |
| D. | \[-\frac{1}{3}\] |
| Answer» B. -3 | |
| 3877. |
\[{{\left[ \sin \left( {{\tan }^{-1}}\frac{3}{4} \right) \right]}^{2}}=\] [EAMCET 1983] |
| A. | \[\frac{3}{5}\] |
| B. | \[\frac{5}{3}\] |
| C. | \[\frac{9}{25}\] |
| D. | \[\frac{25}{9}\] |
| Answer» D. \[\frac{25}{9}\] | |
| 3878. |
If \[x\]takes non-positive permissible value, then \[{{\sin }^{-1}}x\]= |
| A. | \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] |
| B. | \[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] |
| C. | \[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\] |
| D. | \[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\] |
| Answer» C. \[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\] | |
| 3879. |
The smallest and the largest values of \[{{\tan }^{-1}}\left( \frac{1-x}{1+x} \right)\text{ },\,\,0\le x\le 1\]are |
| A. | \[0,\,\,\pi \] |
| B. | \[0,\,\frac{\pi }{4}\] |
| C. | \[-\frac{\pi }{4},\frac{\pi }{4}\] |
| D. | \[\frac{\pi }{4},\,\frac{\pi }{2}\] |
| Answer» C. \[-\frac{\pi }{4},\frac{\pi }{4}\] | |
| 3880. |
The value of \[{{\sin }^{-1}}(\sin 10)\]is |
| A. | 10 |
| B. | \[10-3\pi \] |
| C. | \[3\pi -10\] |
| D. | None of these |
| Answer» D. None of these | |
| 3881. |
\[\cos \text{ }\left( {{\sin }^{-1}}\frac{5}{13} \right)=\] |
| A. | \[\frac{12}{13}\] |
| B. | \[-\frac{12}{13}\] |
| C. | \[\frac{5}{12}\] |
| D. | None of these |
| Answer» B. \[-\frac{12}{13}\] | |
| 3882. |
If \[\pi \le x\le 2\pi \], then \[{{\cos }^{-1}}(\cos x)\]is equal to |
| A. | x |
| B. | \[-x\] |
| C. | \[2\pi +x\] |
| D. | \[2\pi -x\] |
| Answer» E. | |
| 3883. |
If \[\frac{\pi }{2}\le x\le \frac{3\pi }{2},\]then\[{{\sin }^{-1}}(\sin x)\]is equal to |
| A. | x |
| B. | \[-x\] |
| C. | \[\pi +x\] |
| D. | \[\pi -x\] |
| Answer» E. | |
| 3884. |
\[\cot \,\,\left[ {{\cos }^{-1}}\left( \frac{7}{25} \right) \right]=\] [Karnataka CET 1994] |
| A. | \[\frac{25}{24}\] |
| B. | \[\frac{25}{7}\] |
| C. | \[\frac{24}{25}\] |
| D. | None of these |
| Answer» E. | |
| 3885. |
The domain of \[{{\sin }^{-1}}x\]is [Roorkee 1993] |
| A. | \[(-\pi ,\pi )\] |
| B. | [-1, 1] |
| C. | \[(0,\,2\pi )\] |
| D. | \[(-\infty ,\,\infty )\] |
| Answer» C. \[(0,\,2\pi )\] | |
| 3886. |
\[\tan ({{\cos }^{-1}}x)\] is equal to [IIT 1993] |
| A. | \[\frac{\sqrt{1-{{x}^{2}}}}{x}\] |
| B. | \[\frac{x}{1+{{x}^{2}}}\] |
| C. | \[\frac{\sqrt{1+{{x}^{2}}}}{x}\] |
| D. | \[\sqrt{1-{{x}^{2}}}\] |
| Answer» B. \[\frac{x}{1+{{x}^{2}}}\] | |
| 3887. |
If \[{{\sin }^{-1}}x=\theta +\beta \]and \[{{\sin }^{-1}}y=\theta -\beta ,\]then \[1+xy=\] |
| A. | \[{{\sin }^{2}}\theta +{{\sin }^{2}}\beta \] |
| B. | \[{{\sin }^{2}}\theta +{{\cos }^{2}}\beta \] |
| C. | \[{{\cos }^{2}}\theta +{{\cos }^{2}}\beta \] |
| D. | \[{{\cos }^{2}}\theta +{{\sin }^{2}}\beta \] |
| Answer» C. \[{{\cos }^{2}}\theta +{{\cos }^{2}}\beta \] | |
| 3888. |
If \[{{\sin }^{-1}}\frac{1}{3}+{{\sin }^{-1}}\frac{2}{3}={{\sin }^{-1}}x,\]then x is equal to [Roorkee 1995] |
| A. | 0 |
| B. | \[\frac{\sqrt{5}-4\sqrt{2}}{9}\] |
| C. | \[\frac{\sqrt{5}+4\sqrt{2}}{9}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» D. \[\frac{\pi }{2}\] | |
| 3889. |
\[{{\sin }^{-1}}\frac{\sqrt{x}}{\sqrt{x+a}}\]is equal to |
| A. | \[{{\cos }^{-1}}\sqrt{\frac{x}{a}}\] |
| B. | \[\text{cose}{{\text{c}}^{-1}}\sqrt{\frac{x}{a}}\] |
| C. | \[{{\tan }^{-1}}\sqrt{\frac{x}{a}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3890. |
\[\sin ({{\cot }^{-1}}x)\] [MNR 1987; MP PET 2001; DCE 2002] |
| A. | \[\sqrt{1+{{x}^{2}}}\] |
| B. | \[x\] |
| C. | \[{{(1+{{x}^{2}})}^{-3/2}}\] |
| D. | \[{{(1+{{x}^{2}})}^{-1/2}}\] |
| Answer» E. | |
| 3891. |
The value of \[\sin {{\cot }^{-1}}\tan {{\cos }^{-1}}x\]is equal to [Bihar CEE 1974] |
| A. | x |
| B. | \[\frac{\pi }{2}\] |
| C. | 1 |
| D. | None of these |
| Answer» B. \[\frac{\pi }{2}\] | |
| 3892. |
\[{{\cos }^{-1}}\left( \cos \frac{7\pi }{6} \right)=\] |
| A. | \[\frac{7\pi }{6}\] |
| B. | \[\frac{5\pi }{6}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | None of these |
| Answer» C. \[\frac{\pi }{6}\] | |
| 3893. |
If \[{{\tan }^{-1}}\frac{1-x}{1+x}=\frac{1}{2}{{\tan }^{-1}}x\], then x = |
| A. | 1 |
| B. | \[\sqrt{3}\] |
| C. | \[\frac{1}{\sqrt{3}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3894. |
\[{{\sin }^{-1}}\left[ x\sqrt{1-x}-\sqrt{x}\sqrt{1-{{x}^{2}}} \right]=\] |
| A. | \[{{\sin }^{-1}}x+{{\sin }^{-1}}\sqrt{x}\] |
| B. | \[{{\sin }^{-1}}x-{{\sin }^{-1}}\sqrt{x}\] |
| C. | \[{{\sin }^{-1}}\sqrt{x}-{{\sin }^{-1}}x\] |
| D. | None of these |
| Answer» C. \[{{\sin }^{-1}}\sqrt{x}-{{\sin }^{-1}}x\] | |
| 3895. |
\[{{\sec }^{2}}({{\tan }^{-1}}2)+\text{cose}{{\text{c}}^{2}}({{\cot }^{-1}}3)=\] [EAMCET 2001] |
| A. | 5 |
| B. | 13 |
| C. | 15 |
| D. | 6 |
| Answer» D. 6 | |
| 3896. |
The principal value of \[{{\sin }^{-1}}\left( -\frac{1}{2} \right)\]is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{6}\] |
| C. | \[-\frac{\pi }{3}\] |
| D. | \[-\frac{\pi }{6}\] |
| Answer» E. | |
| 3897. |
\[\sin \text{ }\left[ 3\,{{\sin }^{-1}}\left( \frac{1}{5} \right) \right]=\] [Kerala (Engg.) 2005] |
| A. | 71/125 |
| B. | 74/125 |
| C. | 44319 |
| D. | 1/2 |
| E. | - 3/5 |
| Answer» B. 74/125 | |
| 3898. |
For the equation \[{{\cos }^{-1}}x+{{\cos }^{-1}}2x+\pi =0\], the number of real solution is [Orissa JEE 2005] |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | \[\infty \] |
| Answer» D. \[\infty \] | |
| 3899. |
The solution of \[{{\sin }^{-1}}x-{{\sin }^{-1}}2x=\pm \frac{\pi }{3}\] is [Karnataka CET 2005] |
| A. | \[\pm \frac{1}{3}\] |
| B. | \[\pm \frac{1}{4}\] |
| C. | \[\pm \frac{\sqrt{3}}{2}\] |
| D. | \[\pm \frac{1}{2}\] |
| Answer» E. | |
| 3900. |
If \[\angle A={{90}^{o}}\] in the triangle ABC, then \[{{\tan }^{-1}}\left( \frac{c}{a+b} \right)+{{\tan }^{-1}}\left( \frac{b}{a+c} \right)=\] [Kerala (Engg.) 2005] |
| A. | 0 |
| B. | 1 |
| C. | \[\pi /4\] |
| D. | \[\pi /6\] |
| E. | \[\pi /8\] |
| Answer» D. \[\pi /6\] | |