MCQOPTIONS
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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.
| 4701. |
If \[\cos (\alpha -\beta )=1\] and \[\cos (\alpha +\beta )=\frac{1}{e}\], \[-\pi |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» E. | |
| 4702. |
The value of \[\cos (270{}^\circ +\theta )\,\cos (90{}^\circ -\theta )-\sin (270{}^\circ -\theta )\,\cos \theta \] is [Karnataka CET 2005] |
| A. | 0 |
| B. | -1 |
| C. | 44228 |
| D. | 1 |
| Answer» E. | |
| 4703. |
The value of \[\cos A-\sin A\]when \[A=\frac{5\pi }{4},\]is [MP PET 1990] |
| A. | \[\sqrt{2}\] |
| B. | \[\frac{1}{\sqrt{2}}\] |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 4704. |
If \[\tan A=\frac{1}{2},\tan B=\frac{1}{3},\]then \[\cos 2A=\] [CET 1989] |
| A. | \[\sin B\] |
| B. | \[\sin 2B\] |
| C. | \[\sin 3B\] |
| D. | None of these |
| Answer» C. \[\sin 3B\] | |
| 4705. |
The value of \[\tan (-945{}^\circ )\] is [MP PET 1997] |
| A. | -1 |
| B. | -2 |
| C. | -3 |
| D. | -4 |
| Answer» B. -2 | |
| 4706. |
\[(\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A=\][Roorkee 1972] |
| A. | \[\sec A\] |
| B. | \[2\sec A\] |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 4707. |
Given that \[\pi |
| A. | 2 |
| B. | \[2+4\sin \alpha \] |
| C. | \[2-4\sin \alpha \] |
| D. | None of these |
| Answer» D. None of these | |
| 4708. |
If \[x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}\], then \[xy+yz+zx=\] [EAMCET 1994] |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 4709. |
If angle \[\theta \] be divided into two parts such that the tangent of one part is \[k\] times the tangent of the other and \[\varphi \] is their difference, then \[\sin \theta =\] |
| A. | \[\frac{k+1}{k-1}\sin \varphi \] |
| B. | \[\frac{k-1}{k+1}\sin \varphi \] |
| C. | \[\frac{2k-1}{2k+1}\sin \varphi \] |
| D. | None of these |
| Answer» B. \[\frac{k-1}{k+1}\sin \varphi \] | |
| 4710. |
\[\tan \theta \sin \left( \frac{\pi }{2}+\theta \right)\cos \left( \frac{\pi }{2}-\theta \right)=\] [EAMCET 1981] |
| A. | 1 |
| B. | 0 |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | None of these |
| Answer» E. | |
| 4711. |
\[\tan A+\cot (180{}^\circ +A)+\cot (90{}^\circ +A)+\cot (360{}^\circ -A)\] [MP PET 1992] |
| A. | 0 |
| B. | \[2\tan A\] |
| C. | \[2\cot A\] |
| D. | \[2(\tan A-\cot A)\] |
| Answer» B. \[2\tan A\] | |
| 4712. |
\[\tan \left( \frac{\pi }{4}+\theta \right)-\tan \left( \frac{\pi }{4}-\theta \right)=\] |
| A. | \[2\tan 2\theta \] |
| B. | \[2\cot 2\theta \] |
| C. | \[\tan 2\theta \] |
| D. | \[\cot 2\theta \] |
| Answer» B. \[2\cot 2\theta \] | |
| 4713. |
\[\sin (\pi +\theta )\sin (\pi -\theta )\,\text{ cose}{{\text{c}}^{2}}\theta =\] [EAMCET 1980] |
| A. | 1 |
| B. | \[1\] |
| C. | \[\sin \theta \] |
| D. | \[-\sin \theta \] |
| Answer» C. \[\sin \theta \] | |
| 4714. |
If \[\pi |
| A. | \[\frac{2}{\sin \alpha }\] |
| B. | \[-\frac{2}{\sin \alpha }\] |
| C. | \[\frac{1}{\sin \alpha }\] |
| D. | \[-\frac{1}{\sin \alpha }\] |
| Answer» C. \[\frac{1}{\sin \alpha }\] | |
| 4715. |
\[\cos A+\sin (270{}^\circ +A)-\sin (270{}^\circ -A)+\cos (180{}^\circ +A)=\] [MP PET 1990] |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 4716. |
If \[x\sin 45{}^\circ {{\cos }^{2}}60{}^\circ =\frac{{{\tan }^{2}}60{}^\circ \text{cosec}30{}^\circ }{\sec 45{}^\circ {{\cot }^{2}}30{}^\circ },\] then \[x=\] |
| A. | 2 |
| B. | 4 |
| C. | 8 |
| D. | 16 |
| Answer» D. 16 | |
| 4717. |
The value of \[\cos y\cos \left( \frac{\pi }{2}-x \right)-\cos \left( \frac{\pi }{2}-y \right)\cos x\] \[+\sin y\cos \left( \frac{\pi }{2}-x \right)+\cos x\sin \left( \frac{\pi }{2}-y \right)\] is zero, if |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[x=y\] |
| D. | \[x=n\pi -\frac{\pi }{4}+y,\,\,(n\in I)\] |
| Answer» E. | |
| 4718. |
\[\sin \left( \frac{\pi }{10} \right)\sin \left( \frac{3\pi }{10} \right)=\] [MNR 1984] |
| A. | 44228 |
| B. | -0.5 |
| C. | 44287 |
| D. | 1 |
| Answer» D. 1 | |
| 4719. |
The value \[\cos 105{}^\circ +\sin 105{}^\circ \]is [MNR 1975] |
| A. | \[\frac{1}{2}\] |
| B. | 1 |
| C. | \[\sqrt{2}\] |
| D. | \[\frac{1}{\sqrt{2}}\] |
| Answer» E. | |
| 4720. |
\[\sin 15{}^\circ +\cos 105{}^\circ =\] [MP PET 1992] |
| A. | 0 |
| B. | \[2\sin 15{}^\circ \] |
| C. | \[\cos 15{}^\circ +\sin 15{}^\circ \] |
| D. | \[\sin 15{}^\circ -\cos 15{}^\circ \] |
| Answer» B. \[2\sin 15{}^\circ \] | |
| 4721. |
The value of \[6({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-9({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+4\] is [MP PET 2001] |
| A. | -3 |
| B. | 0 |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 4722. |
If \[\alpha =22{}^\circ 30',\]then \[(1+\cos \alpha )(1+\cos 3\alpha )\] \[(1+\cos 5\alpha )(1+\cos 7\alpha )\] equals [AMU 1999] |
| A. | 44409 |
| B. | 44287 |
| C. | \[\frac{1+\sqrt{2}}{2\sqrt{2}}\] |
| D. | \[\frac{\sqrt{2}-1}{\sqrt{2}+1}\] |
| Answer» B. 44287 | |
| 4723. |
The equation \[{{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta \]is possible only when |
| A. | \[2a=b\] |
| B. | \[a=b\] |
| C. | \[a=2b\] |
| D. | None of these |
| Answer» C. \[a=2b\] | |
| 4724. |
The value of \[\sin 10{}^\circ +\sin 20{}^\circ +\sin 30{}^\circ +...+\] \[\sin 360{}^\circ \] is [Pb. CET 2003] |
| A. | 1 |
| B. | 0 |
| C. | -1 |
| D. | None of these |
| Answer» C. -1 | |
| 4725. |
The value of \[\frac{\cot 54{}^\circ }{\tan 36{}^\circ }+\frac{\tan 20{}^\circ }{\cot 70{}^\circ }\] is [Karnataka CET 1999] |
| A. | 2 |
| B. | 3 |
| C. | 1 |
| D. | 0 |
| Answer» B. 3 | |
| 4726. |
\[\cos 1{}^\circ .\cos 2{}^\circ .\cos 3{}^\circ .........\cos 179{}^\circ =\] [Karnataka CET 1999; DCE 2005] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[\frac{1}{2}\] |
| Answer» B. 1 | |
| 4727. |
If \[{{\tan }^{2}}\alpha {{\tan }^{2}}\beta +{{\tan }^{2}}\beta {{\tan }^{2}}\gamma +{{\tan }^{2}}\gamma {{\tan }^{2}}\alpha \]\[+2{{\tan }^{2}}\alpha {{\tan }^{2}}\beta {{\tan }^{2}}\gamma =1,\]then the value of\[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \]is |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 4728. |
If \[{{\sin }^{2}}\theta =\frac{{{x}^{2}}+{{y}^{2}}+1}{2x}\], then x must be [UPSEAT 2004] |
| A. | -3 |
| B. | -2 |
| C. | 1 |
| D. | None of these |
| Answer» E. | |
| 4729. |
If \[\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}=3,\]then \[\cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}=\] [EAMCET 1994] |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 4730. |
If \[(\sec \alpha +\tan \alpha )(\sec \beta +\tan \beta )(\sec \gamma +\tan \gamma )\]\[=\tan \alpha \tan \beta \tan \gamma \], then \[(\sec \alpha -\tan \alpha )(\sec \beta -\tan \beta )\] \[(\sec \gamma -\tan \gamma )=\] [Kurukshetra CEE 1998] |
| A. | \[\cot \alpha \cot \beta \cot \gamma \] |
| B. | \[\tan \alpha \tan \beta \tan \gamma \] |
| C. | \[\cot \alpha +\cot \beta +\cot \gamma \] |
| D. | \[\tan \alpha +\tan \beta +\tan \gamma \] |
| Answer» B. \[\tan \alpha \tan \beta \tan \gamma \] | |
| 4731. |
Which of the following relations is possible |
| A. | \[\sin \theta =\frac{5}{3}\] |
| B. | \[\tan \theta =1002\] |
| C. | \[\cos \theta =\frac{1+{{p}^{2}}}{1-{{p}^{2}}},(p\ne \pm 1)\] |
| D. | \[\sec \theta =\frac{1}{2}\] |
| Answer» C. \[\cos \theta =\frac{1+{{p}^{2}}}{1-{{p}^{2}}},(p\ne \pm 1)\] | |
| 4732. |
If \[(1+\sin A)(1+\sin B)(1+\sin C)\]\[=(1-\sin A)(1-\sin B)(1-\sin C),\]then each side is equal to |
| A. | \[\pm \sin A\sin B\sin C\] |
| B. | \[\pm \cos A\cos B\cos C\] |
| C. | \[\pm \sin A\cos B\cos C\] |
| D. | \[\pm \cos A\sin B\sin C\] |
| Answer» C. \[\pm \sin A\cos B\cos C\] | |
| 4733. |
If \[x{{\sin }^{3}}\alpha +y{{\cos }^{3}}\alpha =\sin \alpha \cos \alpha \] and \[x\sin \alpha -y\cos \alpha =0,\] then \[{{x}^{2}}+{{y}^{2}}=\] [WB JEE 1984] |
| A. | -1 |
| B. | ±1 |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 4734. |
If \[\cos x+{{\cos }^{2}}x=1,\]then the value of \[{{\sin }^{2}}x+{{\sin }^{4}}x\] is |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 2 |
| Answer» B. -1 | |
| 4735. |
If \[\sin x+{{\sin }^{2}}x=1\], then the value of \[{{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x-2\] is equal to [Pb. CET 2002] |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» D. 2 | |
| 4736. |
The value of \[2({{\sin }^{6}}\theta +{{\cos }^{6}}\theta )-3({{\sin }^{4}}\theta +{{\cos }^{4}}\theta )+1\] is [MP PET 1997; UPSEAT 2002] |
| A. | 2 |
| B. | 0 |
| C. | 4 |
| D. | 6 |
| Answer» C. 4 | |
| 4737. |
\[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta =\] [MP PET 1995, 2002; DCE 2005] |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 4738. |
If \[x=a{{\cos }^{3}}\theta ,y=b{{\sin }^{3}}\theta ,\]then |
| A. | \[{{\left( \frac{a}{x} \right)}^{2/3}}+{{\left( \frac{b}{y} \right)}^{2/3}}=1\] |
| B. | \[{{\left( \frac{b}{x} \right)}^{2/3}}+{{\left( \frac{a}{y} \right)}^{2/3}}=1\] |
| C. | \[{{\left( \frac{x}{a} \right)}^{2/3}}+{{\left( \frac{y}{b} \right)}^{2/3}}=1\] |
| D. | \[{{\left( \frac{x}{b} \right)}^{2/3}}+{{\left( \frac{y}{a} \right)}^{2/3}}=1\] |
| Answer» D. \[{{\left( \frac{x}{b} \right)}^{2/3}}+{{\left( \frac{y}{a} \right)}^{2/3}}=1\] | |
| 4739. |
If \[a\cos \theta +b\sin \theta =m\] and \[a\sin \theta -b\cos \theta =n,\] then \[{{a}^{2}}+{{b}^{2}}=\] |
| A. | \[m+n\] |
| B. | \[{{m}^{2}}-{{n}^{2}}\] |
| C. | \[{{m}^{2}}+{{n}^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 4740. |
The incorrect statement is [MNR 1993] |
| A. | \[\sin \theta =-\frac{1}{5}\] |
| B. | \[\cos \theta =1\] |
| C. | \[\sec \theta =\frac{1}{2}\] |
| D. | \[\tan \theta =20\] |
| Answer» D. \[\tan \theta =20\] | |
| 4741. |
If \[\tan \theta +\sin \theta =m\]and \[\tan \theta -\sin \theta =n,\]then [IIT 1970] |
| A. | \[{{m}^{2}}-{{n}^{2}}=4mn\] |
| B. | \[{{m}^{2}}+{{n}^{2}}=4mn\] |
| C. | \[{{m}^{2}}-{{n}^{2}}={{m}^{2}}+{{n}^{2}}\] |
| D. | \[{{m}^{2}}-{{n}^{2}}=4\sqrt{mn}\] |
| Answer» E. | |
| 4742. |
If \[p=\frac{2\sin \,\theta }{1+\cos \theta +\sin \theta }\], and \[q=\frac{\cos \theta }{1+\sin \theta },\] then [MP PET 2001] |
| A. | \[pq=1\] |
| B. | \[\frac{q}{p}=1\] |
| C. | \[q-p=1\] |
| D. | \[q+p=1\] |
| Answer» E. | |
| 4743. |
If \[\tan \theta =\frac{x\,\sin \,\varphi }{1-x\,\cos \,\varphi }\] and \[\tan \,\varphi =\frac{y\sin \,\theta }{1-y\,\cos \,\theta }\], then \[\frac{x}{y}=\] [MP PET 1991] |
| A. | \[\frac{\sin \varphi }{\sin \theta }\] |
| B. | \[\frac{\sin \theta }{\sin \varphi }\] |
| C. | \[\frac{\sin \varphi }{1-\cos \theta }\] |
| D. | \[\frac{\sin \theta }{1-\cos \varphi }\] |
| Answer» C. \[\frac{\sin \varphi }{1-\cos \theta }\] | |
| 4744. |
If \[x=\sec \,\varphi -\tan \varphi ,y=\text{cosec}\varphi +\cot \varphi ,\]then |
| A. | \[x=\frac{y+1}{y-1}\] |
| B. | \[x=\frac{y-1}{y+1}\] |
| C. | \[y=\frac{1-x}{1+x}\] |
| D. | None of these |
| Answer» C. \[y=\frac{1-x}{1+x}\] | |
| 4745. |
If \[2y\,\cos \theta =x\sin \,\theta \text{ and }2x\sec \theta -y\,\text{cosec}\,\theta =3,\] then \[{{x}^{2}}+4{{y}^{2}}=\] [WB JEE 1988] |
| A. | 4 |
| B. | -4 |
| C. | ± 4 |
| D. | None of these |
| Answer» B. -4 | |
| 4746. |
The value of the expression\[1-\frac{{{\sin }^{2}}y}{1+\cos \,y}+\frac{1+\cos \,y}{\sin \,y}-\frac{\sin \,\,y}{1-\cos \,y}\]is equal to |
| A. | 0 |
| B. | 1 |
| C. | \[\sin \,y\] |
| D. | \[\cos \,y\] |
| Answer» E. | |
| 4747. |
\[\frac{2\sin \theta \,\tan \theta (1-\tan \theta )+2\sin \theta {{\sec }^{2}}\theta }{{{(1+\tan \theta )}^{2}}}=\] [Roorkee 1975] |
| A. | \[\frac{\sin \,\theta }{1+\tan \theta }\] |
| B. | \[\frac{2\,\sin \theta }{1+\tan \theta }\] |
| C. | \[\frac{2\sin \theta }{{{(1+\tan \theta )}^{2}}}\] |
| D. | None of these |
| Answer» C. \[\frac{2\sin \theta }{{{(1+\tan \theta )}^{2}}}\] | |
| 4748. |
\[\frac{1+\sin A-\cos A}{1+\sin A+\cos A}\]= |
| A. | \[\sin \frac{A}{2}\] |
| B. | \[\cos \frac{A}{2}\] |
| C. | \[\tan \frac{A}{2}\] |
| D. | \[\cot \frac{A}{2}\] |
| Answer» D. \[\cot \frac{A}{2}\] | |
| 4749. |
If for real values of \[x,\cos \theta =x+\frac{1}{x},\] then [MP PET 1996] |
| A. | \[\theta \] is an acute angle |
| B. | \[\theta \] is a right angle |
| C. | \[\theta \]is an obtuse angle |
| D. | No value of \[\theta \]is possible |
| Answer» E. | |
| 4750. |
The value of \[{{e}^{{{\log }_{10}}\tan 1{}^\circ +{{\log }_{10}}\tan 2{}^\circ +{{\log }_{10}}\tan 3{}^\circ +...........+{{\log }_{10}}\tan 89{}^\circ }}\] is |
| A. | 0 |
| B. | e |
| C. | 1/e |
| D. | None of these |
| Answer» E. | |