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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.
| 201. |
If \[0 |
| A. | \[\frac{(1-\sqrt{7})}{4}\] |
| B. | \[\frac{(4-\sqrt{7})}{3}\] |
| C. | \[-\frac{(4+\sqrt{7})}{3}\] |
| D. | \[\frac{(1+\sqrt{7})}{4}\] |
| Answer» D. \[\frac{(1+\sqrt{7})}{4}\] | |
| 202. |
Find the value of \[\cot 5{}^\circ \cot 10........cot85{}^\circ \]. |
| A. | 1 |
| B. | -1 |
| C. | 2 |
| D. | -2 |
| Answer» B. -1 | |
| 203. |
If \[2x+3y-5z=7,x+y+z=6\], \[3x-4y+2z=1,\] then x = [MP PET 1987] |
| A. | \[\left| \,\begin{matrix} 2 & -5 & 7 \\ 1 & 1 & 6 \\ 3 & 2 & 1 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \\ \end{matrix}\, \right|\] |
| B. | \[\left| \,\begin{matrix} -7 & 3 & -5 \\ -6 & 1 & 1 \\ -1 & -4 & 2 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \\ \end{matrix}\, \right|\] |
| C. | \[\left| \,\begin{matrix} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \\ \end{matrix}\, \right|\] |
| D. | None of these |
| Answer» D. None of these | |
| 204. |
Let \[S=\sum\limits_{k=0}^{n-1}{^{k+2}{{P}_{2}},}\] then |
| A. | n divides 3S |
| B. | n+1 divides 3S |
| C. | n+2 divides 3S |
| D. | All are correct |
| Answer» E. | |
| 205. |
If \[A=[1\,2\,3],B=\left[ \begin{align} & 2 \\ & 3 \\ & 4 \\ \end{align} \right]\] and \[C=\left[ \begin{matrix} 1 & 5 \\ 0 & 2 \\ \end{matrix} \right]\], then which of the following is defined [RPET 1996] |
| A. | AB |
| B. | \[BA\] |
| C. | \[(AB)\,\text{. }C\] |
| D. | \[(AC)\,.\,B\] |
| Answer» C. \[(AB)\,\text{. }C\] | |
| 206. |
If x denotes the number of sixes in four consecutive throws of a dice, then \[P\,(x=4)\]is [BIT Ranchi 1991] |
| A. | \[\frac{1}{1296}\] |
| B. | \[\frac{4}{6}\] |
| C. | 1 |
| D. | \[\frac{1295}{1296}\] |
| Answer» B. \[\frac{4}{6}\] | |
| 207. |
The length of tangent from the point (5, 1) to the circle \[{{x}^{2}}+{{y}^{2}}+6x-4y-3=0\], is [MNR 1981] |
| A. | 81 |
| B. | 29 |
| C. | 7 |
| D. | 21 |
| Answer» D. 21 | |
| 208. |
If \[\sin (\pi \cos x)=cos(\pi sinx),\] then what is one of the values of\[sin\text{ }2x\]? |
| A. | \[-\frac{1}{4}\] |
| B. | \[-\frac{1}{2}\] |
| C. | \[-\frac{3}{4}\] |
| D. | \[-1\] |
| Answer» D. \[-1\] | |
| 209. |
The points of intersection of the circles \[{{x}^{2}}+{{y}^{2}}=25\]and \[{{x}^{2}}+{{y}^{2}}-8x+7=0\]are [MP PET 1988] |
| A. | (4, 3) and (4, -3) |
| B. | (4, -3) and (-4, -3) |
| C. | (-4, 3) and (4, 3) |
| D. | (4, 3) and (3, 4) |
| Answer» B. (4, -3) and (-4, -3) | |
| 210. |
If mth terms of the series 63+65+67+69+........... and 3+10+17+24+..........be equal, then m= |
| A. | 11 |
| B. | 12 |
| C. | 13 |
| D. | 15 |
| Answer» D. 15 | |
| 211. |
If the system of linear equation \[x+2ay+az=0,\] \[x+3by+bz=0,\] \[x+4cy+cz=0\]has a non zero solution, then \[a,b,c\] [AIEEE 2003] |
| A. | Are in A.P. |
| B. | Are in G. P. |
| C. | Are in H. P. |
| D. | Satisfy \[a+2b+3c=0\] |
| Answer» D. Satisfy \[a+2b+3c=0\] | |
| 212. |
If \[\mathbf{a}=2\mathbf{i}+3\mathbf{j}-5\mathbf{k},\,\,\mathbf{b}=m\mathbf{i}+n\mathbf{j}+12\mathbf{k}\] and \[\mathbf{a}\times \mathbf{b}=0,\] then \[(m,\,\,n)=\] |
| A. | \[\left( -\frac{24}{5},\,\frac{36}{5} \right)\] |
| B. | \[\left( \frac{24}{5},\,-\frac{36}{5} \right)\] |
| C. | \[\left( -\frac{24}{5},\,-\frac{36}{5} \right)\] |
| D. | \[\left( \frac{24}{5},\,\frac{36}{5} \right)\] |
| Answer» D. \[\left( \frac{24}{5},\,\frac{36}{5} \right)\] | |
| 213. |
If \[x+\frac{1}{x}=\sqrt{3},\] then x = [RPET 2002] |
| A. | \[\cos \frac{\pi }{3}+i\,\sin \frac{\pi }{3}\] |
| B. | \[\cos \frac{\pi }{2}+i\,\sin \frac{\pi }{2}\] |
| C. | \[\sin \frac{\pi }{6}+i\,\cos \frac{\pi }{6}\] |
| D. | \[\cos \frac{\pi }{6}+i\,\sin \frac{\pi }{6}\] |
| Answer» E. | |
| 214. |
The probability of getting 4 heads in 8 throws of a coin, is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{64}\] |
| C. | \[\frac{^{8}{{C}_{4}}}{8}\] |
| D. | \[\frac{^{8}{{C}_{4}}}{{{2}^{8}}}\] |
| Answer» E. | |
| 215. |
Let a, b, c, be in A.P. with a common difference d. Then \[{{e}^{1/c}},{{e}^{b/ac}},{{e}^{1/a}}\] are in: |
| A. | G.P. with common ratio \[{{e}^{d}}\] |
| B. | G.P. with common ratio \[{{e}^{1/d}}\] |
| C. | G.P. with common ratio \[{{e}^{d/({{b}^{2}}-{{d}^{2}})}}\] |
| D. | A.P. |
| Answer» D. A.P. | |
| 216. |
\[\frac{\sin 70{}^\circ +\cos 40{}^\circ }{\cos 70{}^\circ +\sin 40{}^\circ }=\] [CET 1986; MP PET 1999] |
| A. | 1 |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\sqrt{3}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 217. |
If \[A=\left( \begin{matrix} 2 & -1 \\ -1 & 2 \\ \end{matrix} \right)\]and I is the unit matrix of order 2, then \[{{A}^{2}}\] equals [Kerala (Engg.) 2002] |
| A. | \[4A-3I\] |
| B. | \[3A-AI\] |
| C. | \[A-I\] |
| D. | \[A+I\] |
| Answer» B. \[3A-AI\] | |
| 218. |
The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=50\]at the points where the line \[x+7=0\]meets it, are |
| A. | \[7x\pm y+50=0\] |
| B. | \[7x\pm y-5=0\] |
| C. | \[y\pm 7x+5=0\] |
| D. | \[y\pm 7x-5=0\] |
| Answer» B. \[7x\pm y-5=0\] | |
| 219. |
In a school, there are 20 teachers who teach mathematics of physics of these, 12 teach mathematics and 4 teach both math?s and physics then the number of teachers teaching only physics are |
| A. | 4 |
| B. | 8 |
| C. | 12 |
| D. | 16 |
| Answer» C. 12 | |
| 220. |
The solution of \[3\tan (A-{{15}^{o}})=\tan (A+{{15}^{o}})\] is |
| A. | \[n\pi +\frac{\pi }{4}\] |
| B. | \[2n\pi +\frac{\pi }{4}\] |
| C. | \[2n\pi -\frac{\pi }{4}\] |
| D. | \[\frac{n\pi }{2}+{{(-1)}^{n}}\frac{\pi }{2}\] |
| Answer» B. \[2n\pi +\frac{\pi }{4}\] | |
| 221. |
The value of the infinite product \[{{6}^{\frac{1}{2}}}\times {{6}^{\frac{1}{2}}}\times {{6}^{\frac{3}{8}}}\times {{6}^{\frac{1}{4}}}....\] is |
| A. | 6 |
| B. | 36 |
| C. | 216 |
| D. | \[\infty \] |
| Answer» D. \[\infty \] | |
| 222. |
The common property of points lying on x-axis, is [MP PET 1988] |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[a=0,\,y=0\] |
| D. | \[y=0,b=0\] |
| Answer» C. \[a=0,\,y=0\] | |
| 223. |
The roots of the given equation \[(p-q){{x}^{2}}+(q-r)x+(r-p)=0\] are [RPET 1986; MP PET 1999; Pb. CET 2004] |
| A. | \[\frac{p-q}{r-p},1\] |
| B. | \[\frac{q-r}{p-q},1\] |
| C. | \[\frac{r-p}{p-q},1\] |
| D. | \[1,\frac{q-r}{p-q}\] |
| Answer» D. \[1,\frac{q-r}{p-q}\] | |
| 224. |
Number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour. |
| A. | \[6\times {{(9!)}^{2}}\] |
| B. | 12! |
| C. | \[4\times {{(8!)}^{2}}\] |
| D. | \[5\times {{(9!)}^{2}}\] |
| Answer» E. | |
| 225. |
The probability of the simultaneous occurrence of two events A and B is p. if the probability that exactly one of the events occurs is q, then which of the following is not correct? |
| A. | \[P(A')+P(B')=2+2q-p\] |
| B. | \[P(A')+P(B')=2-2p-q\] |
| C. | \[P(A\cap B|A\cup B)=\frac{p}{p+q}\] |
| D. | \[P(A'\cap B')=1-p-q.\] |
| Answer» B. \[P(A')+P(B')=2-2p-q\] | |
| 226. |
At which point on y-axis the line \[x=0\]is a tangent to circle \[{{x}^{2}}+{{y}^{2}}-2x-6y+9=0\] [RPET 1984] |
| A. | (0, 1) |
| B. | (0, 2) |
| C. | (0, 3) |
| D. | (0, 4) |
| Answer» D. (0, 4) | |
| 227. |
\[\cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\cos \frac{8\pi }{15}\cos \frac{16\pi }{15}\] = [IIT 1985] |
| A. | 44228 |
| B. | 44287 |
| C. | 44409 |
| D. | 42370 |
| Answer» E. | |
| 228. |
A coin is tossed 3 times. The probability of obtaining at least two heads is or Three coins are tossed all together. The probability of getting at least two heads is [MP PET 1995] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 229. |
Two circles \[{{S}_{1}}={{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[{{S}_{2}}={{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\]cut each other orthogonally, then [RPET 1995] |
| A. | \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] |
| B. | \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] |
| C. | \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\] |
| D. | \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}-{{c}_{2}}\] |
| Answer» B. \[2{{g}_{1}}{{g}_{2}}-2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\] | |
| 230. |
If \[\sqrt{x}+\frac{1}{\sqrt{x}}=2\cos \theta ,\]then \[{{x}^{6}}+{{x}^{-6}}=\] [Karnataka CET 2003] |
| A. | \[2\cos 6\theta \] |
| B. | \[2\cos 12\theta \] |
| C. | \[2\cos 3\theta \] |
| D. | \[2\sin 3\theta \] |
| Answer» C. \[2\cos 3\theta \] | |
| 231. |
The equation of the line parallel to the line \[2x-3y=1\] and passing through the middle point of the line segment joining the points (1, 3) and (1, - 7), is |
| A. | \[2x-3y+8=0\] |
| B. | \[2x-3y=8\] |
| C. | \[2x-3y+4=0\] |
| D. | \[2x-3y=4\] |
| Answer» C. \[2x-3y+4=0\] | |
| 232. |
If \[\sin \text{ }\left( \frac{\pi }{4}\cot \theta \right)=\cos \text{ }\left( \frac{\pi }{4}\tan \theta \right)\,\,,\] then \[\theta =\] [Pb. CET 1988] |
| A. | \[n\pi +\frac{\pi }{4}\] |
| B. | \[2n\pi \pm \frac{\pi }{4}\] |
| C. | \[n\pi -\frac{\pi }{4}\] |
| D. | \[2n\pi \pm \frac{\pi }{6}\] |
| Answer» B. \[2n\pi \pm \frac{\pi }{4}\] | |
| 233. |
If \[A=\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ \end{matrix} \right]\], then A is [MP PET 1991] |
| A. | Symmetric |
| B. | Skew-symmetric |
| C. | Non-singular |
| D. | Singular |
| Answer» D. Singular | |
| 234. |
If \[A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right]\]and \[AB=O\], then B = [MP PET 1989] |
| A. | \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 0 & 1 \\ -1 & 0 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} -1 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] |
| Answer» E. | |
| 235. |
Let \[\vec{a}=\hat{i}-\hat{j},\vec{b}=\hat{j}-\hat{k}\] and \[\vec{c}=\hat{k}-\hat{i}\]. If \[\vec{d}\] is a unit vector such that \[\vec{a}\cdot \vec{d}=0=[\vec{b}\vec{c}\vec{d}]\], then \[\vec{d}\] equals |
| A. | \[\pm \frac{\hat{i}+\hat{j}-2\hat{k}}{\sqrt{6}}\] |
| B. | \[\pm \frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\] |
| C. | \[\pm \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\] |
| D. | \[\pm \,\hat{k}\] |
| Answer» B. \[\pm \frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\] | |
| 236. |
If \[\vec{r}\cdot \vec{a}=\vec{r}\cdot b=\vec{r}\cdot \vec{c}=\frac{1}{2}\] for some non-zero vector \[\vec{r}\], then the area of the triangle whose vertices are \[A(\vec{a}),B(\vec{b})\] and \[C\left( {\vec{c}} \right)\] is (\[\vec{a},\text{ }\vec{b},\text{ }\vec{c}\] are non-coplanar) |
| A. | \[\left| [\vec{a}\,\vec{b}\,\vec{c}] \right|\] |
| B. | \[\left| {\vec{r}} \right|\] |
| C. | \[\left| [\vec{a}\,\vec{b}\,\vec{c}]\vec{r} \right|\] |
| D. | None of these |
| Answer» D. None of these | |
| 237. |
If \[\overrightarrow{OA}=\vec{a};\overrightarrow{OB}=\vec{b};\overrightarrow{OC}=2\vec{a}+3\vec{b}\,;\] \[\overrightarrow{OD}=\vec{a}-2\vec{b}\], the length of \[\overrightarrow{OA}\] is three times the length of \[\overrightarrow{OB}\] and \[\overrightarrow{OA}\] is perpendicular to \[\overrightarrow{DB}\] then \[\left( \overrightarrow{BD}\times \overrightarrow{AC} \right).\left( \overrightarrow{OD}\times \overrightarrow{OC} \right)\] is |
| A. | \[7{{\left| \vec{a}\times \vec{b} \right|}^{2}}\] |
| B. | \[42|\vec{a}\times \vec{b}{{|}^{2}}\] |
| C. | 0 |
| D. | None of these |
| Answer» C. 0 | |
| 238. |
A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then |
| A. | \[x=39\] |
| B. | \[x=63\] |
| C. | \[39\le x\le 63\] |
| D. | None of these |
| Answer» D. None of these | |
| 239. |
An orthogonal matrix is |
| A. | \[\left[ \begin{matrix} \cos \alpha & 2\sin \alpha \\ -2\sin \alpha & \cos \alpha \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] |
| Answer» C. \[\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right]\] | |
| 240. |
Equation of the straight line making equal intercepts on the axes and passing through the point (2, 4) is [Karnataka CET 2004] |
| A. | \[4x-y-4=0\] |
| B. | \[2x+y-8=0\] |
| C. | \[x+y-6=0\] |
| D. | \[x+2y-10=0\] |
| Answer» D. \[x+2y-10=0\] | |
| 241. |
Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place. |
| A. | 12 |
| B. | 14 |
| C. | 16 |
| D. | 24 |
| Answer» D. 24 | |
| 242. |
The solution of the differential equation \[\frac{dy}{dx}+\frac{1+\cos 2y}{1-\cos 2x}=0\] [AISSE 1982; Karnataka CET 2004] |
| A. | \[\tan y+\cot x=c\] |
| B. | \[\tan y\cot x=c\] |
| C. | \[\tan y-\cot x=c\] |
| D. | None of these |
| Answer» D. None of these | |
| 243. |
If \[\sin A=\sin B\]and \[\cos A=\cos B,\]then [EAMCET 1994] |
| A. | \[\sin \frac{A-B}{2}=0\] |
| B. | \[\sin \frac{A+B}{2}=0\] |
| C. | \[\cos \frac{A-B}{2}=0\] |
| D. | \[\cos (A+B)=0\] |
| Answer» B. \[\sin \frac{A+B}{2}=0\] | |
| 244. |
\[y=mx\] is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord in origin .The equation of the circle described on this chord as diameter is [MP PET 1990] |
| A. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2ax=0\] |
| B. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x+my)=0\] |
| C. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})+2a(x+my)=0\] |
| D. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x-my)=0\] |
| Answer» C. \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})+2a(x+my)=0\] | |
| 245. |
If, 8, -4 and 13 be three (not necessarily consecutive term) of an A.P., how many such A.P. s are possible? |
| A. | 1 |
| B. | 2 |
| C. | Infinitely many |
| D. | No such A.P. is possible |
| Answer» D. No such A.P. is possible | |
| 246. |
If a circle passes through the point (1, 2) and cuts the circle \[{{x}^{2}}+{{y}^{2}}=4\] orthogonally, then the equation of the locus of its centre is [MNR 1992] |
| A. | \[{{x}^{2}}+{{y}^{2}}-3x-8y+1=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-2x-6y-7=0\] |
| C. | \[2x+4y-9=0\] |
| D. | \[2x+4y-1=0\] |
| Answer» D. \[2x+4y-1=0\] | |
| 247. |
Which one of the following planes is normal the plane \[3x+y+z=5?\] |
| A. | \[x+2y+z=6\] |
| B. | \[x-2y+z=6\] |
| C. | \[x+2y-z=6\] |
| D. | \[x-2y-z=6\] |
| Answer» E. | |
| 248. |
If \[5\cos 2\theta +2{{\cos }^{2}}\frac{\theta }{2}+1=0,-\pi <\theta <\pi \], then \[\theta =\] [Roorkee 1984] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{3},{{\cos }^{-1}}\frac{3}{5}\] |
| C. | \[{{\cos }^{-1}}\frac{3}{5}\] |
| D. | \[\frac{\pi }{3},\pi -{{\cos }^{-1}}\frac{3}{5}\] |
| Answer» E. | |
| 249. |
The number of values of x in the interval [0, 5\[\pi \]] satisfying the equation \[3{{\sin }^{2}}x-7\sin x+2=0\]is [IIT 1998; MP PET 2000; Pb. CET 2003] |
| A. | 0 |
| B. | 5 |
| C. | 6 |
| D. | 10 |
| Answer» D. 10 | |
| 250. |
If the roots of the equation \[{{x}^{2}}-8x+({{a}^{2}}-6a)=0\] are real, then [RPET 1987, 97; MP PET 1999] |
| A. | \[-2<a<8\] |
| B. | \[2<a<8\] |
| C. | \[-2\le a\le 8\] |
| D. | \[2\le a\le 8\] |
| Answer» D. \[2\le a\le 8\] | |