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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.
| 151. |
From a group of 7 men and 4 ladies a committee of 6 persons is formed, then the probability that the committee contains 2 ladies is |
| A. | \[\frac{5}{13}\] |
| B. | \[\frac{5}{11}\] |
| C. | \[\frac{4}{11}\] |
| D. | \[\frac{3}{11}\] |
| Answer» C. \[\frac{4}{11}\] | |
| 152. |
The solution of the differential equation \[\frac{dy}{dx}+\frac{1+{{x}^{2}}}{x}=0\] is |
| A. | \[y=-\frac{1}{2}{{\tan }^{-1}}x+c\] |
| B. | \[y+\log x+\frac{{{x}^{2}}}{2}+c=0\] |
| C. | \[y=\frac{1}{2}{{\tan }^{-1}}x+c\] |
| D. | \[y-\log x-\frac{{{x}^{2}}}{2}=c\] |
| Answer» C. \[y=\frac{1}{2}{{\tan }^{-1}}x+c\] | |
| 153. |
The area of the parallelogram whose diagonals are \[\mathbf{a}=3\,\mathbf{i}+\mathbf{j}-2\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}-3\,\mathbf{j}+4\,\mathbf{k}\] is [MP PET 1988, 93; MNR 1985] |
| A. | \[10\sqrt{3}\] |
| B. | \[5\sqrt{3}\] |
| C. | 8 |
| D. | 4 |
| Answer» C. 8 | |
| 154. |
In a lottery there were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89 is [AMU 2001] |
| A. | \[\frac{2}{801}\] |
| B. | \[\frac{2}{623}\] |
| C. | \[\frac{1}{267}\] |
| D. | \[\frac{1}{623}\] |
| Answer» B. \[\frac{2}{623}\] | |
| 155. |
The d. r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle \[\pi /4\] with plane \[x+y=3\] are |
| A. | \[1,\sqrt{2},1\] |
| B. | \[1,1,\sqrt{2}\] |
| C. | 1, 1, 2 |
| D. | \[\sqrt{2},1,\,1\] |
| Answer» C. 1, 1, 2 | |
| 156. |
Consider n points in a plane no three of which are collinear and the ratio of number of hexagon and octagon that can be formed from these n points is 4:13 then find the value of n. |
| A. | 14 |
| B. | 20 |
| C. | 28 |
| D. | None of these |
| Answer» C. 28 | |
| 157. |
There are 5 volumes of Mathematics among 25 books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is |
| A. | \[\frac{1}{5\,!}\] |
| B. | \[\frac{50\,!}{55\,!}\] |
| C. | \[\frac{1}{{{50}^{5}}}\] |
| D. | None of these |
| Answer» B. \[\frac{50\,!}{55\,!}\] | |
| 158. |
The chance of one event happening is the square of the chance of a second event, but the odds against the first are the cube of the odds against the second. The chance of the first event is |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{9}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{4}{9}\] |
| Answer» C. \[\frac{2}{3}\] | |
| 159. |
A fair coin it tossed 2n times. The probability of getting as many heads in the first n tosses as in the last n is |
| A. | \[\frac{^{2n}{{C}_{n}}}{{{2}^{2n}}}\] |
| B. | \[\frac{^{2n}{{C}_{n-1}}}{{{2}^{n}}}\] |
| C. | \[\frac{n}{{{2}^{2n}}}\] |
| D. | None |
| Answer» B. \[\frac{^{2n}{{C}_{n-1}}}{{{2}^{n}}}\] | |
| 160. |
The equation of a line through \[(3,\,-4)\] and perpendicular to the line \[3x+4y=5\]is [RPET 1981, 84, 86; MP PET 1984] |
| A. | \[4x+3y=24\] |
| B. | \[y-4=(x+3)\] |
| C. | \[3y-4x=24\] |
| D. | \[y+4=\frac{4}{3}(x-3)\] |
| Answer» E. | |
| 161. |
The radius of a cylinder is increasing at the rate of 3 m/sec and its altitude is decreasing at the rate of 4m/sec. The rate of change of volume when radius is 4 meters and altitude is 6 meters is [Kerala (Engg.) 2005] |
| A. | \[80\pi \,\]cu. m/sec |
| B. | \[144\,\pi \,\]cu. m/sec |
| C. | \[80\,\] cu. m/sec |
| D. | \[64\,\] cu. m/sec |
| E. | \[-80\,\pi \] cu. m/sec |
| Answer» B. \[144\,\pi \,\]cu. m/sec | |
| 162. |
The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observations? |
| A. | 5 |
| B. | 10 |
| C. | 20 |
| D. | 40 |
| Answer» D. 40 | |
| 163. |
If \[\theta \] is the angle between the lines \[AB\] and \[CD\], then projection of line segment \[AB\]on line \[CD\], is [MP PET 1995] |
| A. | \[AB\sin \theta \] |
| B. | \[AB\cos \theta \] |
| C. | \[AB\tan \theta \] |
| D. | \[CD\cos \theta \] |
| Answer» C. \[AB\tan \theta \] | |
| 164. |
Given a family of lines a \[a(2x+y+4)+b(x-2y-3)=0\] the number of lines belonging to the family at a distance \[\sqrt{10}\] from \[P(2,-3)\] is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 165. |
The lines \[2x=3y=-z\] and \[6x=-y=-4z\] |
| A. | Are perpendicular |
| B. | Are parallel |
| C. | \[intersect\text{ }at\text{ }an\text{ }angle\,\,45{}^\circ \] |
| D. | \[intersect\text{ }at\text{ }an\text{ }angle\,\,60{}^\circ \] |
| Answer» B. Are parallel | |
| 166. |
The most general value of \[\theta \]satisfying the equations \[\tan \theta =-1\] and \[\cos \theta =\frac{1}{\sqrt{2}}\]is [MNR 1982; Roorkee 1990; UPSEAT 2002; MP PET 2003] |
| A. | \[n\pi +\frac{7\pi }{4}\] |
| B. | \[n\pi +{{(-1)}^{n}}\frac{7\pi }{4}\] |
| C. | \[2n\pi +\frac{7\pi }{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 167. |
A relation R is defined over the set of nonnegative integers as \[xRy\Rightarrow {{x}^{2}}+{{y}^{2}}=36\] what is R? |
| A. | \[\{(0,6)\}\] |
| B. | \[\{(6,0)(\sqrt{11},5),(3,3,\sqrt{3})\] |
| C. | \[\{(6,0)(0,6)\}\] |
| D. | \[(\sqrt{11},5),(2,4\sqrt{2}),(5\sqrt{11}),(4\sqrt{2}2)\}\] |
| Answer» D. \[(\sqrt{11},5),(2,4\sqrt{2}),(5\sqrt{11}),(4\sqrt{2}2)\}\] | |
| 168. |
Let R be a relation on \[N\times N\] defined by \[(a,b)R(c,d)\Rightarrow ad(b+c)=bc(a+d).R\] is |
| A. | A partial order relation |
| B. | An equivalence relation |
| C. | An identity relation |
| D. | None of these |
| Answer» C. An identity relation | |
| 169. |
\[\cos \theta \left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]+\sin \theta \left[ \begin{matrix} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \\ \end{matrix} \right]=\] |
| A. | \[\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] |
| Answer» E. | |
| 170. |
The function \[f(x)=log\left( x+\sqrt{{{x}^{2}}+1} \right)\], is |
| A. | neither an even nor an odd function |
| B. | an even function |
| C. | an odd function |
| D. | a periodic function |
| Answer» D. a periodic function | |
| 171. |
The solution of the differential equation \[\cos y\log (\sec x+\tan x)dx=\cos x\log (\sec y+\tan y)dy\] is [AI CBSE 1990] |
| A. | \[{{\sec }^{2}}x+{{\sec }^{2}}y=c\] |
| B. | \[\sec x+\sec y=c\] |
| C. | \[\sec x-\sec y=c\] |
| D. | None of these |
| Answer» E. | |
| 172. |
The value of \[{{(-i)}^{1/3}}\] is [Roorkee 1995] |
| A. | \[\frac{1+\sqrt{3}i}{2}\] |
| B. | \[\frac{1-\sqrt{3}i}{2}\] |
| C. | \[\frac{-\sqrt{3}-i}{2}\] |
| D. | \[\frac{\sqrt{3}-i}{2}\] |
| Answer» D. \[\frac{\sqrt{3}-i}{2}\] | |
| 173. |
At which point the line \[\frac{x}{a}+\frac{y}{b}=1\], touches the curve \[y=b{{e}^{-x/a}}\] [RPET 1999] |
| A. | (0, 0) |
| B. | (0, a) |
| C. | (0, b) |
| D. | (b, 0) |
| Answer» D. (b, 0) | |
| 174. |
The derivative of \[F(x)=\int_{{{x}^{2}}}^{{{x}^{3}}}{\frac{1}{\log t}\,dt}\], \[(x>0)\] is |
| A. | \[\frac{1}{3\log x}-\frac{1}{2\log x}\] |
| B. | \[\frac{1}{3\log x}\] |
| C. | \[\frac{3{{x}^{2}}}{3\log x}\] |
| D. | \[{{(\log x)}^{-1}}.x(x-1)\] |
| Answer» E. | |
| 175. |
Which one of the following is one of the solutions of the equation of the equation\[\tan 2\theta .\tan \theta =1\]? |
| A. | \[\pi /12\] |
| B. | \[\pi /6\] |
| C. | \[\pi /4\] |
| D. | \[\pi /3\] |
| Answer» C. \[\pi /4\] | |
| 176. |
If normal to the curve \[y=f(x)\] is parallel to x-axis, then correct statement is [RPET 2000] |
| A. | \[\frac{dy}{dx}=0\] |
| B. | \[\frac{dy}{dx}=1\] |
| C. | \[\frac{dx}{dy}=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 177. |
The distance between the line \[\vec{r}.2\hat{i}-2\hat{j}+3\hat{k}\]\[+\lambda (\hat{i}-\hat{j}+4\hat{k})\] and the plane \[\vec{r}.(\hat{i}-5\hat{j}+\hat{k})=5\] is |
| A. | \[\frac{10}{3\sqrt{3}}\] |
| B. | \[\frac{10}{9}\] |
| C. | \[\frac{10}{3}\] |
| D. | \[\frac{3}{10}\] |
| Answer» B. \[\frac{10}{9}\] | |
| 178. |
The number of non-zero integral solutions of the equation \[|1-i{{|}^{x}}={{2}^{x}}\] is |
| A. | Infinite |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» E. | |
| 179. |
If \[\mu \] is the universal set and P is a subset of \[\mu \], then what is \[P\cap (P-\mu )\cup (\mu -P)\}\] equal to? |
| A. | \[\phi \] |
| B. | P? |
| C. | m |
| D. | P |
| Answer» B. P? | |
| 180. |
The value of x + y + z is 15 if a, x, y, z, b are in A.P. while the value of \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] is \[\frac{5}{3}\] if a, x, y, z, b are in H.P. Then the value of a and b are |
| A. | 2 and 8 |
| B. | 1 and 9 |
| C. | 3 and 7 |
| D. | None |
| Answer» C. 3 and 7 | |
| 181. |
A man has bunch of 10 keys out of which only one can open the door. He chooses a key at random for opening the door. If at each trial the wrong key is discarded, then the probability that the door is opened on fifth trial is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{^{10}{{C}_{5}}}{{{10}^{5}}}\] |
| C. | \[\frac{1}{10}\] |
| D. | \[\frac{5!}{10!}\] |
| Answer» D. \[\frac{5!}{10!}\] | |
| 182. |
If two roots of the equation \[{{x}^{3}}-3x+2=0\] are same, then the roots will be [MP PET 1985] |
| A. | 2, 2, 3 |
| B. | 1, 1, -2 |
| C. | - 2, 3, 3 |
| D. | -2, -2, 1 |
| Answer» C. - 2, 3, 3 | |
| 183. |
Let \[A=\{1,2\},B=\{3,4\}.\] Then, number of subsets of \[A\times B\] is |
| A. | 4 |
| B. | 8 |
| C. | 18 |
| D. | 16 |
| Answer» E. | |
| 184. |
The sum of the series 3.6 + 4.7 + 5.8 + ......upto (n - 2) terms |
| A. | \[{{n}^{3}}+{{n}^{2}}+n+2\] |
| B. | \[\frac{1}{6}(2{{n}^{3}}+12{{n}^{2}}+10\,n-84)\] |
| C. | \[{{n}^{3}}+{{n}^{2}}+n\] |
| D. | None of these |
| Answer» C. \[{{n}^{3}}+{{n}^{2}}+n\] | |
| 185. |
The line parallel to the x-axis and passing through the intersection of the lines \[ax+2by+3b=0\] and \[bx-2ay-3a=0\], where \[(a,\,b)\ne (0,\,0)\] is [AIEEE 2005] |
| A. | Above the x-axis at a distance of 3/2 from it |
| B. | Above the x-axis at a distance of 2/3 from it |
| C. | Below the x-axis at a distance of 3/2 from it |
| D. | Below the x-axis at a distance of 2/3 from it |
| Answer» D. Below the x-axis at a distance of 2/3 from it | |
| 186. |
The equation of radical axis of the circles \[{{x}^{2}}+{{y}^{2}}+x-y+2=0\] and \[3{{x}^{2}}+3{{y}^{2}}-4x-12=0,\]is [RPET 1984, 85, 86, 91, 2000] |
| A. | \[2{{x}^{2}}+2{{y}^{2}}-5x+y-14=0\] |
| B. | \[7x-3y+18=0\] |
| C. | \[5x-y+14=0\] |
| D. | None of these |
| Answer» C. \[5x-y+14=0\] | |
| 187. |
Point \[\left( \frac{1}{2},\,\frac{-13}{4} \right)\]divides the line joining the points \[(3,-5)\]and \[(-7,2)\] in the ratio of |
| A. | 1 : 3 internally |
| B. | 3 : 1internally |
| C. | 1 : 3 externally |
| D. | 3 : 1externally |
| Answer» B. 3 : 1internally | |
| 188. |
If \[{{\tan }^{2}}\theta =2{{\tan }^{2}}\varphi +1,\] then \[\cos 2\theta +{{\sin }^{2}}\varphi \] equals |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 189. |
A unit vector perpendicular to the plane of \[a=2i-6j-3k\], \[b=4i+3j-k\] is [MP PET 2000] |
| A. | \[\frac{4i+3j-k}{\sqrt{26}}\] |
| B. | \[\frac{2i-6j-3k}{7}\] |
| C. | \[\frac{3i-2j+6k}{7}\] |
| D. | \[\frac{2i-3j-6k}{7}\] |
| Answer» D. \[\frac{2i-3j-6k}{7}\] | |
| 190. |
If a matrix A is such that \[3{{A}^{3}}+2{{A}^{2}}+5A+I=0,\] then its inverse is |
| A. | \[-(3{{A}^{2}}+2A+5I)\] |
| B. | \[3{{A}^{2}}+2A+5I\] |
| C. | \[3{{A}^{2}}-2A-5I\] |
| D. | None of these |
| Answer» B. \[3{{A}^{2}}+2A+5I\] | |
| 191. |
From the point (4, 3) a perpendicular is dropped on the x-axis as well as on the y-axis. If the lengths of perpendiculars are p, q respectively, then which one of the following is correct? |
| A. | \[p=q~\] |
| B. | \[3p=4q\] |
| C. | \[4p=3q\] |
| D. | \[p+q=5\] |
| Answer» D. \[p+q=5\] | |
| 192. |
A variable plane which remains at a constant distance 3p from the origin cut the coordinate axes at A, B and C. The locus of the centroid of triangle ABC is |
| A. | \[{{x}^{-1}}+{{y}^{-1}}+{{z}^{-1}}={{p}^{-1}}\] |
| B. | \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}={{p}^{-2}}\] |
| C. | \[x+y+z=p\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{p}^{2}}\] |
| Answer» C. \[x+y+z=p\] | |
| 193. |
The solution of the differential equation \[(\sin x+\cos x)dy+(\cos x-\sin x)dx=0\]is |
| A. | \[{{e}^{x}}(\sin x+\cos x)+c=0\] |
| B. | \[{{e}^{y}}(\sin x+\cos x)=c\] |
| C. | \[{{e}^{y}}(\cos x-\sin x)=c\] |
| D. | \[{{e}^{x}}(\sin x-\cos x)=c\] |
| Answer» C. \[{{e}^{y}}(\cos x-\sin x)=c\] | |
| 194. |
If \[\tan \alpha ,\tan \beta \]are the roots of the equation \[{{x}^{2}}+px+q=0\text{ }(p\ne 0),\] then |
| A. | \[{{\sin }^{2}}(\alpha +\beta )+p\sin (\alpha +\beta )\cos (\alpha +\beta )+q{{\cos }^{2}}(\alpha +\beta )=q\] |
| B. | \[\tan (\alpha +\beta )=\frac{p}{q-1}\] |
| C. | \[\cos (\alpha +\beta )=1-q\] |
| D. | \[\sin (\alpha +\beta )=-p\] |
| Answer» C. \[\cos (\alpha +\beta )=1-q\] | |
| 195. |
Which one of the following is not true [Kurukshetra CEE 1998] |
| A. | Matrix addition is commutative |
| B. | Matrix addition is associative |
| C. | Matrix multiplication is commutative |
| D. | Matrix multiplication is associative |
| Answer» D. Matrix multiplication is associative | |
| 196. |
The mean income of a group of 50 persons was calculated as Rs. 169. Later it was discovered that one figure was wrongly taken as 134 instead of correct value 143. The correct mean should be (in Rs.) |
| A. | 168 |
| B. | 169 |
| C. | 168.92 |
| D. | 169.18 |
| Answer» E. | |
| 197. |
The matrix \[\left( \begin{matrix} 1 & a & 2 \\ 1 & 2 & 5 \\ 2 & 1 & 1 \\ \end{matrix} \right)\]is not invertible, if ?a? has the value [MP PET 1998] |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» C. 0 | |
| 198. |
A line is such that its segment between the straight lines \[5x-y-4=0\] and \[3x+4y-4=0\] is bisected at the point (1, 5), then its equation is [Roorkee 1988] |
| A. | \[83x-35y+92=0\] |
| B. | \[35x-83y+92=0\] |
| C. | \[35x+35y+92=0\] |
| D. | None of these |
| Answer» B. \[35x-83y+92=0\] | |
| 199. |
If \[\Delta (x)=\left| \,\begin{matrix} {{x}^{n}} & \sin x & \cos x \\ n! & \sin \frac{n\pi }{2} & \cos \frac{n\pi }{2} \\ a & {{a}^{2}} & {{a}^{3}} \\ \end{matrix}\, \right|,\] then the value of \[\frac{{{d}^{n}}}{d{{x}^{n}}}[\Delta (x)]\] at \[x=0\]is |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | Dependent of a |
| Answer» C. 1 | |
| 200. |
Let \[R=\{(x,y):x,y\in N\] and \[{{x}^{2}}-4xy+3{{y}^{2}}=0\},\] Where N is the set of all natural numbers. Then the relation R is: |
| A. | Reflexive but neither symmetric nor transitive. |
| B. | Symmetric and transitive. |
| C. | Reflexive and symmetric. |
| D. | Reflexive and transitive. |
| Answer» E. | |