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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.
| 301. |
If a function F is such that \[F(0)=2,F(1)=3,\]\[F(x+2)=2F(x)-F(x+1)\] for \[x\ge 0,\] then \[F(5)\] is equal to |
| A. | -7 |
| B. | -3 |
| C. | 17 |
| D. | 13 |
| Answer» E. | |
| 302. |
The area bounded by the curve \[y={{x}^{3}},\] \[x-\]axis and two ordinates \[x=1\] to \[x=2\] equal to [MP PET 1999] |
| A. | \[\frac{15}{2}\] sq. unit |
| B. | \[\frac{15}{4}\] sq. unit |
| C. | \[\frac{17}{2}\] sq. unit |
| D. | \[\frac{17}{4}\] sq. unit |
| Answer» C. \[\frac{17}{2}\] sq. unit | |
| 303. |
The locus of the equation \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+1=0\]is |
| A. | An empty set |
| B. | A sphere |
| C. | A degenerate set |
| D. | A pair of planes |
| Answer» B. A sphere | |
| 304. |
If A and B are two sets, then \[(A-B)\cup (B-A)\]\[\cup (A\cap B)\] is equal to |
| A. | Only A |
| B. | \[A\cup B\] |
| C. | \[(A\cup B')\] |
| D. | None of these |
| Answer» C. \[(A\cup B')\] | |
| 305. |
Let S = the set of all triangles, P= the set of all isosceles triangles, Q= the set of all equilateral triangles, R= the set of all right - angled triangles. What do the sets \[P\cap Q\] and \[R-P\] represents respectively? |
| A. | The set of isosceles triangles; the set of non-isosceles right angled triangles |
| B. | The set of isosceles triangles; the set of right angled triangles |
| C. | The set of equilateral triangles; the set of right angled triangles |
| D. | The set of isosceles triangles; the set of equilateral triangles |
| Answer» B. The set of isosceles triangles; the set of right angled triangles | |
| 306. |
The expression \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\] is \[[a\ne b\ne 0]\] is (where a and b are unequal non-zero numbers) |
| A. | A.M. between a and b if \[n=-1\] |
| B. | G.M. between a and b if \[n=-\frac{1}{2}\] |
| C. | H.M. between a and b if n = 0 |
| D. | All are correct |
| Answer» C. H.M. between a and b if n = 0 | |
| 307. |
If A and B are two matrices such that A+B and AB are both defined, then [Pb. CET 1990] |
| A. | \[A\]and B are two matrices not necessarily of same order |
| B. | A and B are square matrices of same order |
| C. | Number of columns of A= Number of rows of B |
| D. | None of these |
| Answer» C. Number of columns of A= Number of rows of B | |
| 308. |
One hundred identical coins, each with probability P of showing up heads, are tossed. If 0 |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{49}{101}\] |
| C. | \[\frac{50}{101}\] |
| D. | \[\frac{51}{101}\] |
| Answer» E. | |
| 309. |
The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=1\]and \[{{x}^{2}}+{{y}^{2}}-4x+3=0\] is [DCE 2005] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 310. |
The sum to n terms of the series \[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+..........\] is |
| A. | \[n-1-{{2}^{-n}}\] |
| B. | 1 |
| C. | \[n-1+{{2}^{-n}}\] |
| D. | \[1+{{2}^{-n}}\] |
| Answer» D. \[1+{{2}^{-n}}\] | |
| 311. |
If a,b,g be the direction angles of a vector and \[\cos \alpha =\frac{14}{15}\], \[\cos \beta =\frac{1}{3}\] then \[\cos \gamma \]= |
| A. | \[\pm \frac{2}{15}\] |
| B. | \[\frac{1}{5}\] |
| C. | \[\pm \frac{1}{15}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{5}\] | |
| 312. |
Equation of a line passing through the point of intersection of lines \[2x-3y+4=0,\] \[3x+4y-5=0\] and perpendicular to \[6x-7y+3=0,\] then its equation is [RPET 2000] |
| A. | \[119x+102y+125=0\] |
| B. | \[119x+102y=125\] |
| C. | \[119x-102y=125\] |
| D. | None of these |
| Answer» C. \[119x-102y=125\] | |
| 313. |
If \[\cos 7\theta =\cos \theta -\sin 4\theta ,\] then the general value of \[\theta \] is |
| A. | \[\frac{n\pi }{6},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] |
| B. | \[\frac{n\pi }{3},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] |
| C. | \[\frac{n\pi }{4},\frac{n\pi }{3}\pm \frac{\pi }{18}\] |
| D. | \[\frac{n\pi }{4},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] |
| Answer» E. | |
| 314. |
If \[{{a}_{ij}}=\frac{1}{2}(3i-2j)\]and \[A={{[{{a}_{ij}}]}_{2\times 2}}\], then A is equal to [RPET 2001] |
| A. | \[\left[ \begin{matrix} 1/2 & 2 \\ -1/2 & 1 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 1/2 & -1/2 \\ 2 & 1 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 2 & 2 \\ 1/2 & -1/2 \\ \end{matrix} \right]\] |
| D. | None of these |
| Answer» C. \[\left[ \begin{matrix} 2 & 2 \\ 1/2 & -1/2 \\ \end{matrix} \right]\] | |
| 315. |
The greatest common divisor of \[^{20}{{C}_{1}}{{,}^{20}}{{C}_{3}},...{{,}^{20}}{{C}_{19}}\] is |
| A. | 20 |
| B. | 4 |
| C. | 5 |
| D. | None of these |
| Answer» C. 5 | |
| 316. |
Let A and B be two sets then \[(A\cup B{)}'\cup ({A}'\cap B)\] is equal to |
| A. | \[{A}'\] |
| B. | A |
| C. | \[{B}'\] |
| D. | None of these |
| Answer» B. A | |
| 317. |
The general value of \[\theta \] satisfying \[{{\sin }^{2}}\theta +\sin \theta =2\] is [AMU 1996, 99] |
| A. | \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\] |
| B. | \[2n\pi +\frac{\pi }{4}\] |
| C. | \[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\] |
| D. | \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\] |
| Answer» C. \[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\] | |
| 318. |
If \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,\] where a, b and c are coplanar vectors, then for some scalar k [Roorkee 1985; RPET 1997] |
| A. | \[\mathbf{a}+\mathbf{c}=k\,\mathbf{b}\] |
| B. | \[\mathbf{a}+\mathbf{b}=k\,\mathbf{c}\] |
| C. | \[\mathbf{b}+\mathbf{c}=k\,\mathbf{a}\] |
| D. | None of these |
| Answer» B. \[\mathbf{a}+\mathbf{b}=k\,\mathbf{c}\] | |
| 319. |
If \[A=\left[ \begin{matrix} 2 & 2 \\ -3 & 2 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right],\] then \[{{({{B}^{-1}}{{A}^{-1}})}^{-1}}\]= [EAMCET 2001] |
| A. | \[\left[ \begin{matrix} 2 & -2 \\ 2 & 3 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 3 & -2 \\ 2 & 2 \\ \end{matrix} \right]\] |
| C. | \[\frac{1}{10}\left[ \begin{matrix} 2 & 2 \\ -2 & 3 \\ \end{matrix} \right]\] |
| D. | \[\frac{1}{10}\left[ \begin{matrix} 3 & 2 \\ -2 & 2 \\ \end{matrix} \right]\] |
| Answer» B. \[\left[ \begin{matrix} 3 & -2 \\ 2 & 2 \\ \end{matrix} \right]\] | |
| 320. |
The angle between the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=169\]at the points (5, 12) and (12, ?5), is |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» E. | |
| 321. |
\[\frac{\sqrt{2}-\sin \alpha -\cos \alpha }{\sin \alpha -\cos \alpha }=\] [AMU 1999] |
| A. | \[\sec \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] |
| B. | \[\cos \left( \frac{\pi }{8}-\frac{\alpha }{2} \right)\] |
| C. | \[\tan \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] |
| D. | \[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] |
| Answer» D. \[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] | |
| 322. |
The two circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6=0\] and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\] [Karnataka CET 2001] |
| A. | Intersect |
| B. | Are concentric |
| C. | Touch internally |
| D. | Touch externally |
| Answer» D. Touch externally | |
| 323. |
A bag contains 3 white and 7 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red |
| A. | 0 |
| B. | \[\frac{3}{10}\] |
| C. | \[\frac{7}{10}\] |
| D. | \[\frac{10}{10}\] |
| Answer» E. | |
| 324. |
The line \[(3x-y+5)+\lambda (2x-3y-4)=0\]will be parallel to y-axis, if l = |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{-1}{3}\] |
| C. | \[\frac{3}{2}\] |
| D. | \[\frac{-3}{2}\] |
| Answer» C. \[\frac{3}{2}\] | |
| 325. |
If the combined mean of two groups is \[\frac{40}{3}\] and if the mean of one group with 10 observations is 15, then the mean of the other group with 8 observation is equal to |
| A. | \[\frac{46}{3}\] |
| B. | \[\frac{35}{4}\] |
| C. | \[\frac{45}{4}\] |
| D. | \[\frac{41}{4}\] |
| Answer» D. \[\frac{41}{4}\] | |
| 326. |
If the coordinates of vertices of \[\Delta OAB\] are (0,0) \[(\cos \alpha ,\,\sin \alpha )\] and \[(-\sin \alpha ,\,\cos \alpha )\] respectively, then \[O{{A}^{2}}+O{{B}^{2}}=\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 327. |
Let X and Y be two non-empty sets such that \[X\cap A=Y\cap A=\phi \] and \[X\cup A=Y\cup A\]for some non-empty set A. Then |
| A. | X is a proper subset of Y |
| B. | Y is a proper subset of X |
| C. | X = Y |
| D. | X and Y are disjoint sets |
| Answer» D. X and Y are disjoint sets | |
| 328. |
If the three vertices of a rectangle taken in order are the points (2, -2), (8, 4) and (5, 7). The coordinates of the fourth vertex is [CEE 1993] |
| A. | (1, 1) |
| B. | (1, -1) |
| C. | (-1, 1) |
| D. | None of these |
| Answer» D. None of these | |
| 329. |
An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is |
| A. | \[\frac{5}{1296}\] |
| B. | \[\frac{5}{1944}\] |
| C. | \[\frac{5}{2592}\] |
| D. | None of these |
| Answer» D. None of these | |
| 330. |
If the straight lines \[ax+may+1=0,\] \[bx+(m+1)by+1=0\] and \[cx+(m+2)cy+1=0\] are concurrent, then a, b, c form \[(m\ne 0)\] |
| A. | An A.P. only for m=1 |
| B. | An A.P. for all m |
| C. | A G.P. for all m |
| D. | A H.P. for all m |
| Answer» E. | |
| 331. |
What is the equation of the line through \[(1,2)\] so that segment of the line intercepted between the axes is bisected at this point? |
| A. | \[2x-y=4\] |
| B. | \[2x-y+4=0\] |
| C. | \[2x+y=4\] |
| D. | 2x+y+4=0 |
| Answer» D. 2x+y+4=0 | |
| 332. |
The diagonals of the parallelogram whose sides are \[lx+my+n=0,\] \[lx+my+n'=0\], \[mx+1y+n=0\] and \[mx+ly+n'=0\] include an angle |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[{{\tan }^{-1}}\left( \frac{{{1}^{2}}-{{m}^{2}}}{{{1}^{2}}+{{m}^{2}}} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{2lm}{{{1}^{2}}+{{m}^{2}}} \right)\] |
| Answer» C. \[{{\tan }^{-1}}\left( \frac{{{1}^{2}}-{{m}^{2}}}{{{1}^{2}}+{{m}^{2}}} \right)\] | |
| 333. |
If \[f(x)=5lo{{g}_{5}}x\] then \[{{f}^{-1}}(\alpha -\beta )\] where \[\alpha ,\beta \in R\]is equal to |
| A. | \[{{f}^{-1}}(\alpha )-{{f}^{-1}}(\beta )\] |
| B. | \[\frac{{{f}^{-1}}(\alpha )}{{{f}^{-1}}(\beta )}\] |
| C. | \[\frac{1}{f(\alpha -\beta )}\] |
| D. | \[\frac{1}{f(\alpha )-f(\beta )}\] |
| Answer» C. \[\frac{1}{f(\alpha -\beta )}\] | |
| 334. |
A can hit a target 4 times in 5 shots; B can hit a target 3 times in 4 shots; C can hit a target 2 times in 3 shots; All the three a shot each. What is the probability that two shots are at least hit? |
| A. | 44348 |
| B. | 44319 |
| C. | 44352 |
| D. | 44256 |
| Answer» D. 44256 | |
| 335. |
If a and b are two vectors, then \[{{(\mathbf{a}\times \mathbf{b})}^{2}}\] equals [Roorkee 1975, 79, 81, 85] |
| A. | \[\left| \,\begin{matrix} \mathbf{a}\,\,.\,\,\mathbf{b} & \mathbf{a}\,\,.\,\,\mathbf{a} \\ \mathbf{b}\,\,.\,\,\mathbf{b} & \mathbf{b}\,\,.\,\,\mathbf{a} \\ \end{matrix}\, \right|\] |
| B. | \[\left| \,\begin{matrix} \mathbf{a}\,\,.\,\,\mathbf{a} & \mathbf{a}\,\,.\,\,\mathbf{b} \\ \mathbf{b}\,\,.\,\,\mathbf{a} & \mathbf{b}\,\,.\,\,\mathbf{b} \\ \end{matrix}\, \right|\] |
| C. | \[\left| \,\begin{matrix} \mathbf{a}\,\,.\,\,\mathbf{b} \\ \mathbf{b}\,\,.\,\,\mathbf{a} \\ \end{matrix}\, \right|\] |
| D. | None of these |
| Answer» C. \[\left| \,\begin{matrix} \mathbf{a}\,\,.\,\,\mathbf{b} \\ \mathbf{b}\,\,.\,\,\mathbf{a} \\ \end{matrix}\, \right|\] | |
| 336. |
The total number of 3-digit numbers, the sum of whose digits is even, is equal to |
| A. | 450 |
| B. | 350 |
| C. | 250 |
| D. | 325 |
| Answer» B. 350 | |
| 337. |
If \[a,b,c\in Q\], then roots of the equation\[(b+c-2a){{x}^{2}}+\] \[(c+a-2b)x+(a+b-2c)=0\] are |
| A. | Rational |
| B. | Non-real |
| C. | Irrational |
| D. | Equal |
| Answer» B. Non-real | |
| 338. |
\[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{\frac{1}{n}{{e}^{\frac{r}{n}}}}\]is [AIEEE 2004] |
| A. | \[e+1\] |
| B. | \[e-1\] |
| C. | \[1-e\] |
| D. | \[e\] |
| Answer» C. \[1-e\] | |
| 339. |
Equation of the hour hand at 4 O? clock is |
| A. | \[x-\sqrt{3}\ y=0\] |
| B. | \[\sqrt{3}\ x-y=0\] |
| C. | \[x+\sqrt{3}\ y=0\] |
| D. | \[\sqrt{3}\ x+y=0\] |
| Answer» D. \[\sqrt{3}\ x+y=0\] | |
| 340. |
The Domain of the function \[f(x)=\sqrt{\frac{1}{\left| x-2 \right|-(x-2)}}\] is: |
| A. | \[\left( -\infty ,2 \right]\] |
| B. | \[(2,\infty )\] |
| C. | \[(-\infty ,2)\] |
| D. | \[[2,\infty )\] |
| Answer» D. \[[2,\infty )\] | |
| 341. |
The inverse of \[\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]is [EAMCET 1990] |
| A. | \[\left[ \begin{matrix} 1 & -2 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 0 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 1 & -2 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 1 & 2 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] |
| D. | None of these |
| Answer» C. \[\left[ \begin{matrix} 1 & 2 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] | |
| 342. |
If sum of distances of a point from the origin and lines \[x=2\] is 4, then its locus is [RPET 1997] |
| A. | \[{{x}^{2}}-12y=36\] |
| B. | \[{{y}^{2}}+12x=36\] |
| C. | \[{{y}^{2}}-12x=36\] |
| D. | \[{{x}^{2}}+12y=36\] |
| Answer» C. \[{{y}^{2}}-12x=36\] | |
| 343. |
The angle between the pair of planes represented by equation\[2{{x}^{2}}-2{{y}^{2}}+4{{z}^{2}}+6xz+2yz+3xy=0\]is |
| A. | \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\] |
| B. | \[{{\cos }^{-1}}\left( \frac{4}{21} \right)\] |
| C. | \[{{\cos }^{-1}}\left( \frac{4}{9} \right)\] |
| D. | \[{{\cos }^{-1}}\left( \frac{7}{\sqrt{84}} \right)\] |
| Answer» D. \[{{\cos }^{-1}}\left( \frac{7}{\sqrt{84}} \right)\] | |
| 344. |
What is the angle between two planes \[2x-y+z=4\] and \[x+y+2z=6?\] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{4}\] |
| D. | \[\frac{\pi }{6}\] |
| Answer» C. \[\frac{\pi }{4}\] | |
| 345. |
Let \[A(\vec{a})\] and \[B(\vec{b})\] be points on two skew line \[\vec{r}=\vec{a}+\vec{\lambda }\] and \[\vec{r}=\vec{b}+u\vec{q}\] and the shortest distance between the skew line is 1, where \[\vec{p}\] and \[\vec{q}\] are unit vectors forming adjacent sides of a parallelogram enclosing an area of \[\frac{1}{2}\]units. If an angle between AB and the line of shortest distance is \[60{}^\circ \], then \[AB=\] |
| A. | \[\frac{1}{2}\] |
| B. | \[2\] |
| C. | \[1\] |
| D. | \[\lambda \in R-\{0\}\] |
| Answer» C. \[1\] | |
| 346. |
The general solution of \[\sin x-\cos x=\sqrt{2}\], for any integer n is [Karnataka CET 2005] |
| A. | \[n\pi \] |
| B. | \[2n\pi +\frac{3\pi }{4}\] |
| C. | \[2n\pi \] |
| D. | \[(2n+1)\,\pi \] |
| Answer» C. \[2n\pi \] | |
| 347. |
Let \[{{A}_{n}}\] be the sum of the first n terms of the geometric series \[704+\frac{704}{2}+\frac{704}{4}+\frac{704}{8}+......\]and \[{{B}_{n}}\] be the sum of the first n terms of the geometric series \[1984+\frac{1984}{2}+\frac{1984}{4}+\frac{1984}{8}+......\] If \[{{A}_{n}}={{B}_{n}},\]then the value of n is (where \[n\in N\]). |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» C. 6 | |
| 348. |
If \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\] are A. P., then \[\left( \frac{1}{a}+\frac{1}{b}-\frac{a}{c} \right)\] \[\left( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} \right)\] is equal to |
| A. | \[\frac{4}{ac}-\frac{3}{{{b}^{2}}}\] |
| B. | \[\frac{{{b}^{2}}-ac}{{{a}^{2}}{{b}^{2}}{{c}^{2}}}\] |
| C. | \[\frac{4}{ac}-\frac{1}{{{b}^{2}}}\] |
| D. | None of these |
| Answer» B. \[\frac{{{b}^{2}}-ac}{{{a}^{2}}{{b}^{2}}{{c}^{2}}}\] | |
| 349. |
The points of contact of the circle \[{{x}^{2}}+{{y}^{2}}+2x+2y+1=0\]and the co-ordinate axes are |
| A. | \[(1,\,0),(0,\,1)\] |
| B. | \[(-1,\,0),(0,\,1)\] |
| C. | \[(-1,\,0),(0,\,-1)\] |
| D. | \[(1,\,\,0),(0,\,-1)\] |
| Answer» D. \[(1,\,\,0),(0,\,-1)\] | |
| 350. |
The area of the parallelogram whose diagonals are the vectors \[2\mathbf{a}-\mathbf{b}\] and \[4\mathbf{a}-5\mathbf{b},\] where a and b are the unit vectors forming an angle of \[{{45}^{o}},\] is |
| A. | \[3\sqrt{2}\] |
| B. | \[\frac{3}{\sqrt{2}}\] |
| C. | \[\sqrt{2}\] |
| D. | None of these |
| Answer» C. \[\sqrt{2}\] | |