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.
| 251. |
If P, Q and R are subsets of a set A, then \[R\times {{\left( {{P}^{c}}\text{ }\cup \text{ }{{Q}^{c}} \right)}^{c}}=\] [Karnataka CET 1993] |
| A. | \[\left( R\text{ }\times \text{ }P \right)\text{ }\cap \text{ }\left( R\text{ }\times \text{ }Q \right)\] |
| B. | \[(R\times Q)\cap (R\times P)\] |
| C. | \[(R\times P)\cup (R\times Q)\] |
| D. | None of these |
| Answer» C. \[(R\times P)\cup (R\times Q)\] | |
| 252. |
If \[X=\{{{4}^{n}}-3n-1:n\in N\}\] and \[Y=\{9(n-1):n\in N\},\] then \[X\cup Y\] is equal to [Karnataka CET 1997] |
| A. | X |
| B. | Y |
| C. | N |
| D. | None of these |
| Answer» C. N | |
| 253. |
The sum to n terms of the series 2+5+14+41+........is |
| A. | \[{{3}^{n-1}}+8n-3\] |
| B. | \[{{8.3}^{n}}+4n-8\] |
| C. | \[{{3}^{n+1}}+\frac{8}{3}n+1\] |
| D. | None of these |
| Answer» E. | |
| 254. |
The solution of the differential equation \[xy\frac{dy}{dx}=\frac{(1+{{y}^{2}})(1+x+{{x}^{2}})}{(1+{{x}^{2}})}\] is [AISSE 1983] |
| A. | \[\frac{1}{2}\log (1+{{y}^{2}})=\log x-{{\tan }^{-1}}x+c\] |
| B. | \[\frac{1}{2}\log (1+{{y}^{2}})=\log x+{{\tan }^{-1}}x+c\] |
| C. | \[\log (1+{{y}^{2}})=\log x-{{\tan }^{-1}}x+c\] |
| D. | \[\log (1+{{y}^{2}})=\log x+{{\tan }^{-1}}x+c\] |
| Answer» C. \[\log (1+{{y}^{2}})=\log x-{{\tan }^{-1}}x+c\] | |
| 255. |
There are 10 points in a plane, no three are collinear, except 4 which are collinear. All points are joined. Let L be the number of different straight lines and T be the number of different triangles, then |
| A. | \[T=120\] |
| B. | \[L=40\] |
| C. | \[T=3L-5\] |
| D. | None of these |
| Answer» C. \[T=3L-5\] | |
| 256. |
The lines \[2x+y-1=0,ax+3y-3=0\] and \[3x+2y-2=0\] are concurrent for [EAMCET 1994] |
| A. | All a |
| B. | \[a=4\]only |
| C. | \[-1\le a\le 3\] |
| D. | \[a>0\]only |
| Answer» B. \[a=4\]only | |
| 257. |
The equation of normal to the circle \[2{{x}^{2}}+2{{y}^{2}}-2x-5y+3=0\]at (1, 1) is [MP PET 2001] |
| A. | \[2x+y=3\] |
| B. | \[x-2y=3\] |
| C. | \[x+2y=3\] |
| D. | None of these |
| Answer» D. None of these | |
| 258. |
Choose the correct answer [Karnataka CET 1999] |
| A. | Every identity matrix is a scalar matrix |
| B. | Every scalar matrix is an identity matrix |
| C. | Every diagonal matrix is an identity matrix |
| D. | A square matrix whose each element is 1 is an identity matrix |
| Answer» B. Every scalar matrix is an identity matrix | |
| 259. |
The equation \[\sin x+\sin y+\sin z=-3\] for \[0\le x\le 2\pi ,\] \[0\le y\le 2\pi ,\] \[0\le z\le 2\pi \], has [Orissa JEE 2003] |
| A. | One solution |
| B. | Two sets of solutions |
| C. | Four sets of solutions |
| D. | No solution |
| Answer» B. Two sets of solutions | |
| 260. |
The radical axis of the pair of circle \[{{x}^{2}}+{{y}^{2}}=144\]and \[{{x}^{2}}+{{y}^{2}}-15x+12y=0\]is |
| A. | \[15x-12y=0\] |
| B. | \[3x-2y=12\] |
| C. | \[5x-4y=48\] |
| D. | None of these |
| Answer» D. None of these | |
| 261. |
If \[A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right],\]I is the unit matrix of order 2 and a, b are arbitrary constants, then \[{{(aI+bA)}^{2}}\]is equal to [RPET 1992] |
| A. | \[{{a}^{2}}I+abA\] |
| B. | \[{{a}^{2}}I+2abA\] |
| C. | \[{{a}^{2}}I+{{b}^{2}}A\] |
| D. | None of these |
| Answer» C. \[{{a}^{2}}I+{{b}^{2}}A\] | |
| 262. |
The equations of the lines through the point of intersection of the lines \[x-y+1=0\] and \[2x-3y+5=0\] and whose distance from the point (3, 2) is \[\frac{7}{5},\]is [IIT 1963] |
| A. | \[3x-4y-6=0\] and \[4x+3y+1=0\] |
| B. | \[3x-4y+6=0\] and \[4x-3y-1=0\] |
| C. | \[3x-4y+6=0\] and \[4x-3y+1=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 263. |
A force \[\mathbf{F}=2\mathbf{i}+\mathbf{j}-\mathbf{k}\] acts at a point A, whose position vector is \[2\mathbf{i}-\mathbf{j}\]. The moment of F about the origin is [Karnataka CET 2000] |
| A. | \[\mathbf{i}+2\mathbf{j}-4\mathbf{k}\] |
| B. | \[\mathbf{i}-2\mathbf{j}-4\mathbf{k}\] |
| C. | \[\mathbf{i}+2\mathbf{j}+4\mathbf{k}\] |
| D. | \[\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] |
| Answer» D. \[\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] | |
| 264. |
O is the circumventer of the triangle ABC and \[{{R}_{1}},{{R}_{2}},{{R}_{3}}\] are the radii of the circumcircles of the triangles OBA, OCA and OAB respectively, then \[\frac{a}{{{R}_{1}}}+\frac{b}{{{R}_{2}}}+\frac{c}{{{R}_{3}}}\] is equal to |
| A. | \[\frac{abc}{R}\] |
| B. | \[\frac{abc}{{{R}^{3}}}\] |
| C. | \[\frac{abc}{{{R}^{4}}}\] |
| D. | None |
| Answer» C. \[\frac{abc}{{{R}^{4}}}\] | |
| 265. |
For a set A, consider the following statements: 1. \[A\cup P(A)=P(A)\] 2. \[\{A\}\cap P(A)=A\] 3. \[P(A)-\{A\}=P(A)\] where P denotes power set. Which of the statements given above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | 3 only |
| D. | 1, 2 and 3 |
| Answer» B. 2 only | |
| 266. |
Let n be a fixed positive integer such that \[\sin \left( \frac{\pi }{2n} \right)+\cos \left( \frac{\pi }{2n} \right)=\frac{\sqrt{n}}{2},\] then: |
| A. | \[n=4\] |
| B. | \[n=5\] |
| C. | \[n=6\] |
| D. | None of these |
| Answer» D. None of these | |
| 267. |
If \[2{{\tan }^{2}}\theta ={{\sec }^{2}}\theta ,\]then the general value of \[\theta \] is [MP PET 1989] |
| A. | \[n\pi +\frac{\pi }{4}\] |
| B. | \[n\pi -\frac{\pi }{4}\] |
| C. | \[n\pi \pm \frac{\pi }{4}\] |
| D. | \[2n\pi \pm \frac{\pi }{4}\] |
| Answer» D. \[2n\pi \pm \frac{\pi }{4}\] | |
| 268. |
Ten different letters of an alphabet are given, words with five letters are formed form these given letters. Then the number of words which have at least one letter repeated is |
| A. | 69760 |
| B. | 30240 |
| C. | 99784 |
| D. | None of these |
| Answer» B. 30240 | |
| 269. |
The solution of the differential equation \[\frac{dy}{dx}=(a{{e}^{bx}}+c\cos mx)\] is |
| A. | \[y=\frac{a{{e}^{x}}}{b}+\frac{c}{m}\sin mx+k\] |
| B. | \[y=a{{e}^{x}}+c\sin mx+k\] |
| C. | \[y=\frac{a{{e}^{bx}}}{b}+\frac{c}{m}\sin mx+k\] |
| D. | None of these |
| Answer» D. None of these | |
| 270. |
A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through [IIT 1977] |
| A. | A fixed point |
| B. | A variable point |
| C. | Origin |
| D. | None of these |
| Answer» B. A variable point | |
| 271. |
The locus of a point which moves in such a way that its distance from (0,0) is three times its distance from the x-axis, as given by [MP PET 1993] |
| A. | \[{{x}^{2}}-8{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+8{{y}^{2}}=0\] |
| C. | \[4{{x}^{2}}-{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}-4{{y}^{2}}=0\] |
| Answer» B. \[{{x}^{2}}+8{{y}^{2}}=0\] | |
| 272. |
If the coordinates of A and B be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment AB is |
| A. | \[2x+3y=18\] |
| B. | \[2x-3y+18=0\] |
| C. | \[2x+3y-1=0\] |
| D. | \[3x-2y+1=0\] |
| Answer» B. \[2x-3y+18=0\] | |
| 273. |
Suppose a population A has 100 observations \[101,102,.....,200\] and another population B has 100 observations 151, 152 ???? 250. If \[{{V}_{A}}\,\,and\,\,{{V}_{B}}\] represent the variances of the two populations, respectively then \[\frac{{{V}_{A}}}{{{V}_{B}}}\] is |
| A. | 1 |
| B. | \[\frac{9}{4}\] |
| C. | \[\frac{4}{9}\] |
| D. | \[\frac{2}{3}\] |
| Answer» B. \[\frac{9}{4}\] | |
| 274. |
For what value of \[\lambda \], the system of equations \[x+y+z=6,x+2y+3z=10,\]\[x+2y+\lambda z=12\]is inconsistent [AIEEE 2002] |
| A. | \[\lambda =1\] |
| B. | \[\lambda =2\] |
| C. | \[\lambda =-2\] |
| D. | \[\lambda =3\] |
| Answer» E. | |
| 275. |
What is the sum of the series 0.5 + 0.55 + 0.555 +... to n terms? |
| A. | \[\frac{5}{9}\left[ n-\frac{2}{9}\left( 1-\frac{1}{{{10}^{n}}} \right) \right]\] |
| B. | \[\frac{1}{9}\left[ 5-\frac{2}{9}\left( 1-\frac{1}{{{10}^{n}}} \right) \right]\] |
| C. | \[\frac{1}{9}\left[ n-\frac{5}{9}\left( 1-\frac{1}{{{10}^{n}}} \right) \right]\] |
| D. | \[\frac{5}{9}\left[ n-\frac{1}{9}\left( 1-\frac{1}{{{10}^{n}}} \right) \right]\] |
| Answer» E. | |
| 276. |
Let \[\alpha \]and \[\beta \] be the roots of the equation \[{{x}^{2}}+x+1=0\] The equation whose roots are \[{{\alpha }^{19}},{{\beta }^{7}}\] is [IIT Screening 1994] |
| A. | \[{{x}^{2}}-x-1=0\] |
| B. | \[{{x}^{2}}-x+1=0\] |
| C. | \[{{x}^{2}}+x-1=0\] |
| D. | \[{{x}^{2}}+x+1=0\] |
| Answer» E. | |
| 277. |
Solution of the equation \[\cos x\cos y\frac{dy}{dx}=-\sin x\sin y\]is [DSSE 1987] |
| A. | \[\sin y+\cos x=c\] |
| B. | \[\sin y-\cos x=c\] |
| C. | \[\sin y.\cos x=c\] |
| D. | \[\sin y=c\cos x\] |
| Answer» E. | |
| 278. |
The point of the curve \[{{y}^{2}}=2(x-3)\] at which the normal is parallel to the line\[y-2x+1=0\]is [MP PET 1998] |
| A. | (5,2) |
| B. | \[\left( -\frac{1}{2},-2 \right)\] |
| C. | (5, ?2) |
| D. | \[\left( \frac{3}{2},\,2 \right)\] |
| Answer» D. \[\left( \frac{3}{2},\,2 \right)\] | |
| 279. |
If the sum of the two roots of the equation \[4{{x}^{3}}+16{{x}^{2}}-9x-36=0\] is zero, then the roots are [MP PET 1986] |
| A. | 1, 2 -2 |
| B. | \[-2,\frac{2}{3},-\frac{2}{3}\] |
| C. | \[-3,\frac{3}{2},-\frac{3}{2}\] |
| D. | \[-4,\frac{3}{2},-\frac{3}{2}\] |
| Answer» E. | |
| 280. |
\[\sec {{50}^{o}}+\tan {{50}^{o}}\] is equal to [DCE 2002] |
| A. | \[\tan {{20}^{o}}+\tan {{50}^{o}}\] |
| B. | \[2\tan {{20}^{o}}+\tan {{50}^{o}}\] |
| C. | \[\tan {{20}^{o}}+2\tan {{50}^{o}}\] |
| D. | \[2\tan {{20}^{o}}+2\tan {{50}^{o}}\] |
| Answer» D. \[2\tan {{20}^{o}}+2\tan {{50}^{o}}\] | |
| 281. |
The value of \[\sum\limits_{n=1}^{10}{\sum\limits_{m=1}^{10}{({{m}^{2}}+{{n}^{2}})}}\] equals |
| A. | 4235 |
| B. | 5050 |
| C. | 7700 |
| D. | None of these |
| Answer» D. None of these | |
| 282. |
A particle is moving along the curve \[x=a{{t}^{2}}+bt+c.\]If \[ac={{b}^{2}},\] then the particle would be moving with uniform [Orissa JEE 2003] |
| A. | Rotation |
| B. | Velocity |
| C. | Acceleration |
| D. | Retardation |
| Answer» D. Retardation | |
| 283. |
A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is choosen at random. The probability that this pencil is not defective is [EAMCET 1991] |
| A. | \[\frac{3}{5}\] |
| B. | \[\frac{3}{10}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{1}{2}\] |
| Answer» B. \[\frac{3}{10}\] | |
| 284. |
The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}-{{y}^{2}}-8x+12=0\]is [EAMCET 1990] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 285. |
A certain type of missile hits the target with probability p=0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit? |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | None of the above |
| Answer» B. 6 | |
| 286. |
If Q is the image of the point P(2, 3, 4) under the reflection in the plane \[x-2y+5z=6\], then the equation of the line \[PQ\]is |
| A. | \[\frac{x-2}{-1}=\frac{y-3}{2}=\frac{z-4}{5}\] |
| B. | \[\frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-4}{5}\] |
| C. | \[\frac{x-2}{-1}=\frac{y-3}{-2}=\frac{z-4}{5}\] |
| D. | \[\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{5}\] |
| Answer» C. \[\frac{x-2}{-1}=\frac{y-3}{-2}=\frac{z-4}{5}\] | |
| 287. |
If matrix \[A=\left[ \begin{matrix} 3 & 2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \\ \end{matrix} \right]\]and \[{{A}^{-1}}=\frac{1}{K}adj(A),\] then \[K\]is [UPSEAT 2002] |
| A. | 7 |
| B. | -7 |
| C. | \[\frac{1}{7}\] |
| D. | 11 |
| Answer» E. | |
| 288. |
Two given circles \[{{x}^{2}}+{{y}^{2}}+ax+by+c=0\]and \[{{x}^{2}}+{{y}^{2}}+dx+ey+f=0\]will intersect each other orthogonally, only when |
| A. | \[a+b+c=d+e+f\] |
| B. | \[ad+be=c+f\] |
| C. | \[ad+be=2c+2f\] |
| D. | \[2ad+2be=c+f\] |
| Answer» D. \[2ad+2be=c+f\] | |
| 289. |
The real part of \[{{(1-i)}^{-i}}\]is [RPET 1999] |
| A. | \[{{e}^{-\pi /4}}\cos \left( \frac{1}{2}\log 2 \right)\] |
| B. | \[-{{e}^{-\pi /4}}\sin \left( \frac{1}{2}\log 2 \right)\] |
| C. | \[{{e}^{\pi /4}}\cos \left( \frac{1}{2}\log 2 \right)\] |
| D. | \[{{e}^{-\pi /4}}\sin \left( \frac{1}{2}\log 2 \right)\] |
| Answer» B. \[-{{e}^{-\pi /4}}\sin \left( \frac{1}{2}\log 2 \right)\] | |
| 290. |
\[\frac{\sin x-\sin 3x}{{{\sin }^{2}}x-{{\cos }^{2}}x}\] is equal to |
| A. | \[\sin 2x\] |
| B. | \[\cos 2x\] |
| C. | \[\tan 2x\] |
| D. | None of these |
| Answer» E. | |
| 291. |
Two straight lines passing through the point \[A(3,2)\] cut the line \[2y=x+3\] and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is |
| A. | \[7x+y-21=0\] |
| B. | \[x+7y+21=0\] |
| C. | \[2x+y-8=0\] |
| D. | \[x+2y+8=0\] |
| Answer» B. \[x+7y+21=0\] | |
| 292. |
The area of the figure formed by the lines \[ax+by+c=0,ax-by+c=0,ax+by-c=0\]and \[ax-by-c=0\] is |
| A. | \[\frac{{{c}^{2}}}{ab}\] |
| B. | \[\frac{2{{c}^{2}}}{ab}\] |
| C. | \[\frac{{{c}^{2}}}{2ab}\] |
| D. | \[\frac{{{c}^{2}}}{4ab}\] |
| Answer» C. \[\frac{{{c}^{2}}}{2ab}\] | |
| 293. |
Let \[(h,k)\] be a fixed point where \[h>0,k>0.\] A straight line passing through this point cuts the positive direction of the coordinate axes at the points P and Q. Then the minimum area of the \[\Delta OPQ.O\] O being the origin, is |
| A. | 4hk sq. units |
| B. | 2hk sq. units |
| C. | 3hk sq. units |
| D. | None of these |
| Answer» C. 3hk sq. units | |
| 294. |
\[f:R\to \]defined by \[f(x)=(x-1)(x-2)(x-3)\] is |
| A. | one-one and into |
| B. | one-one and onto |
| C. | Many one and into |
| D. | many-one and onto |
| Answer» E. | |
| 295. |
A committee has to be made of 5 members from 6 men and 4 women. The probability that at least one woman is present in committee, is |
| A. | \[\frac{1}{42}\] |
| B. | \[\frac{41}{42}\] |
| C. | \[\frac{2}{63}\] |
| D. | \[\frac{1}{7}\] |
| Answer» C. \[\frac{2}{63}\] | |
| 296. |
The moment of the force \[\overrightarrow{F}\] acting at a point P, about the point C is [MP PET 1987] |
| A. | \[\overrightarrow{F}\times \overrightarrow{CP}\] |
| B. | \[\overrightarrow{CP}\,.\,\overrightarrow{F}\] |
| C. | A vector having the same direction as \[\overrightarrow{F}\] |
| D. | \[\overrightarrow{CP}\times \overrightarrow{F}\] |
| Answer» E. | |
| 297. |
One diagonal of a square is along the line \[8x-15y=0\] and one of its vertex is (1, 2). Then the equation of the sides of the square passing through this vertex, are [IIT 1962] |
| A. | \[23x+7y=9,\ 7x+23y=53\] |
| B. | \[23x-7y+9=0,\ 7x+23y+53=0\] |
| C. | \[23x-7y-9=0,\ 7x+23y-53=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 298. |
A ray of light passing through a point (1, 2) is reflected on the x-axis at point Q and passes through the point (5, 8). Then the abscissa of the point Q is |
| A. | -3 |
| B. | 44325 |
| C. | 13/5 |
| D. | None of these |
| Answer» C. 13/5 | |
| 299. |
The point \[A(2,1)\] is translated parallel to the line \[x-y=3\] by, a distance of 4 units. If the new position A? is in the third quadrant, then the coordinates of A? are |
| A. | \[(2+2\sqrt{2},1+2\sqrt{2})\] |
| B. | \[(-2+\sqrt{2},-1-2\sqrt{2})\] |
| C. | \[(2-2\sqrt{2},1-2\sqrt{2})\] |
| D. | None of these |
| Answer» D. None of these | |
| 300. |
The equation of straight line passing through (-a, 0) and making a triangle with the axes of area T is |
| A. | \[2Tx+{{a}^{2}}y+2aT=0\] |
| B. | \[2Tx-{{a}^{2}}y+2aT=0\] |
| C. | \[2Tx-{{a}^{2}}y-2aT=0\] |
| D. | None of these |
| Answer» C. \[2Tx-{{a}^{2}}y-2aT=0\] | |