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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.
| 501. |
Two cards are drawn successively with replacement from a well shuffled deck of 52 cards then the mean of the number of aces is [J & K 2005] |
| A. | 1/13 |
| B. | 3/13 |
| C. | 2/13 |
| D. | None of these |
| Answer» D. None of these | |
| 502. |
The line which passes through the origin and intersect the two lines \[\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{3},\frac{x-4}{2}=\frac{y+3}{3}=\frac{z-14}{4},\] is |
| A. | \[\frac{x}{1}=\frac{y}{-3}=\frac{z}{5}\] |
| B. | \[\frac{x}{-1}=\frac{y}{3}=\frac{z}{5}\] |
| C. | \[\frac{x}{1}=\frac{y}{3}=\frac{z}{-5}\] |
| D. | \[\frac{x}{1}=\frac{y}{4}=\frac{z}{-5}\] |
| Answer» B. \[\frac{x}{-1}=\frac{y}{3}=\frac{z}{5}\] | |
| 503. |
Let L be the line of intersection of the planes \[2x+3y+z=1\] and\[x+3y+2z=2\]. If L makes an angle \[\alpha \] with the positive x-axis, then \[cos\text{ }\alpha \]equals |
| A. | 1 |
| B. | \[\frac{1}{\sqrt{2}}\] |
| C. | \[\frac{1}{\sqrt{3}}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 504. |
The locus of a point, such that the sum of the squares of its distances from the planes\[x+y+z=0\], \[x\text{-}z=0\] and \[x-2y+z=0\text{ }is\text{ }9,\] is |
| A. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=3\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=9\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12\] | |
| 505. |
What does the series \[1+{{3}^{-\frac{1}{2}}}+3+\frac{1}{3\sqrt{3}}+...\] represents? |
| A. | AP |
| B. | GP |
| C. | HP |
| D. | None of the above series |
| Answer» E. | |
| 506. |
Area of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [Karnataka CET 1993] |
| A. | \[\pi \,ab\]sq. unit |
| B. | \[\frac{1}{2}\pi \,ab\]sq. unit |
| C. | \[\frac{1}{4}\pi \,ab\]sq. unit |
| D. | None of these |
| Answer» B. \[\frac{1}{2}\pi \,ab\]sq. unit | |
| 507. |
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then person travelling by car or bus is |
| A. | 80 percent |
| B. | 40 percent |
| C. | 60 percent |
| D. | 70 percent |
| Answer» D. 70 percent | |
| 508. |
The line \[x+y=4\] divides the line joining the points (-1, 1) and (5, 7) in the ratio [IIT 1965; UPSEAT 1999] |
| A. | 0.0840277777777778 |
| B. | 0.0430555555555556 |
| C. | 1 : 2 externally |
| D. | None of these |
| Answer» C. 1 : 2 externally | |
| 509. |
If \[\left( \frac{1}{2},\frac{1}{3},n \right)\] are the direction cosines of a line, then the value of n is [Kerala (Engg.) 2002] |
| A. | \[\frac{\sqrt{23}}{6}\] |
| B. | \[\frac{23}{6}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{3}{2}\] |
| Answer» B. \[\frac{23}{6}\] | |
| 510. |
A is one of 6 horses entered for a race, and is to be ridden by one of two jockeys B and C. it is 2 to 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, his chance of winning is trebled. What are the odds against winning of A? |
| A. | \[5:13\] |
| B. | \[5:18\] |
| C. | \[13:5\] |
| D. | None of these |
| Answer» D. None of these | |
| 511. |
3 friends A, B and C play the game ?Pahle hum pahle tum? in which they throw a die one after the other and the one who will get a composite number 1st will be announced as winner, if A started the game followed by B and then C then what is the ratio of their winning probabilities? |
| A. | \[9:6:4\] |
| B. | \[8:6:5\] |
| C. | \[10:5:4\] |
| D. | None of these |
| Answer» B. \[8:6:5\] | |
| 512. |
A regular polygon with equal sides has 9 diagonals. Two of the vertices are at \[A(-1,0)\] and\[B(1,0)\]. Possible areas of polygon is |
| A. | \[\frac{3\sqrt{3}}{2},2\sqrt{3},6\sqrt{3}\] |
| B. | \[2\sqrt{3},3\sqrt{3},6\sqrt{3}\] |
| C. | \[9\sqrt{3},6\sqrt{3},2\sqrt{3}\] |
| D. | \[\frac{3\sqrt{3}}{2},3\sqrt{3},6\sqrt{3}\] |
| Answer» B. \[2\sqrt{3},3\sqrt{3},6\sqrt{3}\] | |
| 513. |
A line which makes an acute angle \[\theta \] with the positive direction of x-axis is drawn through the point P(3, 4) to meet the line \[x=6\] at R and \[y=8\] at S, then |
| A. | \[PR=3\cos \theta \] |
| B. | \[PS=-4\cos ec\theta \] |
| C. | \[PR-PS=\frac{2(3sin\theta +4cos\theta )}{\sin 2\theta }\] |
| D. | \[\frac{9}{{{(PR)}^{2}}}+\frac{16}{{{(PS)}^{2}}}=1\] |
| Answer» E. | |
| 514. |
If \[\tan \alpha =\frac{m}{m+1}\]and \[\tan \beta =\frac{1}{2m+1}\], then \[\alpha +\beta =\] [IIT 1978; EAMCET 1992; Roorkee 1998; JMI EEE 2001] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | None of these |
| Answer» C. \[\frac{\pi }{6}\] | |
| 515. |
Locus of centroid of the triangle whose vertices are \[(\alpha cos\,t,a\,sin\,t),(b\,sin\,t,-b\,cos\,t)\] and \[(1,0)\], where t is a parameter, is |
| A. | \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\] |
| B. | \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}\] |
| C. | \[{{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| D. | \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| Answer» D. \[{{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}\] | |
| 516. |
Which of the following set of points are non- collinear [MP PET 1990] |
| A. | (1, ?1, 1), (?1, 1, 1), (0, 0, 1) |
| B. | (1, 2, 3), (3, 2, 1), (2, 2, 2) |
| C. | (?2,4, ?3), (4, ?3, ?2), (?3, ?2, 4) |
| D. | (2, 0, ?1), (3, 2, ?2), (5, 6, ?4) |
| Answer» D. (2, 0, ?1), (3, 2, ?2), (5, 6, ?4) | |
| 517. |
One dice is thrown three times and the sum of the thrown numbers is 15. The probability for which number 4 appears in first throw [MP PET 2004] |
| A. | \[\frac{1}{18}\] |
| B. | \[\frac{1}{36}\] |
| C. | \[\frac{1}{9}\] |
| D. | \[\frac{1}{3}\] |
| Answer» B. \[\frac{1}{36}\] | |
| 518. |
If the points (?1, 3, 2), (?4, 2, ?2) and \[(5,\,\,5,\,\,\lambda )\] are collinear, then \[\lambda \]= |
| A. | ? 10 |
| B. | 5 |
| C. | ? 5 |
| D. | 10 |
| Answer» E. | |
| 519. |
The triangle PQR is inscribed in the circle \[{{x}^{2}}+{{y}^{2}}=25\]. If Q and R have co-ordinates (3,4) and (? 4, 3) respectively, then \[\angle QPR\] is equal to [IIT Screening 2000] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{4}\] |
| D. | \[\frac{\pi }{6}\] |
| Answer» D. \[\frac{\pi }{6}\] | |
| 520. |
For what values of x is the equation \[2\,sin\,\theta =x+\frac{1}{x}\]valid? |
| A. | \[x=\pm 1\] |
| B. | All real values of x |
| C. | \[-1<x<1\] |
| D. | \[x>1\]and \[x<-1\] |
| Answer» B. All real values of x | |
| 521. |
\[\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{n(n+1)}\] equals |
| A. | \[\frac{1}{n(n+1)}\] |
| B. | \[\frac{n}{n+1}\] |
| C. | \[\frac{2n}{n+1}\] |
| D. | \[\frac{2}{n(n+1)}\] |
| Answer» C. \[\frac{2n}{n+1}\] | |
| 522. |
A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated is |
| A. | \[\frac{6!8!10!}{4!6!}\] |
| B. | \[\frac{8!8!10!}{4!6!}\] |
| C. | \[\frac{8!8!6!}{6!4!}\] |
| D. | None of these |
| Answer» C. \[\frac{8!8!6!}{6!4!}\] | |
| 523. |
A line passes through the point of intersection of \[2x+y=5\] and \[x+3y+8=0\] and parallel to the line \[3x+4y=7\] is [RPET 1984; MP PET 1991] |
| A. | \[3x+4y+3=0\] |
| B. | \[3x+4y=0\] |
| C. | \[4x-3y+3=0\] |
| D. | \[4x-3y=3\] |
| Answer» B. \[3x+4y=0\] | |
| 524. |
The probability that a particular day in the month of July is a rainy day is ¾. Two person whose credibility are 4/5 and 2/3. Respectively, claim that 15 July was rainy day. The probability that it was really a rainy day is |
| A. | \[\frac{12}{13}\] |
| B. | \[\frac{11}{12}\] |
| C. | \[\frac{24}{25}\] |
| D. | \[\frac{29}{30}\] |
| Answer» D. \[\frac{29}{30}\] | |
| 525. |
The probability of India winning a test match against Westinies is \[\frac{1}{2}\]assuming independence from match to match the probability that in a 5 match series India?s second win occurs at the third test, is. |
| A. | 44257 |
| B. | 44228 |
| C. | 44287 |
| D. | 44409 |
| Answer» D. 44409 | |
| 526. |
If \[\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}\], then the general value of \[\theta \]is [MP PET 2004; Orissa JEE 2004] |
| A. | \[\frac{n\pi }{3}+\frac{\pi }{12}\] |
| B. | \[\frac{n\pi }{3}+\frac{7\pi }{36}\] |
| C. | \[n\pi +\frac{7\pi }{12}\] |
| D. | \[n\pi +\frac{\pi }{12}\] |
| Answer» C. \[n\pi +\frac{7\pi }{12}\] | |
| 527. |
Which of the following relations is incorrect |
| A. | \[(A+B+....+l{)}'={A}'+{B}'+....+{l}'\] |
| B. | \[(AB....l{)}'={A}'{B}'....{l}'\] |
| C. | \[(kA{)}'=k{A}'\] |
| D. | \[(A{)}'=A\] |
| Answer» C. \[(kA{)}'=k{A}'\] | |
| 528. |
Consider any set of observations \[{{x}_{1}},{{x}_{2}},{{x}_{3,...}}{{x}_{101}};\] it being given that \[{{x}_{1}}<{{x}_{2}}<{{x}_{3}}<...<{{x}_{100}}<{{x}_{101}};\] then the mean deviation of this set of observations about a point k is minimum when k equals |
| A. | \[{{x}_{1}}\] |
| B. | \[{{x}_{51}}\] |
| C. | \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] |
| D. | \[{{x}_{50}}\] |
| Answer» C. \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] | |
| 529. |
The mean of five observations is 4 and their variance is \[5\cdot 2\]. If three of these observations are 2, 4 and 6, then the other two observations are |
| A. | 3 and 6 |
| B. | 2 and 6 |
| C. | 5 and 8 |
| D. | 1 and 7 |
| Answer» E. | |
| 530. |
The mean and SD of 63 children on an arithmetic test are respectively 27, 6 and 7.1. to them are added a new group of 26 who had less training and whose mean is 19.2 and SD. 6.2 The values of the combined group differ from the original as to (i) the mean and (ii) the SD is |
| A. | 25.1, 7.8 |
| B. | 2.3, 0.8 |
| C. | 1.5, 0.9 |
| D. | None of these |
| Answer» B. 2.3, 0.8 | |
| 531. |
Let \[A=R-\{3\},B=R-\{1\},\] and let \[f:A\to B\] be defined by \[f(x)=\frac{x-2}{x-3}f\] is |
| A. | Not one-one |
| B. | Not onto |
| C. | Many-one and onto |
| D. | One-one and onto |
| Answer» E. | |
| 532. |
The image of the interval [1, 3] under the mapping \[f:R\to R,\] given by \[f(x)=2{{x}^{3}}-24x+107\] is |
| A. | \[[0,89]\] |
| B. | \[[75,89]\] |
| C. | \[[0,75]\] |
| D. | None of these |
| Answer» C. \[[0,75]\] | |
| 533. |
Inverse of the function \[f:R\to (-\infty ,1)\]given by\[f(x)=1-{{2}^{-x}}\] is |
| A. | \[-{{\log }_{2}}(1-x)\] |
| B. | \[-{{\log }_{2}}(x)\] |
| C. | 0 |
| D. | 1 |
| Answer» B. \[-{{\log }_{2}}(x)\] | |
| 534. |
A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is |
| A. | \[\frac{5}{11}\] |
| B. | \[\frac{21}{55}\] |
| C. | \[\frac{4}{11}\] |
| D. | None of these |
| Answer» C. \[\frac{4}{11}\] | |
| 535. |
The two circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6=0\]and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\]touch each other. The equation of their common tangent is [DCE 1999] |
| A. | \[x=3\] |
| B. | \[y=6\] |
| C. | \[7x-12y-21=0\] |
| D. | \[7x+12y+21=0\] |
| Answer» B. \[y=6\] | |
| 536. |
A point moves such that the sum of its distances from two fixed points (ae,0) and (-ae,0) is always 2a. Then equation of its locus is [MNR 1981] |
| A. | \[\]\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\] |
| B. | \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\] |
| C. | \[\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\] |
| D. | None of these |
| Answer» B. \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1\] | |
| 537. |
If \[\sin A+\cos A=\sqrt{2},\]then \[{{\cos }^{2}}A=\] |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{3}{2}\] |
| Answer» C. \[\frac{1}{\sqrt{2}}\] | |
| 538. |
If a line makes the angle \[\alpha ,\beta ,\gamma \] with three dimensional co-ordinate axes respectively, then \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma =\] [MP PET 1994, 95,99; RPET 2003; Kerala (Engg.) 2005] |
| A. | ? 2 |
| B. | ? 1 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 539. |
If \[\vec{a}\] is a position vector of a point (1, -3) and A is another point (-1, 5), then what are the coordinates of the point B such that\[\overrightarrow{AB}=\vec{a}\]? |
| A. | (2, 0) |
| B. | (0, 2) |
| C. | (-2, 0) |
| D. | (0, -2) |
| Answer» C. (-2, 0) | |
| 540. |
If \[\overset{\to }{\mathop{{{r}_{1}}}}\,,\overset{\to }{\mathop{{{r}_{2}}}}\,,\overset{\to }{\mathop{{{r}_{3}}}}\,\] are the position vectors of three collinear points and scalars m and n exist such that\[\overset{\to }{\mathop{{{r}_{3}}}}\,=m\overset{\to }{\mathop{{{r}_{1}}}}\,+n\overset{\to }{\mathop{{{r}_{2}}}}\,\], then what is the value of (m+n)? |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» C. -1 | |
| 541. |
Circles \[{{(x+a)}^{2}}+{{(y+b)}^{2}}={{a}^{2}}\] and \[{{(x+\alpha )}^{2}}\] \[+{{(y+\beta )}^{2}}=\]\[{{\beta }^{2}}\] cut orthogonally, if |
| A. | \[a\alpha +b\beta ={{b}^{2}}+{{\alpha }^{2}}\] |
| B. | \[2(a\alpha +b\beta )={{b}^{2}}+{{\alpha }^{2}}\] |
| C. | \[a\alpha +b\beta ={{a}^{2}}+{{b}^{2}}\] |
| D. | None of these |
| Answer» C. \[a\alpha +b\beta ={{a}^{2}}+{{b}^{2}}\] | |
| 542. |
The equation of the normal to the circle \[{{x}^{2}}+{{y}^{2}}-2x=0\]parallel to the line \[x+2y=3\]is |
| A. | \[2x+y-1=0\] |
| B. | \[2x+y+1=0\] |
| C. | \[x+2y-1=0\] |
| D. | \[x+2y+1=0\] |
| Answer» D. \[x+2y+1=0\] | |
| 543. |
If \[\sec \theta =1\frac{1}{4}\], then \[\tan \frac{\theta }{2}=\] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{5}{4}\] |
| Answer» B. \[\frac{3}{4}\] | |
| 544. |
If \[b\sin \alpha =a\sin (\alpha +2\beta ),\] then \[\frac{a+b}{a-b}=\] |
| A. | \[\frac{\tan \beta }{\tan (\alpha +\beta )}\] |
| B. | \[\frac{\cot \beta }{\cot (\alpha -\beta )}\] |
| C. | \[\frac{-\cot \beta }{\cot (\alpha +\beta )}\] |
| D. | \[\frac{\cot \beta }{\cot (\alpha +\beta )}\] |
| Answer» D. \[\frac{\cot \beta }{\cot (\alpha +\beta )}\] | |
| 545. |
The co-ordinates of the point P are \[(x,y,z)\]and the direction cosines of the line OP when O is the origin, are \[l,\,m,\,n\]. If \[OP\], then |
| A. | \[l=x,\,m=y,\,n=z\] |
| B. | \[l=xr,m=yr,n=zr\] |
| C. | \[x=lr,\,y=mr,\,z=nr\] |
| D. | None of these |
| Answer» D. None of these | |
| 546. |
The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2 and 3. |
| A. | 64322 |
| B. | 48522 |
| C. | 38664 |
| D. | 1000 |
| Answer» D. 1000 | |
| 547. |
The inequality \[|z-4|\,<\,|\,z-2|\]represents the region given by [IIT 1982; RPET 1995; AIEEE 2002] |
| A. | \[\operatorname{Re}(z)>0\] |
| B. | \[\operatorname{Re}(z)<0\] |
| C. | \[\operatorname{Re}(z)>2\] |
| D. | None of these |
| Answer» E. | |
| 548. |
The mean mark in statistics of 100 students in a class was 72. The mean mark of boys was 75. While their number was 70. The mean mark of girls in the class was |
| A. | 65 |
| B. | 60 |
| C. | 66 |
| D. | 62 |
| Answer» B. 60 | |
| 549. |
A fair die is tossed 180 times, the standard deviation of the number of sixes equal to |
| A. | \[\sqrt{30}\] |
| B. | 5 |
| C. | 25 |
| D. | \[\sqrt{90}\] |
| Answer» C. 25 | |
| 550. |
Distance of the point \[P(\vec{p})\] from the line \[\vec{r}=\vec{a}+\lambda \vec{b}\] is |
| A. | \[\left| (\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{a}).\vec{b})\vec{b}}{{{\left| {\vec{b}} \right|}^{2}}} \right|\] |
| B. | \[\left| (\vec{b}-\vec{p})+\frac{((\vec{p}-\vec{a}).\vec{b})\vec{b}}{{{\left| {\vec{b}} \right|}^{2}}} \right|\] |
| C. | \[\left| (\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{b}).\vec{b})\vec{b}}{{{\left| {\vec{b}} \right|}^{2}}} \right|\] |
| D. | None of these |
| Answer» C. \[\left| (\vec{a}-\vec{p})+\frac{((\vec{p}-\vec{b}).\vec{b})\vec{b}}{{{\left| {\vec{b}} \right|}^{2}}} \right|\] | |