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.
| 7001. |
A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is [EAMCET 2003] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 7002. |
A particle moves along a straight line so that its distance s in time t sec is \[s=t+6{{t}^{2}}-{{t}^{3}}\]. After what time is the acceleration zero [AMU 1999] |
| A. | 2 sec |
| B. | 3 sec |
| C. | 4 sec |
| D. | 6 sec |
| Answer» B. 3 sec | |
| 7003. |
Angle between the line joining the origin to the points of intersection of the curves \[2{{x}^{2}}+3{{y}^{2}}+10x=0\] and \[3{{x}^{2}}+5{{y}^{2}}+16x=0\] is |
| A. | \[{{\tan }^{-1}}\frac{3}{2}\] |
| B. | \[{{\tan }^{-1}}\frac{4}{5}\] |
| C. | \[{{90}^{o}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7004. |
The speed \[v\] of a particle moving along a straight line is given by \[a+b{{v}^{2}}={{x}^{2}}\] (where x is its distance from the origin). The acceleration of the particle is [MP PET 2002] |
| A. | \[bx\] |
| B. | \[x/a\] |
| C. | \[x/b\] |
| D. | \[x/ab\] |
| Answer» D. \[x/ab\] | |
| 7005. |
The length of the side of a square sheet of metal is increasing at the rate of \[4cm/\sec \]. The rate at which the area of the sheet is increasing when the length of its side is 2 cm, is |
| A. | \[16\,c{{m}^{2}}/\sec \] |
| B. | \[8\,c{{m}^{2}}/\sec \] |
| C. | \[32\,c{{m}^{2}}/\sec \] |
| D. | None of these |
| Answer» B. \[8\,c{{m}^{2}}/\sec \] | |
| 7006. |
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is [AIEEE 2004] |
| A. | \[\frac{28}{256}\] |
| B. | \[\frac{219}{256}\] |
| C. | \[\frac{128}{256}\] |
| D. | \[\frac{37}{256}\] |
| Answer» B. \[\frac{219}{256}\] | |
| 7007. |
If \[|{{z}_{1}}|\,=\,|{{z}_{2}}|\]and \[arg\,\,\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\pi \], then \[{{z}_{1}}+{{z}_{2}}\]is equal to |
| A. | 0 |
| B. | Purely imaginary |
| C. | Purely real |
| D. | None of these |
| Answer» B. Purely imaginary | |
| 7008. |
If \[{{(\sqrt{8}+i)}^{50}}={{3}^{49}}(a+ib)\] then \[{{a}^{2}}+{{b}^{2}}\] is [Kerala (Engg.) 2005] |
| A. | 3 |
| B. | 8 |
| C. | 9 |
| D. | \[\sqrt{8}\] |
| E. | 4 |
| Answer» D. \[\sqrt{8}\] | |
| 7009. |
If the sides of the triangle are \[5K,\ 6K,\ 5K\]and radius of incircle is 6 then value of K is equal to [Pb. CET 2004] |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» B. 5 | |
| 7010. |
A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is [DCE 2002] |
| A. | \[\frac{(2n!)}{{{(n!)}^{2}}}{{\left( \frac{1}{2} \right)}^{2n}}\] |
| B. | \[1-\frac{(2n!)}{{{(n!)}^{2}}}\] |
| C. | \[1-\frac{(2n!)}{{{(n!)}^{2}}}\,.\,\frac{1}{{{4}^{n}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7011. |
The differential equation \[y\frac{dy}{dx}+x=a\](a is any constant) represents |
| A. | A set of circles having centre on the y-axis |
| B. | A set of circles centre on the x-axis |
| C. | A set of ellipses |
| D. | None of these |
| Answer» C. A set of ellipses | |
| 7012. |
In how many ways a garland can be made from exactly 10 flowers [MP PET 1984] |
| A. | \[10\ !\] |
| B. | \[9\ !\] |
| C. | \[2(9\ !)\] |
| D. | \[\frac{9\ !}{2}\] |
| Answer» E. | |
| 7013. |
If the non-zero vectors a and b are perpendicular to each other, then the solution of the equation \[\mathbf{r}\times \mathbf{a}=\mathbf{b}\] is given by |
| A. | \[\mathbf{r}=x\mathbf{a}+\frac{1}{\mathbf{a}\,.\,\,\mathbf{a}}(\mathbf{a}\times \mathbf{b})\] |
| B. | \[\mathbf{r}=x\mathbf{b}-\frac{1}{\mathbf{b}\,.\,\,\mathbf{b}}(\mathbf{a}\times \mathbf{b})\] |
| C. | \[\mathbf{r}=x\mathbf{a}\times \mathbf{b}\] |
| D. | \[\mathbf{r}=x\mathbf{b}\times \mathbf{a}\] |
| Answer» B. \[\mathbf{r}=x\mathbf{b}-\frac{1}{\mathbf{b}\,.\,\,\mathbf{b}}(\mathbf{a}\times \mathbf{b})\] | |
| 7014. |
If \[{{z}_{1}}\] and \[{{z}_{2}}\] are any two complex numbers then \[|{{z}_{1}}+{{z}_{2}}{{|}^{2}}\] \[+|{{z}_{1}}-{{z}_{2}}{{|}^{2}}\] is equal to [MP PET 1993; RPET 1997] |
| A. | \[2|{{z}_{1}}{{|}^{2}}\,|{{z}_{2}}{{|}^{2}}\] |
| B. | \[2|{{z}_{1}}{{|}^{2}}+\,2\,\,|{{z}_{2}}{{|}^{2}}\] |
| C. | \[|{{z}_{1}}{{|}^{2}}+\,|{{z}_{2}}{{|}^{2}}\] |
| D. | \[2|{{z}_{1}}|\,\,|{{z}_{2}}|\] |
| Answer» C. \[|{{z}_{1}}{{|}^{2}}+\,|{{z}_{2}}{{|}^{2}}\] | |
| 7015. |
The minimum value of \[|2z-1|+|3z-2|\]is [RPET 1997] |
| A. | 0 |
| B. | \[1/2\] |
| C. | \[1/3\] |
| D. | 44257 |
| Answer» D. 44257 | |
| 7016. |
If the lines \[x+q=0,y-2=0\] and \[3x+2y+5=0\] are concurrent, then value of q will be [DCE 2002] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 5 |
| Answer» D. 5 | |
| 7017. |
The mean of the series \[a,a+nd,\,\,a+2nd\] is [DCE 2002] |
| A. | \[a+(n-1)\,d\] |
| B. | \[a+nd\] |
| C. | \[a+(n+1)\,d\] |
| D. | None of these |
| Answer» C. \[a+(n+1)\,d\] | |
| 7018. |
The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the co-ordinate axes is [AIEEE 2005] |
| A. | 3 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 7019. |
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is [EAMCET 2003] |
| A. | \[\frac{2}{15}\] |
| B. | \[\frac{7}{15}\] |
| C. | \[\frac{8}{15}\] |
| D. | \[\frac{14}{15}\] |
| Answer» D. \[\frac{14}{15}\] | |
| 7020. |
The angle between the lines given by \[{{x}^{2}}-{{y}^{2}}=0\] is [MP PET 1999] |
| A. | \[{{15}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{75}^{o}}\] |
| D. | \[9{{0}^{o}}\] |
| Answer» E. | |
| 7021. |
Area bounded by the parabola \[y=4{{x}^{2}},\] \[y-\]axis and the lines \[y=1,\,\,y=4\] is [MNR 1990] |
| A. | 3 sq. unit |
| B. | \[\frac{7}{5}\]sq. unit |
| C. | \[\frac{7}{3}\]sq. unit |
| D. | None of these |
| Answer» D. None of these | |
| 7022. |
The probability that a man can hit a target is \[\frac{3}{4}\]. He tries 5 times. The probability that he will hit the target at least three times is [MNR 1994] |
| A. | \[\frac{291}{364}\] |
| B. | \[\frac{371}{464}\] |
| C. | \[\frac{471}{502}\] |
| D. | \[\frac{459}{512}\] |
| Answer» E. | |
| 7023. |
The angle between the lines represented by the equation \[\lambda {{x}^{2}}+{{(1-\lambda )}^{2}}xy-\lambda {{y}^{2}}=0\], is |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» E. | |
| 7024. |
The equation \[{{y}^{2}}-{{x}^{2}}+2x-1=0\] represents [UPSEAT 2004] |
| A. | A hyperbola |
| B. | An ellipse |
| C. | A pair of straight lines |
| D. | A rectangular hyperbola |
| Answer» D. A rectangular hyperbola | |
| 7025. |
The measurement of the area bounded by the co-ordinate axes and the curve \[y={{\log }_{e}}x\] is [MP PET 1998] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | \[\infty \] |
| Answer» E. | |
| 7026. |
If \[{{x}^{2}}-3x+2\]be a factor of \[{{x}^{4}}-p{{x}^{2}}+q,\]then \[(p,q)=\][IIT 1974; MP PET 1995; Pb. CET 2001] |
| A. | (3, 4) |
| B. | (4, 5) |
| C. | (4, 3) |
| D. | (5, 4) |
| Answer» E. | |
| 7027. |
If the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]has the one line as the bisector of angle between the coordinate axes, then [Bihar CEE 1990] |
| A. | \[{{(a-b)}^{2}}={{h}^{2}}\] |
| B. | \[{{(a+b)}^{2}}={{h}^{2}}\] |
| C. | \[{{(a-b)}^{2}}=4{{h}^{2}}\] |
| D. | \[{{(a+b)}^{2}}=4{{h}^{2}}\] |
| Answer» E. | |
| 7028. |
In \[\Delta ABC,\]if \[b=6,\,c=8\,\]and \[\angle A=90{}^\circ \], then R= |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 7 |
| Answer» D. 7 | |
| 7029. |
The lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] are perpendicular to each other, if [MP PET 1996] |
| A. | \[{{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}}=0\] |
| B. | \[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}=0\] |
| C. | \[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\] |
| D. | \[{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}=0\] |
| Answer» C. \[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\] | |
| 7030. |
If \[b>a\], then the equation \[(x-a)\,(x-b)=1\] has [IIT Screening 2000] |
| A. | Both roots in \[[a,\,b]\] |
| B. | Both roots in \[(-\infty ,\,a)\] |
| C. | Both roots in \[(b,\,+\infty )\] |
| D. | One root in \[(-\infty ,\,a)\] and the other in \[(b,\,+\infty )\] |
| Answer» E. | |
| 7031. |
If the acute angles between the pairs of lines \[3{{x}^{2}}-7xy+4{{y}^{2}}=0\] and \[6{{x}^{2}}-5xy+{{y}^{2}}=0\] be \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] respectively, then |
| A. | \[{{\theta }_{1}}={{\theta }_{2}}\] |
| B. | \[{{\theta }_{1}}=2{{\theta }_{2}}\] |
| C. | \[2{{\theta }_{1}}={{\theta }_{2}}\] |
| D. | None of these |
| Answer» B. \[{{\theta }_{1}}=2{{\theta }_{2}}\] | |
| 7032. |
The coefficient of \[x\] in the expansion of \[{{[\sqrt{1+{{x}^{2}}}-x]}^{-1}}\]in ascending powers of x, when \[|x| |
| A. | 0 |
| B. | \[\frac{1}{2}\] |
| C. | \[-\frac{1}{2}\] |
| D. | 1 |
| Answer» E. | |
| 7033. |
The distance between the line \[\mathbf{r}=2\mathbf{i}-2\mathbf{j}+3\mathbf{k}+\lambda (\mathbf{i}-\mathbf{j}+4\mathbf{k})\] and the plane \[\mathbf{r}.(\mathbf{i}+5\mathbf{j}+\mathbf{k})=5\] is [AIEEE 2005] |
| A. | \[\frac{3}{10}\] |
| B. | \[\frac{10}{3}\] |
| C. | \[\frac{10}{9}\] |
| D. | \[\frac{10}{3\sqrt{3}}\] |
| Answer» E. | |
| 7034. |
The centre of \[14{{x}^{2}}-4xy+11{{y}^{2}}-44x-58y+71=0\] [BIT Ranchi 1986] |
| A. | (2, 3) |
| B. | (2, ? 3) |
| C. | (? 2, 3) |
| D. | (? 2, ? 3) |
| Answer» B. (2, ? 3) | |
| 7035. |
Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is [MP PET 2001] |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» E. | |
| 7036. |
Area bounded by the curve \[{{x}^{2}}=4y\] and the straight line \[x=4y-2\] is [SCRA 1986; IIT 1981; Pb. CET 2003] |
| A. | \[\frac{8}{9}\] sq. unit |
| B. | \[\frac{9}{8}\] sq. unit |
| C. | \[\frac{4}{3}\] sq. unit |
| D. | None of these |
| Answer» C. \[\frac{4}{3}\] sq. unit | |
| 7037. |
For the complex number \[z\], one from \[z+\bar{z}\] and \[z\,\bar{z}\] is [RPET 1987] |
| A. | A real number |
| B. | A imaginary number |
| C. | Both are real numbers |
| D. | Both are imaginary numbers |
| Answer» D. Both are imaginary numbers | |
| 7038. |
Which of the following sequence is an arithmetic sequence |
| A. | \[f(n)=an+b;\,n\in N\] |
| B. | \[f(n)=k{{r}^{n}};\,n\in N\] |
| C. | \[f(n)=(an+b)\,k{{r}^{n}};\,n\in N\] |
| D. | \[f(n)=\frac{1}{a\left( n+\frac{b}{n} \right)};\,n\in N\] |
| Answer» B. \[f(n)=k{{r}^{n}};\,n\in N\] | |
| 7039. |
The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers [DCE 1999] |
| A. | \[{}^{5}{{C}_{4}}{{\left( \frac{4}{5} \right)}^{4}}\frac{1}{5}\] |
| B. | \[{{\left( \frac{4}{5} \right)}^{4}}\frac{1}{5}\] |
| C. | \[{}^{5}{{C}_{1}}\frac{1}{5}{{\left( \frac{4}{5} \right)}^{4}}\times {}^{5}{{C}_{4}}\] |
| D. | None of these |
| Answer» B. \[{{\left( \frac{4}{5} \right)}^{4}}\frac{1}{5}\] | |
| 7040. |
A and B are two events such that P = 0.8, P=0.6 and \[P(A\cap B)=0.5,\] then the value of \[P\,(A/B)\] is |
| A. | \[\frac{5}{6}\] |
| B. | \[\frac{5}{8}\] |
| C. | \[\frac{9}{10}\] |
| D. | None of these |
| Answer» B. \[\frac{5}{8}\] | |
| 7041. |
If \[arg\,z |
| A. | \[\pi \] |
| B. | \[-\pi \] |
| C. | \[-\frac{\pi }{2}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» B. \[-\pi \] | |
| 7042. |
A coin is tossed 10 times. The probability of getting exactly six heads is [Kerala (Engg.) 2002] |
| A. | \[\frac{512}{513}\] |
| B. | \[\frac{105}{512}\] |
| C. | \[\frac{100}{153}\] |
| D. | \[{}^{10}{{C}_{6}}\] |
| Answer» C. \[\frac{100}{153}\] | |
| 7043. |
If the lines \[ax+by+c=0\], \[bx+cy+a=0\] and \[cx+ay+b=0\] be concurrent, then [IIT 1985; DCE 2000, 02] |
| A. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}+3abc=0\] |
| B. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-abc=0\] |
| C. | \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 7044. |
Area bounded by curve \[xy=c,\] \[x-\]axis between \[x=1\] and \[x=4,\] is |
| A. | \[c\log 3\]sq. unit |
| B. | \[2\log c\]sq. unit |
| C. | \[2c\log 2\]sq. unit |
| D. | \[2c\log 5\]sq. unit |
| Answer» B. \[2\log c\]sq. unit | |
| 7045. |
The area enclosed between the curves \[y={{x}^{3}}\]and \[y=\sqrt{x}\] is, (in square units) [Karnataka CET 2004] |
| A. | \[\frac{5}{3}\] |
| B. | \[\frac{5}{4}\] |
| C. | \[\frac{5}{12}\] |
| D. | \[\frac{12}{5}\] |
| Answer» D. \[\frac{12}{5}\] | |
| 7046. |
Let \[{{z}_{1}}\] be a complex number with \[|{{z}_{1}}|=1\] and \[{{z}_{2}}\]be any complex number, then \[\left| \frac{{{z}_{1}}-{{z}_{2}}}{1-{{z}_{1}}{{{\bar{z}}}_{2}}} \right|=\] [Orissa JEE 2004] |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» C. -1 | |
| 7047. |
In a Boolean Algebra B, for all x, y in B, \[x\vee (x\wedge y)=\] |
| A. | y |
| B. | x |
| C. | 1 |
| D. | 0 |
| Answer» C. 1 | |
| 7048. |
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 | |
| 7049. |
The arithmetic mean of first n natural number [RPET 1986] |
| A. | \[\frac{n-1}{2}\] |
| B. | \[\frac{n+1}{2}\] |
| C. | \[\frac{n}{2}\] |
| D. | \[n\] |
| Answer» C. \[\frac{n}{2}\] | |
| 7050. |
If \[{{A}_{1}},\,{{A}_{2}}\] be two arithmetic means between \[\frac{1}{3}\] and \[\frac{1}{24}\] , then their values are |
| A. | \[\frac{7}{72},\,\frac{5}{36}\] |
| B. | \[\frac{17}{72},\,\frac{5}{36}\] |
| C. | \[\frac{7}{36},\,\frac{5}{72}\] |
| D. | \[\frac{5}{72},\,\frac{17}{72}\] |
| Answer» C. \[\frac{7}{36},\,\frac{5}{72}\] | |