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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.
| 6851. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+.....)}^{-n}}\]is |
| A. | \[\frac{(2n)!}{n!}\] |
| B. | \[\frac{(2n)!}{{{(n!)}^{2}}}\] |
| C. | \[\frac{1}{2}\frac{(2n)!}{{{(n!)}^{2}}}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{2}\frac{(2n)!}{{{(n!)}^{2}}}\] | |
| 6852. |
The items produced by a firm are supposed to contain 5% defective items. The probability that a sample of 8 items will contain less than 2 defective items, is [MP PET 1993] |
| A. | \[\frac{27}{20}\,{{\left( \frac{19}{20} \right)}^{7}}\] |
| B. | \[\frac{533}{400}\,{{\left( \frac{19}{20} \right)}^{6}}\] |
| C. | \[\frac{153}{20}\,{{\left( \frac{1}{20} \right)}^{7}}\] |
| D. | \[\frac{35}{16}\,{{\left( \frac{1}{20} \right)}^{6}}\] |
| Answer» B. \[\frac{533}{400}\,{{\left( \frac{19}{20} \right)}^{6}}\] | |
| 6853. |
The straight lines joining the origin to the points of intersection of the line \[2x+y=1\] and curve \[3{{x}^{2}}+4xy-4x+1=0\] include an angle [MP PET 1993] |
| A. | p/2 |
| B. | p/3 |
| C. | p/4 |
| D. | p/6 |
| Answer» B. p/3 | |
| 6854. |
\[\frac{1}{{{(2+x)}^{4}}}=\] |
| A. | \[\frac{1}{2}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\] |
| B. | \[\frac{1}{16}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\] |
| C. | \[\frac{1}{16}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\] |
| D. | \[\frac{1}{2}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\] |
| Answer» C. \[\frac{1}{16}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\] | |
| 6855. |
If the coordinates of the vertices A, B, C of the triangle ABC be \[(-\ 4,\ 2),\] \[(12,\ -2)\] and \[(8,\ 6)\]respectively, then \[\angle \ B\]= |
| A. | \[{{\tan }^{-1}}\left( -\frac{6}{7} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{6}{7} \right)\] |
| C. | \[{{\tan }^{-1}}\left( -\frac{7}{6} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{7}{6} \right)\] |
| Answer» E. | |
| 6856. |
If three dice are thrown together, then the probability of getting 5 on at least one of them is |
| A. | \[\frac{125}{216}\] |
| B. | \[\frac{215}{216}\] |
| C. | \[\frac{1}{216}\] |
| D. | \[\frac{91}{216}\] |
| Answer» E. | |
| 6857. |
The edge of a cube is increasing at the rate of \[5cm/\sec .\]How fast is the volume of the cube increasing when the edge is 12cm long |
| A. | \[432\,c{{m}^{3}}/\sec \] |
| B. | \[2160\,c{{m}^{3}}/\sec \] |
| C. | \[180\,c{{m}^{3}}/\sec \] |
| D. | None of these |
| Answer» C. \[180\,c{{m}^{3}}/\sec \] | |
| 6858. |
In a Boolean Algebra B, for all x in B, \[{1}'=\] |
| A. | 0 |
| B. | 1 |
| C. | \[x\wedge 1\] |
| D. | None of these |
| Answer» B. 1 | |
| 6859. |
A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes [AI CBSE 1985] |
| A. | \[\mu =1,\,\,{{\sigma }^{2}}=2/3\] |
| B. | \[\mu =2/3,\,\,{{\sigma }^{2}}=1\] |
| C. | \[\mu =2,\,\,{{\sigma }^{2}}=2/3\] |
| D. | None of these |
| Answer» B. \[\mu =2/3,\,\,{{\sigma }^{2}}=1\] | |
| 6860. |
The angle between the pair of lines represented by \[2{{x}^{2}}-7xy+3{{y}^{2}}=0\], is [Kurukshetra CEE 2002] |
| A. | \[{{60}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{\tan }^{-1}}\left( \frac{7}{6} \right)\] |
| D. | \[{{30}^{o}}\] |
| Answer» B. \[{{45}^{o}}\] | |
| 6861. |
A stone thrown vertically upwards rises ?s? metre in t seconds, where \[s=80t-16{{t}^{2}}\], then the velocity after 2 seconds is [SCRA 1996] |
| A. | 8 m per sec |
| B. | 16 m per sec |
| C. | 32 m per sec |
| D. | 64 m per sec |
| Answer» C. 32 m per sec | |
| 6862. |
If a dice is thrown 5 times, then the probability of getting 6 exact three times, is |
| A. | \[\frac{125}{388}\] |
| B. | \[\frac{125}{3888}\] |
| C. | \[\frac{625}{23328}\] |
| D. | \[\frac{250}{2332}\] |
| Answer» C. \[\frac{625}{23328}\] | |
| 6863. |
Which of the following is a point on the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x-3y+6=0\]and \[{{x}^{2}}+{{y}^{2}}+x-8y-13=0\] Karnataka CET 2003] |
| A. | (1, -2) |
| B. | (1, 4) |
| C. | (1, 2) |
| D. | (1, -4) |
| Answer» E. | |
| 6864. |
The angle between the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is given by [RPET 1995] |
| A. | \[\tan \theta =\frac{2({{h}^{2}}-ab)}{(a+b)}\] |
| B. | \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{(a+b)}\] |
| C. | \[\tan \theta =\frac{2({{h}^{2}}-ab)}{\sqrt{a+b}}\] |
| D. | \[\tan \theta =\frac{2\sqrt{{{h}^{2}}+ab}}{(a+b)}\] |
| Answer» C. \[\tan \theta =\frac{2({{h}^{2}}-ab)}{\sqrt{a+b}}\] | |
| 6865. |
If \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\] be the A.M. of \[a\] and \[b\], then \[n=\] [MP PET 1995] |
| A. | 1 |
| B. | \[-1\] |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 6866. |
The area in the first quadrant between \[{{x}^{2}}+{{y}^{2}}={{\pi }^{2}}\] and \[y=\sin x\] is [MP PET 1997] |
| A. | \[\frac{({{\pi }^{3}}-8)}{4}\] |
| B. | \[\frac{{{\pi }^{3}}}{4}\] |
| C. | \[\frac{({{\pi }^{3}}-16)}{4}\] |
| D. | \[\frac{({{\pi }^{3}}-8)}{2}\] |
| Answer» B. \[\frac{{{\pi }^{3}}}{4}\] | |
| 6867. |
The locus of the middle points of those chords of the circle \[{{x}^{2}}+{{y}^{2}}=4\]which subtend a right angle at the origin is [MP PET 1990; IIT 1984; RPET 1997; DCE 2000, 01] |
| A. | \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}=4\] |
| C. | \[{{x}^{2}}+{{y}^{2}}=2\] |
| D. | \[{{(x-1)}^{2}}+{{(y-2)}^{2}}=5\] |
| Answer» D. \[{{(x-1)}^{2}}+{{(y-2)}^{2}}=5\] | |
| 6868. |
Equation of angle bisectors between x and y -axes are [MP PET 1984] |
| A. | \[y=\pm x\] |
| B. | \[y=\pm 2x\] |
| C. | \[y=\pm \frac{1}{\sqrt{2}}x\] |
| D. | \[y=\pm 3x\] |
| Answer» B. \[y=\pm 2x\] | |
| 6869. |
A coin is tossed 3 times. The probability of getting exactly two heads is [SCRA 1980; MNR 1979] |
| A. | \[\frac{3}{8}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{2}\] | |
| 6870. |
Let \[f(x)={{x}^{2}}+4x+1\]. Then |
| A. | \[f(x)>0\] for all x |
| B. | \[f(x)>1\] when \[x\ge 0\] |
| C. | \[f(x)\ge 1\] when \[x\le -4\] |
| D. | \[f(x)=f(-x)\] for all \[x\] |
| Answer» D. \[f(x)=f(-x)\] for all \[x\] | |
| 6871. |
If \[{{z}_{1}}\text{ and }{{z}_{2}}\] be complex numbers such that \[{{z}_{1}}\ne {{z}_{2}}\] and \[|{{z}_{1}}|\,=\,|{{z}_{2}}|\]. If \[{{z}_{1}}\] has positive real part and \[{{z}_{2}}\] has negative imaginary part, then \[\frac{({{z}_{1}}+{{z}_{2}})}{({{z}_{1}}-{{z}_{2}})}\]may be [IIT 1986] |
| A. | Purely imaginary |
| B. | Real and positive |
| C. | Real and negative |
| D. | None of these |
| Answer» B. Real and positive | |
| 6872. |
The ratio of the areas bounded by the curves \[y=\cos x\] and \[y=\cos 2x\] between \[x=0,\] \[x=\pi /3\] and \[x-\]axis, is [MP PET 1997] |
| A. | \[\sqrt{2}:1\] |
| B. | \[1:1\] |
| C. | \[1:2\] |
| D. | \[2:1\] |
| Answer» E. | |
| 6873. |
The vector equation of a plane, which is at a distance of 8 unit from the origin and which is normal to the vector \[2\mathbf{i}+\mathbf{j}+2\mathbf{k},\] is |
| A. | \[\mathbf{r}.(2\mathbf{i}+\mathbf{j}+\mathbf{k})=24\] |
| B. | \[\mathbf{r}.(2\mathbf{i}+\mathbf{j}+2\mathbf{k})=24\] |
| C. | \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=24\] |
| D. | None of these |
| Answer» C. \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=24\] | |
| 6874. |
The angle between the pair of lines \[2{{x}^{2}}+5xy+2{{y}^{2}}+3x+3y+1=0\] is [EAMCET 1994] |
| A. | \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\] |
| C. | 0 |
| D. | p/2 |
| Answer» B. \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\] | |
| 6875. |
A line \[lx+my+n=0\]meets the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]at the points P and Q. The tangents drawn at the points P and Q meet at R, then the coordinates of R is |
| A. | \[\left( \frac{{{a}^{2}}l}{n},\frac{{{a}^{2}}m}{n} \right)\] |
| B. | \[\left( \frac{-{{a}^{2}}l}{n},\frac{-{{a}^{2}}m}{n} \right)\] |
| C. | \[\left( \frac{{{a}^{2}}n}{l},\frac{{{a}^{2}}n}{m} \right)\] |
| D. | None of these |
| Answer» C. \[\left( \frac{{{a}^{2}}n}{l},\frac{{{a}^{2}}n}{m} \right)\] | |
| 6876. |
If \[{{a}_{1}},\,{{a}_{2}},....,{{a}_{n+1}}\] are in A.P., then \[\frac{1}{{{a}_{1}}{{a}_{2}}}+\frac{1}{{{a}_{2}}{{a}_{3}}}+.....+\frac{1}{{{a}_{n}}{{a}_{n+1}}}\] is [AMU 2002] |
| A. | \[\frac{n-1}{{{a}_{1}}{{a}_{n+1}}}\] |
| B. | \[\frac{1}{{{a}_{1}}{{a}_{n+1}}}\] |
| C. | \[\frac{n+1}{{{a}_{1}}{{a}_{n+1}}}\] |
| D. | \[\frac{n}{{{a}_{1}}{{a}_{n+1}}}\] |
| Answer» E. | |
| 6877. |
If \[\frac{1}{p+q},\ \frac{1}{r+p},\ \frac{1}{q+r}\] are in A.P., then [RPET 1995] |
| A. | \[p,\ ,q,\ r\] are in A.P. |
| B. | \[{{p}^{2}},\ {{q}^{2}},\ {{r}^{2}}\] are in A.P. |
| C. | \[\frac{1}{p},\ \frac{1}{q},\ \frac{1}{r}\] are in A.P. |
| D. | None of these |
| Answer» C. \[\frac{1}{p},\ \frac{1}{q},\ \frac{1}{r}\] are in A.P. | |
| 6878. |
In how many ways can 5 keys be put in a ring |
| A. | \[\frac{1}{2}4!\] |
| B. | \[\frac{1}{2}5\,!\] |
| C. | \[4\,!\] |
| D. | \[5\,!\] |
| Answer» B. \[\frac{1}{2}5\,!\] | |
| 6879. |
Angle of intersection of the curves \[r=\sin \theta +\cos \theta \] and \[r=2\sin \theta \] is equal to [UPSEAT 2004] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6880. |
The equation of the bisectors of the angles between the lines represented by \[{{x}^{2}}+2xy\cot \theta +{{y}^{2}}=0\], is |
| A. | \[{{x}^{2}}-{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=xy\] |
| C. | \[({{x}^{2}}-{{y}^{2}})\cot \theta =2xy\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}-{{y}^{2}}=xy\] | |
| 6881. |
A point on the parabola \[{{y}^{2}}=18x\]at which the ordinate increases at twice the rate of the abscissa is [AIEEE 2004] |
| A. | \[\left( \frac{9}{8},\frac{9}{2} \right)\] |
| B. | (2, ? 4) |
| C. | \[\left( \frac{-9}{8},\frac{9}{2} \right)\] |
| D. | (2, 4) |
| Answer» B. (2, ? 4) | |
| 6882. |
Area under the curve \[y={{x}^{2}}-4x\]within the x-axis and the line \[x=2\], is [SCRA 1991] |
| A. | \[\frac{16}{3}sq.\,unit\] |
| B. | \[-\frac{16}{3}sq.\,unit\] |
| C. | \[\frac{4}{7}sq.\,unit\] |
| D. | Cannot be calculated |
| Answer» B. \[-\frac{16}{3}sq.\,unit\] | |
| 6883. |
Let y be the function which passes through (1, 2) having slope \[(2x+1)\]. The area bounded between the curve and x-axis is [DCE 2005] |
| A. | 6 sq. unit |
| B. | 5/6 sq. unit |
| C. | 1/6 sq. unit |
| D. | None of these |
| Answer» D. None of these | |
| 6884. |
If r be position vector of any point on a sphere and a, b are respectively position vectors of the extremities of a diameter, then [MP PET 1994] |
| A. | \[\mathbf{r}\,.\,(\mathbf{a}-\mathbf{b})=0\] |
| B. | \[\mathbf{r}\,.\,(\mathbf{r}-\mathbf{a})=0\] |
| C. | \[(\mathbf{r}+\mathbf{a})\,.\,(\mathbf{r}+\mathbf{b})=0\] |
| D. | \[(\mathbf{r}-\mathbf{a})\,.\,(\mathbf{r}-\mathbf{b})=0\] |
| Answer» E. | |
| 6885. |
The length of the perpendicular from the origin to the plane passing through three non-collinear points \[\mathbf{a},\,\mathbf{b},\,\mathbf{c}\] is |
| A. | \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{c}\times \mathbf{a}+\mathbf{b}\times \mathbf{c}|}\] |
| B. | \[\frac{2\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\] |
| C. | \[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\] |
| D. | None of these |
| Answer» B. \[\frac{2\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\] | |
| 6886. |
The position vector of the point in which the line joining the points \[\mathbf{i}-2\mathbf{j}+\mathbf{k}\] and \[3\mathbf{k}-2\mathbf{j}\] cuts the plane through the origin and the points \[4\mathbf{j}\] and \[2\mathbf{i}+\mathbf{k}\], is |
| A. | \[6\mathbf{i}-10\mathbf{j}+3\mathbf{k}\] |
| B. | \[\frac{1}{5}(6\mathbf{i}-10\mathbf{j}+3\mathbf{k})\] |
| C. | \[-6\mathbf{i}+10\mathbf{j}-3\mathbf{k}\] |
| D. | None of these |
| Answer» C. \[-6\mathbf{i}+10\mathbf{j}-3\mathbf{k}\] | |
| 6887. |
A particle starts at the origin and moves along the x?axis in such a way that its velocity at the point (x, 0) is given by the formula \[\frac{dx}{dt}={{\cos }^{2}}\pi x.\] Then the particle never reaches the point on [AMU 2000] |
| A. | \[x=\frac{1}{4}\] |
| B. | \[x=\frac{3}{4}\] |
| C. | \[x=\frac{1}{2}\] |
| D. | x = 1 |
| Answer» D. x = 1 | |
| 6888. |
The product of two complex numbers each of unit modulus is also a complex number, of |
| A. | Unit modulus |
| B. | Less than unit modulus |
| C. | Greater than unit modulus |
| D. | None of these |
| Answer» B. Less than unit modulus | |
| 6889. |
If \[z\] is a complex number such that \[{{z}^{2}}={{(\bar{z})}^{2}},\] then |
| A. | \[z\]is purely real |
| B. | \[z\]is purely imaginary |
| C. | Either \[z\]is purely real or purely imaginary |
| D. | None of these |
| Answer» D. None of these | |
| 6890. |
A 10cm long rod AB moves with its ends on two mutually perpendicular straight lines OX and OY. If the end A be moving at the rate of \[2cm/\sec \], then when the distance of A from O is \[8cm\], the rate at which the end B is moving, is [SCRA 1996] |
| A. | \[\frac{8}{3}cm/\sec \] |
| B. | \[\frac{4}{3}cm/\sec \] |
| C. | \[\frac{2}{9}cm/\sec \] |
| D. | None of these |
| Answer» B. \[\frac{4}{3}cm/\sec \] | |
| 6891. |
If \[x\] be real, the least value of \[{{x}^{2}}-6x+10\] is [Kurukshetra CEE 1998] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 10 |
| Answer» B. 2 | |
| 6892. |
The sum of numbers from 250 to 1000 which are divisible by 3 is [RPET 1997] |
| A. | 135657 |
| B. | 136557 |
| C. | 161575 |
| D. | 156375 |
| Answer» E. | |
| 6893. |
Let \[z\] be a complex number. Then the angle between vectors \[z\] and \[-iz\] is |
| A. | \[\pi \] |
| B. | 0 |
| C. | \[-\frac{\pi }{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6894. |
If for complex numbers \[{{z}_{1}}\] and \[{{z}_{2}}\], \[arg({{z}_{1}}/{{z}_{2}})=0,\] then \[|{{z}_{1}}-{{z}_{2}}|\] is equal to |
| A. | \[|{{z}_{1}}|+|{{z}_{2}}|\] |
| B. | \[|{{z}_{1}}|-|{{z}_{2}}|\] |
| C. | \[||{{z}_{1}}|-|{{z}_{2}}||\] |
| D. | 0 |
| Answer» D. 0 | |
| 6895. |
If \[|{{z}_{1}}|=|{{z}_{2}}|=..........=|{{z}_{n}}|=1,\] then the value of \[|{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+.............+{{z}_{n}}|\]= |
| A. | 1 |
| B. | \[|{{z}_{1}}|+|{{z}_{2}}|+.......+|{{z}_{n}}|\] |
| C. | \[\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+.........+\frac{1}{{{z}_{n}}} \right|\] |
| D. | None of these |
| Answer» D. None of these | |
| 6896. |
Tangents AB and AC are drawn from the point \[A(0,\,1)\]to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+1=0\]. Equation of the circle through A, B and C is |
| A. | \[{{x}^{2}}+{{y}^{2}}+x+y-2=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-x+y-2=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+x-y-2=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}+x-y-2=0\] | |
| 6897. |
The equation of the conic with focus at (1, ?1), directrix along \[x-y+1=0\] and with eccentricity \[\sqrt{2}\] is [EAMCET 1994] |
| A. | \[{{x}^{2}}-{{y}^{2}}=1\] |
| B. | \[xy=1\] |
| C. | \[2xy-4x+4y+1=0\] |
| D. | \[2xy+4x-4y-1=0\] |
| Answer» D. \[2xy+4x-4y-1=0\] | |
| 6898. |
In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together |
| A. | 9 ! |
| B. | 10 ! |
| C. | 3 ! 10 ! |
| D. | 3 ! 9 ! |
| Answer» E. | |
| 6899. |
If R is the radius of the circumcircle of the \[\Delta ABC\]and \[\Delta \]is its area, then [Karnataka CET 2000] |
| A. | \[R=\frac{a+b+c}{\Delta }\] |
| B. | \[R=\frac{a+b+c}{4\Delta }\] |
| C. | \[R=\frac{abc}{4\Delta }\] |
| D. | \[R=\frac{abc}{\Delta }\] |
| Answer» D. \[R=\frac{abc}{\Delta }\] | |
| 6900. |
If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is [RPET 1996] |
| A. | \[\pi /3\] |
| B. | \[\pi /2\] |
| C. | \[3\pi /2\] |
| D. | \[\pi /4\] |
| Answer» E. | |