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.
| 6801. |
A series whose nth term is \[\left( \frac{n}{x} \right)+y,\]the sum of r terms will be [UPSEAT 1999] |
| A. | \[\left\{ \frac{r(r+1)}{2x} \right\}+ry\] |
| B. | \[\left\{ \frac{r(r-1)}{2x} \right\}\] |
| C. | \[\left\{ \frac{r(r-1)}{2x} \right\}-ry\] |
| D. | \[\left\{ \frac{r(r+1)}{2y} \right\}-rx\] |
| Answer» B. \[\left\{ \frac{r(r-1)}{2x} \right\}\] | |
| 6802. |
If z1, z2 are any two complex numbers, then \[|{{z}_{1}}+\sqrt{z_{1}^{2}-z_{2}^{2}}|\] \[+|{{z}_{1}}-\sqrt{z_{1}^{2}-z_{2}^{2}}|\] is equal to |
| A. | \[|{{z}_{1}}|\] |
| B. | \[|{{z}_{2}}|\] |
| C. | \[|{{z}_{1}}+{{z}_{2}}|\] |
| D. | \[|{{z}_{1}}+{{z}_{2}}|+|{{z}_{1}}-{{z}_{2}}|\] |
| Answer» E. | |
| 6803. |
The number of ways in which 5 beads of different colours form a necklace is [RPET 2002] |
| A. | 12 |
| B. | 24 |
| C. | 120 |
| D. | 60 |
| Answer» B. 24 | |
| 6804. |
Bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted it is green. The probability that it comes bag B [DCE 2005] |
| A. | \[\frac{2}{7}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{3}{7}\] |
| D. | \[\frac{1}{3}\] |
| Answer» D. \[\frac{1}{3}\] | |
| 6805. |
\[|{{z}_{1}}+{{z}_{2}}|\,=\,|{{z}_{1}}|+|{{z}_{2}}|\] is possible if [MP PET 1999; Pb. CET 2002] |
| A. | \[{{z}_{2}}={{\overline{z}}_{1}}\] |
| B. | \[{{z}_{2}}=\frac{1}{{{z}_{1}}}\] |
| C. | \[arg\,({{z}_{1}})=\]arg \[({{z}_{2}})\] |
| D. | \[|{{z}_{1}}|\,=\,|{{z}_{2}}|\] |
| Answer» D. \[|{{z}_{1}}|\,=\,|{{z}_{2}}|\] | |
| 6806. |
A biased coin with probability \[p,\,\,0 |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{4}\] | |
| 6807. |
If \[{{S}_{n}}\] denotes the sum of \[n\] terms of an arithmetic progression, then the value of \[({{S}_{2n}}-{{S}_{n}})\] is equal to |
| A. | \[2{{S}_{n}}\] |
| B. | \[{{S}_{3n}}\] |
| C. | \[\frac{1}{3}{{S}_{3n}}\] |
| D. | \[\frac{1}{2}{{S}_{n}}\] |
| Answer» D. \[\frac{1}{2}{{S}_{n}}\] | |
| 6808. |
If the lines \[y=3x+1\] and \[2y=x+3\] are equally inclined to the line \[y=mx+4,\] then m = [ISM Dhanbad 1976] |
| A. | \[\frac{1+3\sqrt{2}}{7}\] |
| B. | \[\frac{1-3\sqrt{2}}{7}\] |
| C. | \[\frac{1\pm 3\sqrt{2}}{7}\] |
| D. | \[\frac{1\pm 5\sqrt{2}}{7}\] |
| Answer» E. | |
| 6809. |
If X has binomial distribution with mean np and variance npq, then \[\frac{P(X=k)}{P(X=k-1)}\] is [Pb. CET 2004] |
| A. | \[\frac{n-k}{k-1}.\frac{p}{q}\] |
| B. | \[\frac{n-k+1}{k}.\frac{p}{q}\] |
| C. | \[\frac{n+1}{k}.\frac{q}{p}\] |
| D. | \[\frac{n-1}{k+1}.\frac{q}{p}\] |
| Answer» C. \[\frac{n+1}{k}.\frac{q}{p}\] | |
| 6810. |
If \[|x| |
| A. | 1 |
| B. | n |
| C. | \[n+1\] |
| D. | None of these |
| Answer» D. None of these | |
| 6811. |
In an equilateral triangle the inradius and the circum-radius are connected by [EAMCET 1983] |
| A. | \[r=4R\] |
| B. | \[r=R/2\] |
| C. | \[r=R/3\] |
| D. | None of these |
| Answer» C. \[r=R/3\] | |
| 6812. |
The angle between the lines represented by the equation \[4{{x}^{2}}-24xy+11{{y}^{2}}=0\] are [MP PET 1990] |
| A. | \[{{\tan }^{-1}}\frac{3}{4},{{\tan }^{-1}}\left( -\frac{3}{4} \right)\] |
| B. | \[{{\tan }^{-1}}\frac{1}{3},{{\tan }^{-1}}\left( -\frac{1}{3} \right)\] |
| C. | \[{{\tan }^{-1}}\frac{4}{3},{{\tan }^{-1}}\left( -\frac{4}{3} \right)\] |
| D. | \[{{\tan }^{-1}}\frac{1}{2},{{\tan }^{-1}}\left( -\frac{1}{2} \right)\] |
| Answer» D. \[{{\tan }^{-1}}\frac{1}{2},{{\tan }^{-1}}\left( -\frac{1}{2} \right)\] | |
| 6813. |
The area of the triangle formed by the tangent to the hyperbola \[xy={{a}^{2}}\] and co-ordinate axes is [RPET 2000] |
| A. | \[{{a}^{2}}\] |
| B. | \[2{{a}^{2}}\] |
| C. | \[3{{a}^{2}}\] |
| D. | \[4{{a}^{2}}\] |
| Answer» C. \[3{{a}^{2}}\] | |
| 6814. |
The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution is [MP PET 2002] |
| A. | \[{}^{16}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{10}}{{\left( \frac{3}{4} \right)}^{6}}\] |
| B. | \[{}^{16}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{6}}{{\left( \frac{3}{4} \right)}^{10}}\] |
| C. | \[{}^{12}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{10}}{{\left( \frac{3}{4} \right)}^{6}}\] |
| D. | \[^{12}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{6}}{{\left( \frac{3}{4} \right)}^{6}}\] |
| Answer» C. \[{}^{12}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{10}}{{\left( \frac{3}{4} \right)}^{6}}\] | |
| 6815. |
If \[x\] be real, then the maximum value of \[5+4x-4{{x}^{2}}\] will be equal to [MNR 1979] |
| A. | 5 |
| B. | 6 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 6816. |
The area of the smaller segment cut off from the circle \[{{x}^{2}}+{{y}^{2}}=9\] by \[x=1\] is [RPET 2002] |
| A. | \[\frac{1}{2}(9{{\sec }^{-1}}3-\sqrt{8})\] |
| B. | \[9{{\sec }^{-1}}(3)-\sqrt{8}\] |
| C. | \[\sqrt{8}-9{{\sec }^{-1}}(3)\] |
| D. | None of these |
| Answer» C. \[\sqrt{8}-9{{\sec }^{-1}}(3)\] | |
| 6817. |
The line \[x-2y=0\]will be a bisector of the angle between the lines represented by the equation \[{{x}^{2}}-2hxy-2{{y}^{2}}=0\], if \[h=\] |
| A. | 1/2 |
| B. | 2 |
| C. | \[-2\] |
| D. | -1/2 |
| Answer» D. -1/2 | |
| 6818. |
The sum of all natural numbers between 1 and 100 which are multiples of 3 is [MP PET 1984] |
| A. | 1680 |
| B. | 1683 |
| C. | 1681 |
| D. | 1682 |
| Answer» C. 1681 | |
| 6819. |
The angle between the straight lines \[x-y\sqrt{3}=5\] and \[\sqrt{3x}+y=7\]is [MP PET 2003] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{75}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» B. \[{{60}^{o}}\] | |
| 6820. |
The vector equation of the plane through the point (2, 1, ?1) and passing through the line of intersection of the plane \[\mathbf{r}.(\mathbf{i}+3\mathbf{j}-\mathbf{k})=0\] and \[\mathbf{r}.(\mathbf{j}+2\mathbf{k})=0\] is |
| A. | \[\mathbf{r}.(\mathbf{i}+9\mathbf{j}+11\mathbf{k})=0\] |
| B. | \[\mathbf{r}.(\mathbf{i}+9\mathbf{j}+11\mathbf{k})=6\] |
| C. | \[\mathbf{r}.(\mathbf{i}-3\mathbf{j}-13\mathbf{k})=0\] |
| D. | None of these |
| Answer» B. \[\mathbf{r}.(\mathbf{i}+9\mathbf{j}+11\mathbf{k})=6\] | |
| 6821. |
If \[a,\ b,\ c,\ d,\ e,\ f\] are in A.P., then the value of \[e-c\] will be [Pb. CET 1989, 91] |
| A. | \[2(c-a)\] |
| B. | \[2(f-d)\] |
| C. | \[2(d-c)\] |
| D. | \[d-c\] |
| Answer» D. \[d-c\] | |
| 6822. |
A stone is falling freely and describes a distance s in t seconds given by equation \[s=\frac{1}{2}g\,{{t}^{2}}\]. The acceleration of the stone is |
| A. | Uniform |
| B. | Zero |
| C. | Non-uniform |
| D. | Indeterminate |
| Answer» B. Zero | |
| 6823. |
The argument of the complex number \[\frac{13-5i}{4-9i}\]is [MP PET 1997] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{5}\] |
| D. | \[\frac{\pi }{6}\] |
| Answer» C. \[\frac{\pi }{5}\] | |
| 6824. |
If \[{{z}_{1}},{{z}_{2}}\] are two complex numbers such that \[\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|=1\] and \[i{{z}_{1}}=k{{z}_{2}}\], where \[k\in R\], then the angle between \[{{z}_{1}}-{{z}_{2}}\] and \[{{z}_{1}}+{{z}_{2}}\] is |
| A. | \[{{\tan }^{-1}}\left( \frac{2k}{{{k}^{2}}+1} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{2k}{1-{{k}^{2}}} \right)\] |
| C. | - \[2{{\tan }^{-1}}k\] |
| D. | \[2{{\tan }^{-1}}k\] |
| Answer» D. \[2{{\tan }^{-1}}k\] | |
| 6825. |
The volume of the solid generated by revolving about the y-axis the figure bounded by the parabola \[y={{x}^{2}}\] and \[x={{y}^{2}}\] is [UPSEAT 2002] |
| A. | \[\frac{21}{5}\pi \] |
| B. | \[\frac{24}{5}\pi \] |
| C. | \[\frac{2}{15}\pi \] |
| D. | \[\frac{5}{24}\pi \] |
| Answer» D. \[\frac{5}{24}\pi \] | |
| 6826. |
The sum of the first \[n\] terms of the series \[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.........\] is [IIT 1988; MP PET 1996; RPET 1996, 2000; Pb. CET 1994; DCE 1995, 96] |
| A. | \[{{2}^{n}}-n-1\] |
| B. | \[1-{{2}^{-n}}\] |
| C. | \[n+{{2}^{-n}}-1\] |
| D. | \[{{2}^{n}}-1\] |
| Answer» D. \[{{2}^{n}}-1\] | |
| 6827. |
If the radius of the circumcircle of an isosceles triangle \[PQR\] is equal to \[PQ(=PR),\]then the angle P is [IIT Screening 1992; Pb. CET 2004] |
| A. | \[\frac{\pi }{6}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{2\pi }{3}\] |
| Answer» E. | |
| 6828. |
8 coins are tossed simultaneously. The probability of getting at least 6 heads is [AISSE 1985; MNR 1985; MP PET 1994] |
| A. | \[\frac{57}{64}\] |
| B. | \[\frac{229}{256}\] |
| C. | \[\frac{7}{64}\] |
| D. | \[\frac{37}{256}\] |
| Answer» E. | |
| 6829. |
If the lines \[ax+2y+1=0,bx+3y+1=0\] and \[cx+4y+1=0\] are concurrent, then a, b, c are in |
| A. | A. P. |
| B. | G. P. |
| C. | H. P. |
| D. | None of these |
| Answer» B. G. P. | |
| 6830. |
The area of the equilateral triangle which containing three coins of unity radius is [IIT Screening 2005] |
| A. | \[6+4\sqrt{3}\ sq.\ units\] |
| B. | \[8+\sqrt{3}\] sq. units |
| C. | \[4+\frac{7\sqrt{3}}{2}\] sq. units |
| D. | \[12+2\sqrt{3}\]sq. units |
| Answer» B. \[8+\sqrt{3}\] sq. units | |
| 6831. |
The sum of 24 terms of the following series \[\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+.........\] is |
| A. | 300 |
| B. | \[300\sqrt{2}\] |
| C. | \[200\sqrt{2}\] |
| D. | None of these |
| Answer» C. \[200\sqrt{2}\] | |
| 6832. |
If \[|x|\, |
| A. | \[\frac{1}{1-x}\] |
| B. | \[\frac{1}{1+x}\] |
| C. | \[\frac{1}{{{(1+x)}^{2}}}\] |
| D. | \[\frac{1}{{{(1-x)}^{2}}}\] |
| Answer» E. | |
| 6833. |
Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is [MP PET 1998] |
| A. | \[\frac{1}{4}\] |
| B. | 1 |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{8}\] |
| Answer» D. \[\frac{1}{8}\] | |
| 6834. |
If \[x,\,y,\,z\]are perpendicular drawn \[a,\,b\] and \[c\], then the value of \[\frac{bx}{c}+\frac{cy}{a}+\frac{az}{b}\]will be [UPSEAT 1999] |
| A. | \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{2R}\] |
| B. | \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{R}\] |
| C. | \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{4R}\] |
| D. | \[\frac{2({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{R}\] |
| Answer» B. \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{R}\] | |
| 6835. |
The number of ways that 8 beads of different colours be string as a necklace is [EAMCET 2002] |
| A. | 2520 |
| B. | 2880 |
| C. | 5040 |
| D. | 4320 |
| Answer» B. 2880 | |
| 6836. |
Argument of \[-1-i\sqrt{3}\] is [RPET 2003] |
| A. | \[\frac{2\pi }{3}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[-\frac{\pi }{3}\] |
| D. | \[-\frac{2\pi }{3}\] |
| Answer» E. | |
| 6837. |
The expression \[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\] is a polynomial of degree [Pb. CET 2000] |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» D. 8 | |
| 6838. |
The image of the point with position vector \[\mathbf{i}+3\mathbf{k}\]in the plane \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=1\]is [J & K 2005] |
| A. | \[\mathbf{i}+2\mathbf{j}+\mathbf{k}\] |
| B. | \[\mathbf{i}-2\mathbf{i}+\mathbf{k}\] |
| C. | \[-\mathbf{i}-2\mathbf{j}+\mathbf{k}\] |
| D. | \[\mathbf{i}+2\mathbf{j}-\mathbf{k}\] |
| Answer» D. \[\mathbf{i}+2\mathbf{j}-\mathbf{k}\] | |
| 6839. |
The area bounded by the curves \[y=\sqrt{x},\] \[2y+3=x\] and \[x-\]axis in the 1st quadrant is [IIT Screening 2003] |
| A. | 9 |
| B. | \[\frac{27}{4}\] |
| C. | 36 |
| D. | 18 |
| Answer» B. \[\frac{27}{4}\] | |
| 6840. |
If the distance ?s? traveled by a particle in time t is\[s=a\sin t+b\cos 2t\], then the acceleration at t = 0 is |
| A. | a |
| B. | ? a |
| C. | 4b |
| D. | ? 4b |
| Answer» E. | |
| 6841. |
If the sum of the series \[54+51+48+.............\] is 513, then the number of terms are [Roorkee 1970] |
| A. | 18 |
| B. | 20 |
| C. | 17 |
| D. | None of these |
| Answer» B. 20 | |
| 6842. |
If the numbers \[a,\ b,\ c,\ d,\ e\] form an A.P., then the value of \[a-4b+6c-4d+e\] is |
| A. | 1 |
| B. | 2 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 6843. |
If S is a set of \[P(x)\] is polynomial of degree \[\le 2\] such that \[P(0)=0,\]\[P(1)=1\],\[P'(x)>0\text{ }\forall x\in (0,\,1)\], then [IIT Screening 2005] |
| A. | \[S=0\] |
| B. | \[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,\infty )\] |
| C. | \[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in R\] |
| D. | \[S=ax+(1-a){{x}^{2}}\text{ }\forall a\in (0,2)\] |
| Answer» E. | |
| 6844. |
The slope of the tangent at (x, y) to a curve passing through a point (2, 1) is \[\frac{{{x}^{2}}+{{y}^{2}}}{2xy}\], then the equation of the curve is [MP PET 2002] |
| A. | \[2({{x}^{2}}-{{y}^{2}})=3x\] |
| B. | \[2({{x}^{2}}-{{y}^{2}})=6y\] |
| C. | \[x({{x}^{2}}-{{y}^{2}})=6\] |
| D. | \[x({{x}^{2}}+{{y}^{2}})=10\] |
| Answer» B. \[2({{x}^{2}}-{{y}^{2}})=6y\] | |
| 6845. |
The complex numbers \[\sin x+i\cos 2x\] and \[\cos x-i\sin 2x\] are conjugate to each other for [IIT 1988] |
| A. | \[x=n\pi \] |
| B. | \[x=\left( n+\frac{1}{2} \right)\pi \] |
| C. | \[x=0\] |
| D. | No value of x |
| Answer» E. | |
| 6846. |
If lines \[4x+3y=1,y=x+5\] and \[5y+bx=3\] are concurrent, then b equals [RPET 1996; MP PET 1997; EAMCET 2003; Pb. CET 2002] |
| A. | 1 |
| B. | 3 |
| C. | 6 |
| D. | 0 |
| Answer» D. 0 | |
| 6847. |
If \[y={{x}^{3}}+5\]and x changes from 3 to 2.99, then the approximate change in y is |
| A. | 2.7 |
| B. | ? 0. 27 |
| C. | 27 |
| D. | None of these |
| Answer» C. 27 | |
| 6848. |
Let the sequence \[{{a}_{1}},{{a}_{2}},{{a}_{3}},.............{{a}_{2n}}\] form an A.P. Then \[a_{1}^{2}-a_{2}^{2}+a_{3}^{3}-.........+a_{2n-1}^{2}-a_{2n}^{2}=\] |
| A. | \[\frac{n}{2n-1}(a_{1}^{2}-a_{2n}^{2})\] |
| B. | \[\frac{2n}{n-1}(a_{2n}^{2}-a_{1}^{2})\] |
| C. | \[\frac{n}{n+1}(a_{1}^{2}+a_{2n}^{2})\] |
| D. | None of these |
| Answer» B. \[\frac{2n}{n-1}(a_{2n}^{2}-a_{1}^{2})\] | |
| 6849. |
The locus of a point equidistant from two given points a and b is given by |
| A. | \[[\mathbf{r}-\frac{1}{2}(\mathbf{a}+\mathbf{b})]\,.\,\,(\mathbf{a}-\mathbf{b})=0\] |
| B. | \[[\mathbf{r}-\frac{1}{2}(\mathbf{a}-\mathbf{b})]\,.\,\,(\mathbf{a}+\mathbf{b})=0\] |
| C. | \[[\mathbf{r}-\frac{1}{2}(\mathbf{a}+\mathbf{b})].(\mathbf{a}+\mathbf{b})=0\] |
| D. | \[[\mathbf{r}-\frac{1}{2}(\mathbf{a}-\mathbf{b})]\,.\,\,(\mathbf{a}-\mathbf{b})=0\] |
| Answer» B. \[[\mathbf{r}-\frac{1}{2}(\mathbf{a}-\mathbf{b})]\,.\,\,(\mathbf{a}+\mathbf{b})=0\] | |
| 6850. |
A particle moves in a straight line with a velocity given by \[\frac{dx}{dt}=x+1\](x is the distance described). The time taken by a particle to traverse a distance of 99 metre is |
| A. | \[{{\log }_{10}}e\] |
| B. | \[2{{\log }_{e}}10\] |
| C. | \[2{{\log }_{10}}e\] |
| D. | \[\frac{1}{2}{{\log }_{10}}e\] |
| Answer» C. \[2{{\log }_{10}}e\] | |