MCQOPTIONS
Saved Bookmarks
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.
| 6751. |
The amplitude of \[\frac{1+\sqrt{3}\,i}{\sqrt{3}-i}\] is [RPET 2001] |
| A. | 0 |
| B. | \[\pi /6\] |
| C. | \[\pi /3\] |
| D. | \[\pi /2\] |
| Answer» E. | |
| 6752. |
A vector \[\mathbf{n}\] of magnitude 8 units is inclined to x-axis at \[{{45}^{o}}\], y-axis at \[{{60}^{o}}\] and an acute angle with z-axis. If a plane passes through a point \[(\sqrt{2},\,-1,\,1)\] and is normal to \[\mathbf{n}\], then its equation in vector form is |
| A. | \[\mathbf{r}.(\sqrt{2}\mathbf{i}+\mathbf{j}+\mathbf{k})=4\] |
| B. | \[\mathbf{r}.(\sqrt{2}\mathbf{i}+\mathbf{j}+\mathbf{k})=2\] |
| C. | \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=4\] |
| D. | None of these |
| Answer» C. \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=4\] | |
| 6753. |
Moving along the x-axis are two points with \[x=10+6t;x=3+{{t}^{2}}.\]The speed with which they are reaching from each other at the time of encounter is (x is in cm and t is in seconds) [MP PET 2003] |
| A. | 16 cm/sec |
| B. | 20 cm/sec |
| C. | 8 cm/sec |
| D. | 12 cm/sec |
| Answer» D. 12 cm/sec | |
| 6754. |
If \[z=\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\] then [AMU 2002] |
| A. | \[|z|\,=1,\,\,\,\,arg\,z=\frac{\pi }{4}\] |
| B. | \[|z|\,=1,arg\,z=\frac{\pi }{6}\] |
| C. | \[|z|\,=\frac{\sqrt{3}}{2},\,arg\,z=\frac{5\pi }{24}\] |
| D. | \[|z|\,=\frac{\sqrt{3}}{2},\,\,arg\,z={{\tan }^{-1}}\frac{1}{\sqrt{2}}\] |
| Answer» C. \[|z|\,=\frac{\sqrt{3}}{2},\,arg\,z=\frac{5\pi }{24}\] | |
| 6755. |
If the angle between the pair of straight lines represented by the equation \[{{x}^{2}}-3xy+\lambda {{y}^{2}}+3x-5y+2=0\] is \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\], where \['\lambda \,'\]is a non negative real number. Then\[\lambda \]is [Orissa JEE 2002] |
| A. | 2 |
| B. | 0 |
| C. | 3 |
| D. | 1 |
| Answer» B. 0 | |
| 6756. |
Which of the following are correct for any two complex numbers \[{{z}_{1}}\] and \[{{z}_{2}}\] [Roorkee 1998] |
| A. | \[|{{z}_{1}}{{z}_{2}}|\,=\,|{{z}_{1}}||{{z}_{2}}|\] |
| B. | \[arg\,\,({{z}_{1}}{{z}_{2}})=(arg\,{{z}_{1}})(arg\,{{z}_{2}})\] |
| C. | \[|{{z}_{1}}+{{z}_{2}}|\,=\,|{{z}_{1}}|+|{{z}_{2}}|\] |
| D. | \[|{{z}_{1}}-{{z}_{2}}|\,\ge \,|{{z}_{1}}|-|{{z}_{2}}|\] |
| Answer» E. | |
| 6757. |
Area bounded by the curve \[xy-3x-2y-10=0,\]x-axis and the lines \[x=3,x=4\]is [AI CBSE 1991] |
| A. | \[16\log 2-13\] |
| B. | \[16\log 2-3\] |
| C. | \[16\log 2+3\] |
| D. | None of these |
| Answer» D. None of these | |
| 6758. |
A fair coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then n is equal to [Kurukshetra CEE 1998; AMU 2000] |
| A. | 15 |
| B. | 14 |
| C. | 12 |
| D. | 7 |
| Answer» C. 12 | |
| 6759. |
The cartesian equation of the plane \[\mathbf{r}=(1+\lambda -\mu )\mathbf{i}+(2-\lambda )\mathbf{j}+(3-2\lambda +2\mu )\mathbf{k}\] is |
| A. | \[2x+y=5\] |
| B. | \[2x-y=5\] |
| C. | \[2x+z=5\] |
| D. | \[2x-z=5\] |
| Answer» D. \[2x-z=5\] | |
| 6760. |
The shortest distance between the lines \[\mathbf{r}=(3\mathbf{i}-2\mathbf{j}-2\mathbf{k})+\mathbf{i}t\] and \[\mathbf{r}=\mathbf{i}-\mathbf{j}+2\mathbf{k}+\mathbf{j}s\] (t and s being parameters) is [AMU 1999] |
| A. | \[\sqrt{21}\] |
| B. | \[\sqrt{102}\] |
| C. | 4 |
| D. | 3 |
| Answer» D. 3 | |
| 6761. |
The inequality \[|z-4|\, |
| A. | \[\operatorname{Re}(z)>0\] |
| B. | \[\operatorname{Re}(z)<0\] |
| C. | \[\operatorname{Re}(z)>2\] |
| D. | None of these |
| Answer» E. | |
| 6762. |
If \[a,\ b,\ c\] are in H.P., then which one of the following is true [MNR 1985] |
| A. | \[\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{b}\] |
| B. | \[\frac{ac}{a+c}=b\] |
| C. | \[\frac{b+a}{b-a}+\frac{b+c}{b-c}=1\] |
| D. | None of these |
| Answer» E. | |
| 6763. |
If \[\frac{c+i}{c-i}=a+ib\], where \[a,b,c\]are real, then \[{{a}^{2}}+{{b}^{2}}=\] [MP PET 1996] |
| A. | 1 |
| B. | \[-1\] |
| C. | \[{{c}^{2}}\] |
| D. | \[-{{c}^{2}}\] |
| Answer» B. \[-1\] | |
| 6764. |
\[{{2}^{1/4}}{{.4}^{1/8}}{{.8}^{1/16}}{{.16}^{1/32}}..........\]is equal to [MNR 1984; MP PET 1998; AIEEE 2002] |
| A. | 1 |
| B. | 2 |
| C. | \[\frac{3}{2}\] |
| D. | \[\frac{5}{2}\] |
| Answer» C. \[\frac{3}{2}\] | |
| 6765. |
A function \[y=f(x)\] has a second order derivatives \[{{f}'}'(x)=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is \[y=3x-5\], then the function is [AIEEE 2004] |
| A. | \[{{(x+1)}^{3}}\] |
| B. | \[{{(x-1)}^{3}}\] |
| C. | \[{{(x+1)}^{2}}\] |
| D. | \[{{(x-1)}^{2}}\] |
| Answer» C. \[{{(x+1)}^{2}}\] | |
| 6766. |
The distance between the planes given by \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})+5=0\] and \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})-8=0\] is |
| A. | 1 unit |
| B. | \[\frac{13}{3}\] unit |
| C. | 13 unit |
| D. | None of these |
| Answer» C. 13 unit | |
| 6767. |
If the sum of \[n\] terms of an A.P. is \[nA+{{n}^{2}}B\], where \[A,B\] are constants, then its common difference will be [MNR 1977] |
| A. | \[A-B\] |
| B. | \[A+B\] |
| C. | \[2A\] |
| D. | \[2B\] |
| Answer» E. | |
| 6768. |
A particle is moving in a straight line. Its displacement at time t is given by \[s=-4{{t}^{2}}+2t\], then its velocity and acceleration at time \[t=\frac{1}{2}\] second are [AISSE 1981] |
| A. | ? 2, ? 8 |
| B. | 2, 6 |
| C. | ? 2, 8 |
| D. | 2, 8 |
| Answer» B. 2, 6 | |
| 6769. |
The angle between the lines \[y=(2-\sqrt{3})x+5\] and \[y=(2+\sqrt{3})x-7\] is [MP PET 1997] |
| A. | \[{{30}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» C. \[{{45}^{o}}\] | |
| 6770. |
The equation of the bisector of the acute angle between the lines \[3x-4y+7=0\]and \[12x+5y-2=0\]is [IIT 1975, 1983; RPET 2003; UPSEAT 2004] |
| A. | \[21x+77y-101=0\] |
| B. | \[11x-3y+9=0\] |
| C. | \[31x+77y+101=0\] |
| D. | \[11x-3y-9=0\] |
| Answer» C. \[31x+77y+101=0\] | |
| 6771. |
If the line passing through (4, 3) and (2, k) is perpendicular to \[y=2x+3\], then k = [RPET 1985; MP PET 1999] |
| A. | -1 |
| B. | 1 |
| C. | 4 |
| D. | 4 |
| Answer» E. | |
| 6772. |
Area bounded by curves \[y={{x}^{2}}\] and \[y=2-{{x}^{2}}\] is [Orissa JEE 2005] |
| A. | 8/3 |
| B. | 3/8 |
| C. | 3/2 |
| D. | None of these |
| Answer» B. 3/8 | |
| 6773. |
If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is [RPET 1986] |
| A. | \[1:2\] |
| B. | \[2:1\] |
| C. | \[2:3\] |
| D. | \[3:2\] |
| Answer» B. \[2:1\] | |
| 6774. |
The length of the common chord of the circles \[{{x}^{2}}+{{y}^{2}}+2x+3y+1=0\]and \[{{x}^{2}}+{{y}^{2}}+4x+3y+2=0\]is [MP PET 2000] |
| A. | \[9/2\] |
| B. | \[2\sqrt{2}\] |
| C. | \[3\sqrt{2}\] |
| D. | \[3/2\] |
| Answer» C. \[3\sqrt{2}\] | |
| 6775. |
If every pair of the equations\[{{x}^{2}}+px+qr=0\], \[{{x}^{2}}+qx+rp=0,\] \[{{x}^{2}}+rx+pq=0\] have a common root, then the sum of three common roots is |
| A. | \[\frac{-(p+q+r)}{2}\] |
| B. | \[\frac{-p+q+r}{2}\] |
| C. | \[-(p+q+r)\] |
| D. | \[-p+q+r\] |
| Answer» B. \[\frac{-p+q+r}{2}\] | |
| 6776. |
From the origin chords are drawn to the circle\[{{(x-1)}^{2}}+{{y}^{2}}=1\]. The equation of the locus of the middle points of these chords is [IIT 1985; EAMCET 1991] |
| A. | \[{{x}^{2}}+{{y}^{2}}-3x=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-3y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-x=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-y=0\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}-y=0\] | |
| 6777. |
The sum of infinite terms of the following series \[1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+.........\] will be [MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000] |
| A. | \[\frac{3}{16}\] |
| B. | \[\frac{35}{8}\] |
| C. | \[\frac{35}{4}\] |
| D. | \[\frac{35}{16}\] |
| Answer» E. | |
| 6778. |
The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes though the point (4, 3). The equation of the curve is |
| A. | \[{{x}^{2}}=y+5\] |
| B. | \[{{y}^{2}}=x-5\] |
| C. | \[{{y}^{2}}=x+5\] |
| D. | \[{{x}^{2}}=y-5\] |
| Answer» D. \[{{x}^{2}}=y-5\] | |
| 6779. |
Area bounded by curve \[y=k\sin x\]between \[x=\pi \] and \[x=2\pi ,\] is |
| A. | \[2k\] sq. unit |
| B. | 0 |
| C. | \[\frac{{{k}^{2}}}{2}\] sq. unit |
| D. | \[k\] sq. unit |
| Answer» B. 0 | |
| 6780. |
Coefficient of \[{{x}^{r}}\] in the expansion of \[{{(1-2x)}^{-1/2}}\] is[Kurukshetra CEE 2001] |
| A. | \[\frac{(2r)\,!}{{{(r\,!)}^{2}}}\] |
| B. | \[\frac{(2r)\,!}{{{2}^{r}}{{(r!)}^{2}}}\] |
| C. | \[\frac{(2r)!}{{{(r!)}^{2}}{{2}^{2r}}}\] |
| D. | \[\frac{(2r)!}{{{2}^{r}}.(r+1)!.(r-1)!}\] |
| Answer» C. \[\frac{(2r)!}{{{(r!)}^{2}}{{2}^{2r}}}\] | |
| 6781. |
If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are [RPET 1987] |
| A. | 5 |
| B. | 8 |
| C. | 10 |
| D. | 15 |
| Answer» D. 15 | |
| 6782. |
The maximum height is reached in 5 seconds by a stone thrown vertically upwards and moving under the equation 10s = 10ut ? 49\[{{t}^{2}}\], where s is in metre and t is in second. The value of u is |
| A. | \[4.9m/\sec \] |
| B. | \[49m/\sec \] |
| C. | \[98m/\sec \] |
| D. | None of these |
| Answer» C. \[98m/\sec \] | |
| 6783. |
The \[{{n}^{th}}\] term of the following series \[(1\times 3)+(3\times 5)+(5\times 7)+(7\times 9)+.......\] will be |
| A. | \[n\,(2n+1)\] |
| B. | \[2n\,(2n-1)\] |
| C. | \[(2n+1)(2n-1)\] |
| D. | \[4{{n}^{2}}+1\] |
| Answer» D. \[4{{n}^{2}}+1\] | |
| 6784. |
If the angle between the two lines represented by \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+4=0\] is \[{{\tan }^{-1}}m\], then \[m=\] [MNR 1993] |
| A. | 1/5 |
| B. | 1 |
| C. | 7/5 |
| D. | 7 |
| Answer» B. 1 | |
| 6785. |
The vector equation of the line joining the points \[i-2j+k\] and \[-2j+3k\] is [MP PET 2003] |
| A. | \[r=t(i+j+k)\] |
| B. | \[r={{t}_{1}}(i-2j+k)+{{t}_{2}}(3k-2j)\] |
| C. | \[r=(i-2j+k)+t(2k-i)\] |
| D. | \[r=t(2k-i)\] |
| Answer» D. \[r=t(2k-i)\] | |
| 6786. |
The area enclosed by the parabola \[{{y}^{2}}=4ax\] and the straight line \[y=2ax,\] is [MP PET 1993] |
| A. | \[\frac{{{a}^{2}}}{3}\] sq. unit |
| B. | \[\frac{1}{3{{a}^{2}}}\] sq. unit |
| C. | \[\frac{1}{3a}\] sq. unit |
| D. | \[\frac{2}{3a}\] sq. unit |
| Answer» D. \[\frac{2}{3a}\] sq. unit | |
| 6787. |
Equation of curve through point \[(1,\,0)\]which satisfies the differential equation \[(1+{{y}^{2}})dx-xydy=0\], is [WB JEE 1986] |
| A. | \[{{x}^{2}}+{{y}^{2}}=1\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=1\] |
| C. | \[2{{x}^{2}}+{{y}^{2}}=2\] |
| D. | None of these |
| Answer» C. \[2{{x}^{2}}+{{y}^{2}}=2\] | |
| 6788. |
The inradius of the triangle whose sides are 3, 5, 6, is [EAMCET 1982] |
| A. | \[\sqrt{8/7}\] |
| B. | \[\sqrt{8}\] |
| C. | \[\sqrt{7}\] |
| D. | \[\sqrt{7/8}\] |
| Answer» B. \[\sqrt{8}\] | |
| 6789. |
The solution of the equation\[(x+1)+(x+4)+(x+7)+.........+(x+28)=155\] is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 6790. |
The equation of plane passing through a point \[A(2,-1,\,3)\] and parallel to the vectors \[\mathbf{a}=(3,\,0,-1)\] and \[\mathbf{b}=(-3,\,\,2,\,2)\] is [Orissa JEE 2005] |
| A. | \[2x-3y+6z-25=0\] |
| B. | \[2x-3y+6z+25=0\] |
| C. | \[3x-2y+6z-25=0\] |
| D. | \[3x-2y+6z+25=0\] |
| Answer» B. \[2x-3y+6z+25=0\] | |
| 6791. |
A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is [AIEEE 2002] |
| A. | \[\frac{8}{3}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{5}{4}\] |
| Answer» E. | |
| 6792. |
Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is 11, if 5 appears on the first |
| A. | \[\frac{1}{36}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{5}{6}\] |
| D. | None of these |
| Answer» C. \[\frac{5}{6}\] | |
| 6793. |
. If \[(a+3b)(3a+b)=4{{h}^{2}}\], then the angle between the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{\tan }^{-1}}\frac{1}{2}\] |
| Answer» D. \[{{\tan }^{-1}}\frac{1}{2}\] | |
| 6794. |
The equation \[12{{x}^{2}}+7xy+a{{y}^{2}}+13x-y+3=0\] represents a pair of perpendicular lines. Then the value of ?a? is [Karnataka CET 2001] |
| A. | \[\frac{7}{2}\] |
| B. | - 19 |
| C. | - 12 |
| D. | 12 |
| Answer» D. 12 | |
| 6795. |
If the area above the x-axis, bounded by the curves \[y={{2}^{kx}}\] and \[x=0\] and \[x=2\] is \[\frac{3}{\ln 2},\] then the value of k is [Orissa JEE 2003] |
| A. | \[\frac{1}{2}\] |
| B. | 1 |
| C. | \[-1\] |
| D. | 2 |
| Answer» C. \[-1\] | |
| 6796. |
The equation of the common chord of the circles \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and \[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\] is |
| A. | \[x-y=0\] |
| B. | \[x+y=0\] |
| C. | \[x+y={{a}^{2}}+{{b}^{2}}\] |
| D. | \[x-y={{a}^{2}}-{{b}^{2}}\] |
| Answer» B. \[x+y=0\] | |
| 6797. |
The sum of integers from 1 to 100 that are divisible by 2 or 5 is [IIT 1984] |
| A. | 3000 |
| B. | 3050 |
| C. | 4050 |
| D. | None of these |
| Answer» C. 4050 | |
| 6798. |
If the two equations \[{{x}^{2}}-cx+d=0\] and \[{{x}^{2}}-ax+b=0\] have one common root and the second has equal roots, then \[2(b+d)=\] |
| A. | 0 |
| B. | \[a+c\] |
| C. | \[ac\] |
| D. | \[-ac\] |
| Answer» D. \[-ac\] | |
| 6799. |
If the sides of a right angled traingle are in A.P., then the sides are proportional to [Roorkee 1974] |
| A. | 0.0430902777777778 |
| B. | 0.085462962962963 |
| C. | 0.127835648148148 |
| D. | 0.170208333333333 |
| Answer» D. 0.170208333333333 | |
| 6800. |
If \[\log 2,\ \log ({{2}^{n}}-1)\] and \[\log ({{2}^{n}}+3)\] are in A.P., then n = [MP PET 1998; Karnataka CET 2000; Pb. CET 2001] |
| A. | 44232 |
| B. | \[{{\log }_{2}}5\] |
| C. | \[{{\log }_{3}}5\] |
| D. | 44230 |
| Answer» C. \[{{\log }_{3}}5\] | |