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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.
| 7051. |
The area of the curve \[x{{y}^{2}}={{a}^{2}}(a-x)\] bounded by y-axis is [RPET 1996] |
| A. | \[\pi {{a}^{2}}\] |
| B. | \[2\pi {{a}^{2}}\] |
| C. | \[3\pi {{a}^{2}}\] |
| D. | \[4\pi {{a}^{2}}\] |
| Answer» B. \[2\pi {{a}^{2}}\] | |
| 7052. |
The line passing through the points (3, -4) and (-2, 6) and a line passing through (-3,6) and (9, -18) are [AMU 1974] |
| A. | Perpendicular |
| B. | Parallel |
| C. | Makes an angle \[{{60}^{o}}\]with each other |
| D. | None of these |
| Answer» C. Makes an angle \[{{60}^{o}}\]with each other | |
| 7053. |
If x is so small that \[{{x}^{3}}\] and higher powers of x may be neglected, then \[\frac{{{(1+x)}^{\frac{3}{2}}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{\frac{1}{2}}}}\] may be approximated as [AIEEE 2005] |
| A. | \[-\frac{3}{8}{{x}^{2}}\] |
| B. | \[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\] |
| C. | \[1-\frac{3}{8}{{x}^{2}}\] |
| D. | \[3x+\frac{3}{8}{{x}^{2}}\] |
| Answer» B. \[\frac{x}{2}-\frac{3}{8}{{x}^{2}}\] | |
| 7054. |
The angle between the lines represented by the equation \[({{x}^{2}}+{{y}^{2}})\sin \theta +2xy=0\]is |
| A. | \[\theta \] |
| B. | \[\frac{\theta }{2}\] |
| C. | \[\frac{\pi }{2}-\theta \] |
| D. | \[\frac{\pi }{2}-\frac{\theta }{2}\] |
| Answer» D. \[\frac{\pi }{2}-\frac{\theta }{2}\] | |
| 7055. |
The sum of \[i-2-3i+4+.........\]upto 100 terms, where \[i=\sqrt{-1}\] is |
| A. | \[50(1-i)\] |
| B. | \[25i\] |
| C. | \[25(1+i)\] |
| D. | \[100(1-i)\] |
| Answer» B. \[25i\] | |
| 7056. |
Conjugate of 1 + i is [RPET 2003] |
| A. | i |
| B. | 1 |
| C. | 1 - i |
| D. | 1 + i |
| Answer» D. 1 + i | |
| 7057. |
If x is real, the expression \[\frac{x+2}{2{{x}^{2}}+3x+6}\] takes all value in the interval [IIT 1969] |
| A. | \[\left( \frac{1}{13},\frac{1}{3} \right)\] |
| B. | \[\left[ -\frac{1}{13},\frac{1}{3} \right]\] |
| C. | \[\left( -\frac{1}{3},\frac{1}{13} \right)\] |
| D. | None of these |
| Answer» C. \[\left( -\frac{1}{3},\frac{1}{13} \right)\] | |
| 7058. |
Sum of n terms of series \[12+16+24+40+.....\] will be [UPSEAT 1999] |
| A. | \[2\,({{2}^{n}}-1)+8n\] |
| B. | \[2({{2}^{n}}-1)+6n\] |
| C. | \[3({{2}^{n}}-1)+8n\] |
| D. | \[4({{2}^{n}}-1)+8n\] |
| Answer» E. | |
| 7059. |
The sum of the series \[1+3x+6{{x}^{2}}+10{{x}^{3}}+........\infty \] will be |
| A. | \[\frac{1}{{{(1-x)}^{2}}}\] |
| B. | \[\frac{1}{1-x}\] |
| C. | \[\frac{1}{{{(1+x)}^{2}}}\] |
| D. | \[\frac{1}{{{(1-x)}^{3}}}\] |
| Answer» E. | |
| 7060. |
If \[a,\ b,\ c\] are in A.P., then \[\frac{{{(a-c)}^{2}}}{({{b}^{2}}-ac)}=\] [Roorkee 1975] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 7061. |
Area bounded by the curve \[y=\sin x\] between \[x=0\] and \[x=2\pi \] is |
| A. | 2 sq. unit |
| B. | 4 sq. unit |
| C. | 8 sq. unit |
| D. | None of these |
| Answer» C. 8 sq. unit | |
| 7062. |
The area of figure bounded by \[y={{e}^{x}},\,y={{e}^{-x}}\] and the straight line \[x=1\] is [Karnataka CET 1999] |
| A. | \[e+\frac{1}{e}\] |
| B. | \[e-3\] |
| C. | \[e+\frac{1}{e}-2\] |
| D. | \[e+\frac{1}{e}+2\] |
| Answer» D. \[e+\frac{1}{e}+2\] | |
| 7063. |
If the circle \[{{x}^{2}}+{{y}^{2}}=4\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+6y+a=0\], then a equals [RPET 1999] |
| A. | 4 |
| B. | -4 |
| C. | 16 |
| D. | -16 |
| Answer» D. -16 | |
| 7064. |
If the 9th term of an A.P. be zero, then the ratio of its 29th and 19th term is |
| A. | 0.0430555555555556 |
| B. | 0.0840277777777778 |
| C. | 0.04375 |
| D. | 0.125694444444444 |
| Answer» C. 0.04375 | |
| 7065. |
If the \[{{9}^{th}}\] term of an A.P. is 35 and is 75, then its \[{{20}^{th}}\] terms will be [RPET 1989] |
| A. | 78 |
| B. | 79 |
| C. | 80 |
| D. | 81 |
| Answer» C. 80 | |
| 7066. |
If \[|z|\,=4\] and \[arg\,\,z=\frac{5\pi }{6},\]then z = [MP PET 1987] |
| A. | \[2\sqrt{3}-2i\] |
| B. | \[2\sqrt{3}+2i\] |
| C. | \[-2\sqrt{3}+2i\] |
| D. | \[-\sqrt{3}+i\] |
| Answer» D. \[-\sqrt{3}+i\] | |
| 7067. |
The amplitude of \[\frac{1+\sqrt{3}\,i}{\sqrt{3}+i}\] is [DCE 1999; Karnataka CET 2005] |
| A. | \[\frac{\pi }{6}\] |
| B. | \[-\frac{\pi }{6}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | None of these |
| Answer» B. \[-\frac{\pi }{6}\] | |
| 7068. |
\[arg\,(5-\sqrt{3}i)=\] |
| A. | \[{{\tan }^{-1}}\frac{5}{\sqrt{3}}\] |
| B. | \[{{\tan }^{-1}}\left( -\,\frac{5}{\sqrt{3}} \right)\] |
| C. | \[{{\tan }^{-1}}\frac{\sqrt{3}}{5}\] |
| D. | \[{{\tan }^{-1}}\left( -\frac{\sqrt{3}}{5} \right)\] |
| Answer» E. | |
| 7069. |
A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is [AMU 2001] |
| A. | \[\frac{8}{141}\] |
| B. | \[\frac{10}{243}\] |
| C. | \[\frac{11}{243}\] |
| D. | \[\frac{8}{41}\] |
| Answer» D. \[\frac{8}{41}\] | |
| 7070. |
In a single throw of two dice what is the probability of obtaining a number greater than 7, if 4 appears on the first dice |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{12}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{12}\] | |
| 7071. |
A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times is |
| A. | \[\frac{5}{16}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{3}{16}\] |
| D. | \[\frac{3}{2}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 7072. |
A NOT gate is the Boolean function defined by |
| A. | \[f(x)=x,\,\,x\in \{0,\,1\}\] |
| B. | \[f(x)={x}',\,\,x\in \{0,\,1\}\] |
| C. | \[f(x)=x+{x}',\,\,x\in \{0,\,1\}\] |
| D. | None of these |
| Answer» C. \[f(x)=x+{x}',\,\,x\in \{0,\,1\}\] | |
| 7073. |
If \[x\] be real, then the minimum value of \[{{x}^{2}}-8x+17\] is [MNR 1980] |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 7074. |
A straight line through origin bisect the line passing through the given points \[(a\cos \alpha ,a\sin \alpha )\]and \[(a\cos \beta ,a\sin \beta )\], then the lines are |
| A. | Perpendicular |
| B. | Parallel |
| C. | Angle between them is \[\frac{\pi }{4}\] |
| D. | None of these |
| Answer» B. Parallel | |
| 7075. |
The equation of the circle having as a diameter, the chord \[x-y-1=0\] of the circle \[2{{x}^{2}}+2{{y}^{2}}-2x-6y-25=0\], is |
| A. | \[{{x}^{2}}+{{y}^{2}}-3x-y-\frac{29}{2}=0\] |
| B. | \[2{{x}^{2}}+2{{y}^{2}}+2x-5y-\frac{29}{2}=0\] |
| C. | \[2{{x}^{2}}+2{{y}^{2}}-6x-2y-21=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 7076. |
The area bounded by the curves \[y={{\log }_{e}}x\] and \[y={{({{\log }_{e}}x)}^{2}}\] is [RPET 2000] |
| A. | \[3-e\] |
| B. | \[e-3\] |
| C. | \[\frac{1}{2}(3-e)\] |
| D. | \[\frac{1}{2}(e-3)\] |
| Answer» B. \[e-3\] | |
| 7077. |
The amplitude of \[\sin \frac{\pi }{5}+i\,\left( 1-\cos \frac{\pi }{5} \right)\] [Karnataka CET 2003] |
| A. | \[\pi /5\] |
| B. | \[2\pi /5\] |
| C. | \[\pi /10\] |
| D. | \[\pi /15\] |
| Answer» D. \[\pi /15\] | |
| 7078. |
If the sum of \[n\] terms of an A.P. is \[2{{n}^{2}}+5n\], then the \[{{n}^{th}}\] term will be [RPET 1992] |
| A. | \[4n+3\] |
| B. | \[4n+5\] |
| C. | \[4n+6\] |
| D. | \[4n+7\] |
| Answer» B. \[4n+5\] | |
| 7079. |
The maximum sum of the series \[20+19\frac{1}{3}+18\frac{2}{3}+.........\] is |
| A. | 310 |
| B. | 300 |
| C. | 320 |
| D. | None of these |
| Answer» B. 300 | |
| 7080. |
If the set of natural numbers is partitioned into subsets \[{{S}_{1}}=\left\{ 1 \right\},\ {{S}_{2}}=\left\{ 2,\ 3 \right\},\ {{S}_{3}}=\left\{ 4,\ 5,\ 6 \right\}\] and so on. Then the sum of the terms in \[{{S}_{50}}\] is |
| A. | 62525 |
| B. | 25625 |
| C. | 62500 |
| D. | None of these |
| Answer» B. 25625 | |
| 7081. |
The angle between the lines \[2x-y+3=0\] and \[x+2y+3=0\] is [Kerala (Engg.) 2002] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» B. \[{{60}^{o}}\] | |
| 7082. |
If \[2x,\ x+8,\ 3x+1\] are in A.P., then the value of \[x\] will be [MP PET 1984] |
| A. | 3 |
| B. | 7 |
| C. | 5 |
| D. | -2 |
| Answer» D. -2 | |
| 7083. |
If the path of a moving point is the curve \[x=at\], \[y=b\sin at\], then its acceleration at any instant [SCRA 1996] |
| A. | Is constant |
| B. | Varies as the distance from the axis of x |
| C. | Varies as the distance from the axis of y |
| D. | Varies as the distance of the point from the origin |
| Answer» D. Varies as the distance of the point from the origin | |
| 7084. |
A particle is moving in a straight line according to the formula \[s={{t}^{2}}+8t+12.\]If s be measured in metre and t be measured in second, then the average velocity of the particle in third second is |
| A. | \[14\,m/\sec \] |
| B. | \[13\,m/\sec \] |
| C. | \[15\,m/\sec \] |
| D. | None of these |
| Answer» C. \[15\,m/\sec \] | |
| 7085. |
If by dropping a stone in a quiet lake a wave moves in circle at a speed of 3.5 cm/sec, then the rate of increase of the enclosed circular region when the radius of the circular wave is 10 cm, is \[\left( \pi =\frac{22}{7} \right)\] [MP PET 1998] |
| A. | 220 sq. cm/sec |
| B. | 110 sq. cm/sec |
| C. | 35 sq. cm/sec |
| D. | 350 sq. cm/sec |
| Answer» B. 110 sq. cm/sec | |
| 7086. |
If \[a{{x}^{2}}+bx+c=0\] and \[b{{x}^{2}}+cx+a=0\] have a common root \[a\ne 0\], then \[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}}{abc}=\] [IIT 1982; Kurukshetra CEE 1983] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | None of these |
| Answer» D. None of these | |
| 7087. |
Solution of differential equation \[x\,dy-y\,dx=0\] represents [MP PET 1996] |
| A. | Rectangular hyperbola |
| B. | Straight line passing through origin |
| C. | Parabola whose vertex is at origin |
| D. | Circle whose centre is at origin |
| Answer» C. Parabola whose vertex is at origin | |
| 7088. |
The length of the chord intercepted by the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]on the line \[\frac{x}{a}+\frac{y}{b}=1\] is |
| A. | \[\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] |
| B. | \[2\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] |
| C. | \[2\frac{\sqrt{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}}{{{a}^{2}}+{{b}^{2}}}\] |
| D. | None of these |
| Answer» C. \[2\frac{\sqrt{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}}{{{a}^{2}}+{{b}^{2}}}\] | |
| 7089. |
Three number are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is [UPSEAT 2004] |
| A. | 10 |
| B. | 11 |
| C. | 12 |
| D. | None of these |
| Answer» C. 12 | |
| 7090. |
The area between the parabola \[{{y}^{2}}=4ax\]and \[{{x}^{2}}=8ay\] is [RPET 1997] |
| A. | \[\frac{8}{3}{{a}^{2}}\] |
| B. | \[\frac{4}{3}{{a}^{2}}\] |
| C. | \[\frac{32}{3}{{a}^{2}}\] |
| D. | \[\frac{16}{3}{{a}^{2}}\] |
| Answer» D. \[\frac{16}{3}{{a}^{2}}\] | |
| 7091. |
The value of \[\sum\limits_{r=1}^{n}{\log \left( \frac{{{a}^{r}}}{{{b}^{r-1}}} \right)}\] is |
| A. | \[\frac{n}{2}\log \left( \frac{{{a}^{n}}}{{{b}^{n}}} \right)\] |
| B. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n}}} \right)\] |
| C. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n-1}}} \right)\] |
| D. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n+1}}} \right)\] |
| Answer» D. \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n+1}}} \right)\] | |
| 7092. |
If the sides of triangle are 13, 14, 15, then the radius of its incircle is [EAMCET 1987] |
| A. | \[\frac{67}{8}\] |
| B. | \[\frac{65}{4}\] |
| C. | 4 |
| D. | 24 |
| Answer» D. 24 | |
| 7093. |
If a point \[(x,\ y)\equiv (\tan \theta +\sin \theta ,\ \tan \theta -\sin \theta )\], then locus of (x, y) is [EAMCET 2002] |
| A. | \[{{({{x}^{2}}y)}^{2/3}}+{{(x{{y}^{2}})}^{2/3}}=1\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=4xy\] |
| C. | \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=16xy\] |
| D. | \[{{x}^{2}}-{{y}^{2}}=6xy\] |
| Answer» D. \[{{x}^{2}}-{{y}^{2}}=6xy\] | |
| 7094. |
\[1+\frac{3}{2}+\frac{5}{{{2}^{2}}}+\frac{7}{{{2}^{3}}}+......\,\infty \,\]is equal to [DCE 1999] |
| A. | 3 |
| B. | 6 |
| C. | 9 |
| D. | 12 |
| Answer» E. | |
| 7095. |
The angle between the lines \[{{x}^{2}}-xy-6{{y}^{2}}-7x+31y-18=0\] is [Karnataka CET 2003] |
| A. | \[{{45}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» B. \[{{60}^{o}}\] | |
| 7096. |
If x denotes the number of sixes in four consecutive throws of a dice, then \[P\,(x=4)\]is [BIT Ranchi 1991] |
| A. | \[\frac{1}{1296}\] |
| B. | \[\frac{4}{6}\] |
| C. | 1 |
| D. | \[\frac{1295}{1296}\] |
| Answer» B. \[\frac{4}{6}\] | |
| 7097. |
If the \[{{n}^{th}}\] term of an A.P. be \[(2n-1)\], then the sum of its first \[n\] terms will be |
| A. | \[{{n}^{2}}-1\] |
| B. | \[{{(2n-1)}^{2}}\] |
| C. | \[{{n}^{2}}\] |
| D. | \[{{n}^{2}}+1\] |
| Answer» D. \[{{n}^{2}}+1\] | |
| 7098. |
If the conjugate of \[(x+iy)(1-2i)\]be \[1+i\], then [MP PET 1996] |
| A. | \[x=\frac{1}{5}\] |
| B. | \[y=\frac{3}{5}\] |
| C. | \[x+iy=\frac{1-i}{1-2i}\] |
| D. | \[x-iy=\frac{1-i}{1+2i}\] |
| Answer» D. \[x-iy=\frac{1-i}{1+2i}\] | |
| 7099. |
The angle between the pair of straight lines \[{{x}^{2}}-{{y}^{2}}-2y-1=0\], is [MNR 1991; UPSEAT 2000] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{75}^{o}}\] |
| D. | \[{{36}^{o}}\] |
| Answer» B. \[{{60}^{o}}\] | |
| 7100. |
If A is the area of the region bounded by the curve \[y=\sqrt{3x+4}\], x axis and the line \[x=-1\] and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4\], x- axis and the lines \[x=-1\]and \[x=4\] then \[A:B\] is equal to [J& K 2005] |
| A. | \[1:1\] |
| B. | \[2:1\] |
| C. | \[1:2\] |
| D. | None of these |
| Answer» B. \[2:1\] | |