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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.
| 6951. |
In a triangle ABC, \[a:b:c=4:5:6\]. The ratio of the radius of the circumcircle to that of the incircle is [IIT 1996] |
| A. | \[\frac{16}{9}\] |
| B. | \[\frac{16}{7}\] |
| C. | \[\frac{11}{7}\] |
| D. | \[\frac{7}{16}\] |
| Answer» C. \[\frac{11}{7}\] | |
| 6952. |
A ladder is resting with the wall at an angle of \[{{30}^{o}}\]. A man is ascending the ladder at the rate of 3 ft/sec. His rate of approaching the wall is |
| A. | 3 ft/sec |
| B. | \[\frac{3}{2}\]ft/sec |
| C. | \[\frac{3}{4}\]ft/sec |
| D. | \[\frac{3}{\sqrt{2}}\]ft/sec |
| Answer» C. \[\frac{3}{4}\]ft/sec | |
| 6953. |
The area of region \[\{\,(x,\,y):{{x}^{2}}+{{y}^{2}}\le 1\le x+y\}\] is [Kerala (Engg.) 2002] |
| A. | \[\frac{{{\pi }^{2}}}{5}\] |
| B. | \[\frac{{{\pi }^{2}}}{2}\] |
| C. | \[\frac{{{\pi }^{2}}}{3}\] |
| D. | \[\frac{\pi }{4}-\frac{1}{2}\] |
| Answer» E. | |
| 6954. |
A straight line \[(\sqrt{3}-1)x=(\sqrt{3}+1)y\] makes an angle \[{{75}^{o}}\]with another straight line which passes through origin. Then the equation of the line is |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[x+y=0\] |
| D. | \[x-y=0\] |
| Answer» B. \[y=0\] | |
| 6955. |
The distance of the point \[2\mathbf{i}+\mathbf{j}-\mathbf{k}\] from the plane \[\mathbf{r}.(\mathbf{i}-2\mathbf{j}+4\mathbf{k})=9\] is |
| A. | \[\frac{13}{\sqrt{21}}\] |
| B. | \[\frac{13}{21}\] |
| C. | \[\frac{13}{3\sqrt{21}}\] |
| Answer» B. \[\frac{13}{21}\] | |
| 6956. |
If the lines \[(p-q){{x}^{2}}+2(p+q)xy+(q-p){{y}^{2}}=0\] are mutually perpendicular, then |
| A. | \[p=q\] |
| B. | \[q=0\] |
| C. | \[p=0\] |
| D. | p and q may have any value |
| Answer» E. | |
| 6957. |
The pole of the straight line \[9x+y-28=0\]with respect to circle \[2{{x}^{2}}+2{{y}^{2}}-3x+5y-7=0\], is [RPET 1990, 99; MNR 1984; UPSEAT 2000] |
| A. | (3, 1) |
| B. | (1, 3) |
| C. | (3, -1) |
| D. | (-3, 1) |
| Answer» D. (-3, 1) | |
| 6958. |
The equation of motion of a stone, thrown vertically upwards is \[s=ut-6.3{{t}^{2}},\]where the units of s and t are cm and sec. If the stone reaches at maximum height in 3 sec, then u = |
| A. | \[18.9\,\,cm/\sec \] |
| B. | \[12.6\,\,cm/\sec \] |
| C. | \[37.8\,\,cm/\sec \] |
| D. | None of these |
| Answer» D. None of these | |
| 6959. |
The polar of the point (5, ?1/2) w.r.t circle \[{{(x-2)}^{2}}+{{y}^{2}}=4\]is [RPET 1996] |
| A. | \[5x-10y+2=0\] |
| B. | \[6x-y-20=0\] |
| C. | \[10x-y-10=0\] |
| D. | \[x-10y-2=0\] |
| Answer» C. \[10x-y-10=0\] | |
| 6960. |
The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is [Kerala (Engg.) 2002] |
| A. | 5 |
| B. | 10 |
| C. | 12 |
| D. | 14 |
| Answer» E. | |
| 6961. |
If A and B are two events such that \[P\,(A)\ne 0\] and \[P\,(B)\ne 1,\] then \[P\,\left( \frac{{\bar{A}}}{{\bar{B}}} \right)=\] [IIT 1982; RPET 1995, 2000; DCE 2000; UPSEAT 2001] |
| A. | \[1-P\,\left( \frac{A}{B} \right)\] |
| B. | \[1-P\,\left( \frac{{\bar{A}}}{B} \right)\] |
| C. | \[\frac{1-P\,(A\cup B)}{P\,(\bar{B})}\] |
| D. | \[\frac{P\,(\bar{A})}{P\,(\bar{B})}\] |
| Answer» D. \[\frac{P\,(\bar{A})}{P\,(\bar{B})}\] | |
| 6962. |
The position of a point in time ?t? is given by \[x=a+bt-c{{t}^{2}}\], \[y=at+b{{t}^{2}}\]. Its acceleration at time ?t? is[MP PET 2003] |
| A. | \[b-c\] |
| B. | \[b+c\] |
| C. | \[2b-2c\] |
| D. | \[2\sqrt{{{b}^{2}}+{{c}^{2}}}\] |
| Answer» E. | |
| 6963. |
\[(z+a)(\bar{z}+a)\], where \[a\] is real, is equivalent to |
| A. | \[|z-a|\] |
| B. | \[{{z}^{2}}+{{a}^{2}}\] |
| C. | \[|z+a{{|}^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6964. |
A particle moves so that \[S=6+48t-{{t}^{3}}\]. The direction of motion reverses after moving a distance of [Kurukshetra CEE 1998] |
| A. | 63 |
| B. | 104 |
| C. | 134 |
| D. | 288 |
| Answer» D. 288 | |
| 6965. |
If \[{{a}_{1}},\ {{a}_{2}},............,{{a}_{n}}\] are in A.P. with common difference , \[d\], then the sum of the following series is \[\sin d(\cos \text{ec}\,{{a}_{1}}.co\text{sec}\,{{a}_{2}}+\text{cosec}\,{{a}_{2}}.\text{cosec}\,{{a}_{3}}+...........\]\[+\text{cosec}\ {{a}_{n-1}}\text{cosec}\ {{a}_{n}})\] [RPET 2000] |
| A. | \[\sec {{a}_{1}}-\sec {{a}_{n}}\] |
| B. | \[\cot {{a}_{1}}-\cot {{a}_{n}}\] |
| C. | \[\tan {{a}_{1}}-\tan {{a}_{n}}\] |
| D. | \[c\text{osec}\ {{a}_{1}}-\text{cosec}\ {{a}_{n}}\] |
| Answer» C. \[\tan {{a}_{1}}-\tan {{a}_{n}}\] | |
| 6966. |
If \[2a+3b+6c=0\] then at least one root of the equation \[a{{x}^{2}}+bx+c=0\]lies in the interval [Kurukshetra CEE 2002; AIEEE 2002, 04] |
| A. | (0, 1) |
| B. | (1, 2) |
| C. | (2, 3) |
| D. | (3, 4) |
| Answer» B. (1, 2) | |
| 6967. |
The area between the curve \[{{y}^{2}}=4ax,\] x-axis and the ordinates \[x=0\] and \[x=a\] is [RPET 1996] |
| A. | \[\frac{4}{3}{{a}^{2}}\] |
| B. | \[\frac{8}{3}{{a}^{2}}\] |
| C. | \[\frac{2}{3}{{a}^{2}}\] |
| D. | \[\frac{5}{3}{{a}^{2}}\] |
| Answer» C. \[\frac{2}{3}{{a}^{2}}\] | |
| 6968. |
If \[z=1-\cos \alpha +i\sin \alpha \], then amp\[z\]= |
| A. | \[\frac{\alpha }{2}\] |
| B. | \[-\frac{\alpha }{2}\] |
| C. | \[\frac{\pi }{2}+\frac{\alpha }{2}\] |
| D. | \[\frac{\pi }{2}-\frac{\alpha }{2}\] |
| Answer» E. | |
| 6969. |
If a dice is thrown 7 times, then the probability of obtaining 5 exactly 4 times is |
| A. | \[^{7}{{C}_{4}}\,{{\left( \frac{1}{6} \right)}^{4}}{{\left( \frac{5}{6} \right)}^{3}}\] |
| B. | \[^{7}{{C}_{4}}\,{{\left( \frac{1}{6} \right)}^{3}}{{\left( \frac{5}{6} \right)}^{4}}\] |
| C. | \[{{\left( \frac{1}{6} \right)}^{4}}{{\left( \frac{5}{6} \right)}^{3}}\] |
| D. | \[{{\left( \frac{1}{6} \right)}^{3}}{{\left( \frac{5}{6} \right)}^{4}}\] |
| Answer» B. \[^{7}{{C}_{4}}\,{{\left( \frac{1}{6} \right)}^{3}}{{\left( \frac{5}{6} \right)}^{4}}\] | |
| 6970. |
The amplitude of the complex number \[z=\sin \alpha +i(1-\cos \alpha )\] is |
| A. | \[2\sin \frac{\alpha }{2}\] |
| B. | \[\frac{\alpha }{2}\] |
| C. | \[\alpha \] |
| D. | None of these |
| Answer» C. \[\alpha \] | |
| 6971. |
If \[{{z}_{1}}=1+2i\] and \[{{z}_{2}}=3+5i\], and then \[\operatorname{Re}\,\left( \frac{{{{\bar{z}}}_{2}}{{z}_{1}}}{{{z}_{2}}} \right)\] is equal to [J & K 2005] |
| A. | \[\frac{-31}{17}\] |
| B. | \[\frac{17}{22}\] |
| C. | \[\frac{-17}{31}\] |
| D. | \[\frac{22}{17}\] |
| Answer» E. | |
| 6972. |
If \[x\] is real, then the maximum and minimum values of the expression \[\frac{{{x}^{2}}-3x+4}{{{x}^{2}}+3x+4}\] will be [IIT 1984] |
| A. | 2, 1 |
| B. | \[5,\frac{1}{5}\] |
| C. | \[7,\frac{1}{7}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6973. |
The fourth term in the expansion of \[{{(1-2x)}^{3/2}}\]will be [RPET 1989] |
| A. | \[-\frac{3}{4}{{x}^{4}}\] |
| B. | \[\frac{{{x}^{3}}}{2}\] |
| C. | \[-\frac{{{x}^{3}}}{2}\] |
| D. | \[\frac{3}{4}{{x}^{4}}\] |
| Answer» C. \[-\frac{{{x}^{3}}}{2}\] | |
| 6974. |
A coin is tossed successively three times. The probability of getting exactly one head or 2 heads, is [AISSE 1990] |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{3}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6975. |
The length of the perpendicular from the origin to the plane passing through the point a and containing the line \[\mathbf{r}=\mathbf{b}+\lambda \mathbf{c}\] is |
| A. | \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\] |
| B. | \[\frac{\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}|}\] |
| C. | \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\] |
| D. | \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{c}\times \mathbf{a}+\mathbf{a}\times \mathbf{b}|}\] |
| Answer» D. \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{c}\times \mathbf{a}+\mathbf{a}\times \mathbf{b}|}\] | |
| 6976. |
If the radius of a circle increases from 3 cm to 3.2 cm, then the increase in the area of the circle is |
| A. | \[1.2\pi \,\,c{{m}^{2}}\] |
| B. | \[12\pi \,\,c{{m}^{2}}\] |
| C. | \[6\pi \,\,c{{m}^{2}}\] |
| D. | None of these |
| Answer» B. \[12\pi \,\,c{{m}^{2}}\] | |
| 6977. |
The value of k for which the lines \[7x-8y+5=0\], \[3x-4y+5=0\] and \[4x+5y+k=0\] are concurrent is given by [MP PET 1993] |
| A. | - 45 |
| B. | 44 |
| C. | 54 |
| D. | - 54 |
| Answer» B. 44 | |
| 6978. |
Area bounded by \[y=x\sin x\] and \[x-\]axis between \[x=0\] and \[x=2\pi ,\] is [Roorkee 1981; RPET 1995] |
| A. | 0 |
| B. | \[2\pi \] sq. unit |
| C. | \[\pi \] sq. unit |
| D. | \[4\pi \] sq. unit |
| Answer» E. | |
| 6979. |
. If \[x\] is real, then the value of \[{{x}^{2}}-6x+13\] will not be less than [RPET 1986] |
| A. | 4 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» B. 6 | |
| 6980. |
The vector equation of the plane through the point \[2\mathbf{i}-\mathbf{j}-4\mathbf{k}\] and parallel to the plane \[\mathbf{r}.(4\mathbf{i}-12\mathbf{j}-3\mathbf{k})-7=0\] is |
| A. | \[\mathbf{r}.(4\mathbf{i}-12\mathbf{j}-3\mathbf{k})=0\] |
| B. | \[\mathbf{r}.(4\mathbf{i}-12\mathbf{j}-3\mathbf{k})=32\] |
| C. | \[\mathbf{r}.(4\mathbf{i}-12\mathbf{j}-3\mathbf{k})=12\] |
| D. | None of these |
| Answer» C. \[\mathbf{r}.(4\mathbf{i}-12\mathbf{j}-3\mathbf{k})=12\] | |
| 6981. |
Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail, is |
| A. | \[\frac{1}{7}\] |
| B. | \[\frac{1}{8}\] |
| C. | \[\frac{2}{7}\] |
| D. | \[\frac{1}{6}\] |
| Answer» B. \[\frac{1}{8}\] | |
| 6982. |
If \[1,\,\,{{\log }_{9}}({{3}^{1-x}}+2),\,\,{{\log }_{3}}({{4.3}^{x}}-1)\] are in A.P. then x equals [AIEEE 2002] |
| A. | \[{{\log }_{3}}4\] |
| B. | \[1-{{\log }_{3}}4\] |
| C. | \[1-{{\log }_{4}}3\] |
| D. | \[{{\log }_{4}}3\] |
| Answer» C. \[1-{{\log }_{4}}3\] | |
| 6983. |
The distance from the point \[-\mathbf{i}+2\mathbf{j}+6\mathbf{k}\] to the straight line through the point (2, 3, ?4) and parallel to the vector \[6\mathbf{i}+3\mathbf{j}-4\mathbf{k}\] is |
| A. | 7 |
| B. | 10 |
| C. | 9 |
| D. | None of these |
| Answer» B. 10 | |
| 6984. |
If the lines represented by the equation \[a{{x}^{2}}-bxy-{{y}^{2}}=0\] make angles \[\alpha \] and \[\beta \] with the x-axis, then \[\tan (\alpha +\beta )\]= |
| A. | \[\frac{b}{1+a}\]. |
| B. | \[\frac{-b}{1+a}\] |
| C. | \[\frac{a}{1+b}\] |
| D. | None of these |
| Answer» C. \[\frac{a}{1+b}\] | |
| 6985. |
If am denotes the mth term of an A.P. then am = |
| A. | \[\frac{2}{{{a}_{m+k}}+{{a}_{m-k}}}\] |
| B. | \[\frac{{{a}_{m+k}}-{{a}_{m-k}}}{2}\] |
| C. | \[\frac{{{a}_{m+k}}+{{a}_{m-k}}}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6986. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1+x+{{x}^{2}}+....)}^{-n}}\] is |
| A. | 1 |
| B. | \[{{(-1)}^{n}}\] |
| C. | n |
| D. | \[n+1\] |
| Answer» C. n | |
| 6987. |
In a Boolean Algebra B, for all x in B, \[x\vee 1=\] |
| A. | 0 |
| B. | 1 |
| C. | x |
| D. | None of these |
| Answer» C. x | |
| 6988. |
The co-ordinates of pole of line \[lx+my+n=0\]with respect to circles \[{{x}^{2}}+{{y}^{2}}=1\], is [RPET 1987] |
| A. | \[\left( \frac{l}{n},\frac{m}{n} \right)\] |
| B. | \[\left( -\frac{l}{n},-\frac{m}{n} \right)\] |
| C. | \[\left( \frac{l}{n},-\frac{m}{n} \right)\] |
| D. | \[\left( -\frac{l}{n},\frac{m}{n} \right)\] |
| Answer» C. \[\left( \frac{l}{n},-\frac{m}{n} \right)\] | |
| 6989. |
The equation of the bisectors of angle between the lines represented by equation \[{{(y-mx)}^{2}}={{(x+my)}^{2}}\]is |
| A. | \[m{{x}^{2}}+({{m}^{2}}-1)xy-m{{y}^{2}}=0\] |
| B. | \[m{{x}^{2}}-({{m}^{2}}-1)xy-m{{y}^{2}}=0\] |
| C. | \[m{{x}^{2}}+({{m}^{2}}-1)xy+m{{y}^{2}}=0\] |
| D. | None of these |
| Answer» B. \[m{{x}^{2}}-({{m}^{2}}-1)xy-m{{y}^{2}}=0\] | |
| 6990. |
If the roots of \[{{x}^{2}}+x+a=0\]exceed a, then [EAMCET 1994] |
| A. | \[2<a<3\] |
| B. | \[a>3\] |
| C. | \[-3<a<3\] |
| D. | \[a<-2\] |
| Answer» E. | |
| 6991. |
Dual of \[({x}'\vee {y}'{)}'=x\wedge y\] is |
| A. | \[({x}'\vee {y}')=x\vee y\] |
| B. | \[({x}'\wedge {y}'{)}'=x\vee y\] |
| C. | \[({x}'\wedge {y}'{)}'=x\wedge y\] |
| D. | None of these |
| Answer» C. \[({x}'\wedge {y}'{)}'=x\wedge y\] | |
| 6992. |
Area bounded by lines \[y=2+x,\] \[y=2-x\] and \[x=2\] is [MP PET 1996] |
| A. | 3 |
| B. | 4 |
| C. | 8 |
| D. | 16 |
| Answer» C. 8 | |
| 6993. |
The three straight lines \[ax+by=c,\,\,bx+cy=a\] and \[cx+ay=b\] are collinear, if [MP PET 2004] |
| A. | \[a+b+c=0\] |
| B. | \[b+c=a\] |
| C. | \[c+a=b\] |
| D. | \[a+b=c\] |
| Answer» B. \[b+c=a\] | |
| 6994. |
The area enclosed between the parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] is [Karnataka CET 1999, 2003] |
| A. | \[\frac{14}{3}\] sq. unit |
| B. | \[\frac{3}{4}\] sq. unit |
| C. | \[\frac{3}{16}\] sq. unit |
| D. | \[\frac{16}{3}\] sq. unit |
| Answer» E. | |
| 6995. |
Angle between \[x=2\] and \[x-3y=6\] is [MNR 1988] |
| A. | \[\infty \] |
| B. | \[{{\tan }^{-1}}(3)\] |
| C. | \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\] |
| D. | None of these |
| Answer» C. \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\] | |
| 6996. |
If a, b, c are three non-coplanar vectors, then the vector equation \[\mathbf{r}=(1-\mathbf{p}-\mathbf{q})\,\mathbf{a}+p\mathbf{b}+q\mathbf{c}\] represents a [EAMCET 2003] |
| A. | Straight line |
| B. | Plane |
| C. | Plane passing through the origin |
| D. | Sphere |
| Answer» C. Plane passing through the origin | |
| 6997. |
The angle between the lines \[x\cos {{30}^{o}}+y\sin 30{}^\circ =3\] and \[x\cos {{60}^{o}}+y\sin {{60}^{o}}=5\] is |
| A. | \[{{90}^{o}}\] |
| B. | \[{{30}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | None of these |
| Answer» C. \[{{60}^{o}}\] | |
| 6998. |
The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is [MP PET 2003] |
| A. | 1 |
| B. | 8 |
| C. | 4 |
| D. | 6 |
| Answer» D. 6 | |
| 6999. |
The argument of the complex number \[-1+i\sqrt{3}\] is [MP PET 1994] |
| A. | \[-{{60}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{120}^{o}}\] |
| D. | \[-{{120}^{o}}\] |
| Answer» D. \[-{{120}^{o}}\] | |
| 7000. |
If \[z\] is a complex number, then which of the following is not true [MP PET 1987] |
| A. | \[|{{z}^{2}}|\,=\,|z{{|}^{2}}\] |
| B. | \[|{{z}^{2}}|\,=\,|\bar{z}{{|}^{2}}\] |
| C. | \[z=\bar{z}\] |
| D. | \[{{\bar{z}}^{2}}={{\bar{z}}^{2}}\] |
| Answer» D. \[{{\bar{z}}^{2}}={{\bar{z}}^{2}}\] | |