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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.
| 5301. |
The positive integer just greater than (1 + 0.0001)10000 is [AIEEE 2002] |
| A. | 4 |
| B. | 5 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 5302. |
The approximate value of (1.0002)3000 is [EAMCET 2002] |
| A. | 1.6 |
| B. | 1.4 |
| C. | 1.8 |
| D. | 1.2 |
| Answer» B. 1.4 | |
| 5303. |
The greatest integer which divides the number \[{{101}^{100}}-1\], is [MP PET 1998] |
| A. | 100 |
| B. | 1000 |
| C. | 10000 |
| D. | 100000 |
| Answer» D. 100000 | |
| 5304. |
The number of non-zero terms in the expansion of \[{{(1+3\sqrt{2}x)}^{9}}+{{(1-3\sqrt{2}x)}^{9}}\] is [EAMCET 1991] |
| A. | 9 |
| B. | 0 |
| C. | 5 |
| D. | 10 |
| Answer» D. 10 | |
| 5305. |
\[{{(\sqrt{2}+1)}^{6}}-{{(\sqrt{2}-1)}^{6}}=\] [MP PET 1984] |
| A. | 101 |
| B. | \[70\sqrt{2}\] |
| C. | \[140\sqrt{2}\] |
| D. | \[120\sqrt{2}\] |
| Answer» D. \[120\sqrt{2}\] | |
| 5306. |
The solution of the differential equation \[x\,dy+y\,dx-\sqrt{1-{{x}^{2}}{{y}^{2}}}dx=0\] is |
| A. | \[{{\sin }^{-1}}xy=c-x\] |
| B. | \[xy=\sin (x+c)\] |
| C. | \[\log (1-{{x}^{2}}{{y}^{2}})=x+c\] |
| D. | \[y=x\sin x+c\] |
| Answer» C. \[\log (1-{{x}^{2}}{{y}^{2}})=x+c\] | |
| 5307. |
The solution of \[y{{e}^{-x/y}}dx-(x{{e}^{-x/y}}+{{y}^{3}})dy=0\] is |
| A. | \[\frac{{{y}^{2}}}{2}+{{e}^{-x/y}}=k\] |
| B. | \[\frac{{{x}^{2}}}{2}+{{e}^{-x/y}}=k\] |
| C. | \[\frac{{{x}^{2}}}{2}+{{e}^{x/y}}=k\] |
| D. | \[\frac{{{y}^{2}}}{2}+{{e}^{x/y}}=k\] |
| Answer» B. \[\frac{{{x}^{2}}}{2}+{{e}^{-x/y}}=k\] | |
| 5308. |
The solution of \[(x-{{y}^{3}})dx+3x{{y}^{2}}dy=0\] is |
| A. | \[\log x+\frac{x}{y}\] |
| B. | \[\log x+\frac{{{y}^{3}}}{x}=k\] |
| C. | \[\log x-\frac{x}{{{y}^{3}}}=k\] |
| D. | \[\log xy-{{y}^{3}}=k\] |
| Answer» C. \[\log x-\frac{x}{{{y}^{3}}}=k\] | |
| 5309. |
Solution of \[(xy\cos xy+\sin xy)dx+{{x}^{2}}\cos xy\,dy=0\] is |
| A. | \[x\sin (xy)=k\] |
| B. | \[xy\sin (xy)=k\] |
| C. | \[\frac{x}{y}\sin (xy)=k\] |
| D. | \[x\sin (xy)=k\] |
| Answer» B. \[xy\sin (xy)=k\] | |
| 5310. |
The solution of the differential equation, \[y\,dx+(x+{{x}^{2}}y)dy=0\] is [AIEEE 2004] |
| A. | \[\log y=cx\] |
| B. | \[-\frac{1}{xy}+\log y=c\] |
| C. | \[-\frac{1}{xy}+\log y=c\] |
| D. | \[-\frac{1}{xy}+\log y=c\] |
| Answer» C. \[-\frac{1}{xy}+\log y=c\] | |
| 5311. |
The solution of \[(1+xy)y\,dx+(1-xy)x\,dy=0\] is |
| A. | \[\frac{x}{y}+\frac{1}{xy}=k\] |
| B. | \[\log \left( \frac{x}{y} \right)=\frac{1}{xy}+k\] |
| C. | \[\frac{x}{y}+\frac{1}{xy}=k\] |
| D. | \[\log \left( \frac{x}{y} \right)=xy+k\] |
| Answer» C. \[\frac{x}{y}+\frac{1}{xy}=k\] | |
| 5312. |
If \[xdy=y\,(dx+ydy),\,y>0\] and \[y(1)=1,\] then \[y(-3)\] is equal to [IIT Screening 2005] |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | ?1 |
| Answer» C. 5 | |
| 5313. |
\[({{x}^{2}}+{{y}^{2}})dy=xydx\]. If \[y({{x}_{0}})=e\], \[y(1)=1\], then value of \[{{x}_{0}}=\] [IIT Screening 2005] |
| A. | \[\sqrt{3}e\] |
| B. | \[\sqrt{{{e}^{2}}-\frac{1}{2}}\] |
| C. | \[\sqrt{\frac{{{e}^{2}}-1}{2}}\] |
| D. | \[\sqrt{\frac{{{e}^{2}}+1}{2}}\] |
| Answer» B. \[\sqrt{{{e}^{2}}-\frac{1}{2}}\] | |
| 5314. |
If c is any arbitrary constant, then the general solution of the differential equation \[ydx-xdy=xy\,dx\] is given by [J & K 2005] |
| A. | \[y=cx\,{{e}^{-x}}\] |
| B. | \[x=cy{{e}^{-x}}\] |
| C. | \[y+{{e}^{x}}=cx\] |
| D. | \[y{{e}^{x}}=cx\] |
| Answer» E. | |
| 5315. |
The solution of \[y\,dx-xdy+3{{x}^{2}}{{y}^{2}}{{e}^{{{x}^{3}}}}dx=0\] is |
| A. | \[\frac{x}{y}+{{e}^{{{x}^{3}}}}=c\] |
| B. | \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\] |
| C. | \[\frac{-x}{y}+{{e}^{{{x}^{3}}}}=0\] |
| D. | None of these |
| Answer» B. \[\frac{x}{y}-{{e}^{{{x}^{3}}}}=0\] | |
| 5316. |
The centre of the circle \[x=-1+2\cos \theta \], \[y=3+2\sin \theta \], is [MP PET 1995] |
| A. | (1, ?3) |
| B. | (?1, 3) |
| C. | (1, 3) |
| D. | None of these |
| Answer» C. (1, 3) | |
| 5317. |
A line is drawn through a fixed point \[P(\alpha ,\ \beta )\] to cut the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\] at A and B. Then \[PA\ .\ PB\] is equal to |
| A. | \[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] |
| B. | \[{{(\alpha +\beta )}^{2}}-{{r}^{2}}\] |
| C. | \[{{(\alpha -\beta )}^{2}}+{{r}^{2}}\] |
| D. | None of these |
| Answer» C. \[{{(\alpha -\beta )}^{2}}+{{r}^{2}}\] | |
| 5318. |
For \[a{{x}^{2}}+2hxy+3{{y}^{2}}+4x+8y-6=0\] to represent a circle, one must have |
| A. | \[a=3,\ h=0\] |
| B. | \[a=1,\ h=0\] |
| C. | \[a=h=3\] |
| D. | \[a=h=0\] |
| Answer» B. \[a=1,\ h=0\] | |
| 5319. |
The locus of the centre of a circle of radius 2 which rolls on the outside of circle \[{{x}^{2}}+{{y}^{2}}+3x-6y-9=0\], is |
| A. | \[{{x}^{2}}+{{y}^{2}}+3x-6y+5=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+3x-6y-31=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0\] | |
| 5320. |
If the coordinates of one end of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}-8x-4y+c=0\] are (-3, 2), then the coordinates of other end are [Roorkee 1995] |
| A. | (5, 3) |
| B. | (6, 2) |
| C. | (1, -8) |
| D. | (11, 2) |
| Answer» E. | |
| 5321. |
The circle passing through point of intersection of the circle \[S=0\] and the line \[P=0\] is [RPET 1995] |
| A. | \[S+\lambda P=0\] |
| B. | \[S-\lambda P=0\] |
| C. | \[\lambda S+P=0\] |
| D. | \[P-\lambda S=0\] |
| E. | All of these |
| Answer» F. | |
| 5322. |
Area of the circle in which a chord of length \[\sqrt{2}\] makes an angle \[\frac{\pi }{2}\] at the centre is |
| A. | \[\frac{\pi }{2}\] |
| B. | \[2\pi \] |
| C. | \[\pi \] |
| D. | \[\frac{\pi }{4}\] |
| Answer» D. \[\frac{\pi }{4}\] | |
| 5323. |
The equation of the circle which passes through the points \[(3,\ -2)\] and \[(-2,\ 0)\] and centre lies on the line \[2x-y=3\], is [Roorkee 1971] |
| A. | \[{{x}^{2}}+{{y}^{2}}-3x-12y+2=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-3x+12y+2=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+3x+12y+2=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 5324. |
The equation of circle whose diameter is the line joining the points (?4, 3) and (12, ?1) is [IIT 1971; RPET 1984, 87, 89; MP PET 1984; Roorkee 1969; AMU 1979] |
| A. | \[{{x}^{2}}+{{y}^{2}}+8x+2y+51=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+8x-2y-51=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+8x+2y-51=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-8x-2y-51=0\] |
| Answer» E. | |
| 5325. |
If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is [MNR 1975] |
| A. | \[(a,\ b)\] |
| B. | \[(b,\ a)\] |
| C. | \[\left( \frac{a}{2},\ \frac{b}{2} \right)\] |
| D. | \[\left( \frac{b}{2},\ -\frac{a}{2} \right)\] |
| Answer» D. \[\left( \frac{b}{2},\ -\frac{a}{2} \right)\] | |
| 5326. |
A circle has radius 3 units and its centre lies on the line \[y=x-1\]. Then the equation of this circle if it passes through point (7,3), is [Roorkee 1988] |
| A. | \[{{x}^{2}}+{{y}^{2}}-8x-6y+16=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+8x+6y+16=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-8x-6y-16=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+8x+6y+16=0\] | |
| 5327. |
If the equation \[\frac{K{{(x+1)}^{2}}}{3}+\frac{{{(y+2)}^{2}}}{4}=1\] represents a circle, then \[K=\] [MP PET 1994] |
| A. | 3/4 |
| B. | 1 |
| C. | 4/3 |
| D. | 12 |
| Answer» B. 1 | |
| 5328. |
The area of a circle whose centre is (h, k) and radius a is [MP PET 1994] |
| A. | \[\pi ({{h}^{2}}+{{k}^{2}}-{{a}^{2}})\] |
| B. | \[\pi {{a}^{2}}hk\] |
| C. | \[\pi {{a}^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5329. |
The locus of the centre of a circle which touches externally the circle \[{{x}^{2}}+{{y}^{2}}-6x-6y+14=0\] and also touches the y-axis, is given by the equation [IIT 1993; DCE 2000] |
| A. | \[{{x}^{2}}-6x-10y+14=0\] |
| B. | \[{{x}^{2}}-10x-6y+14=0\] |
| C. | \[{{y}^{2}}-6x-10y+14=0\] |
| D. | \[{{y}^{2}}-10x-6y+14=0\] |
| Answer» E. | |
| 5330. |
The equation of a circle passing through the point (4, 5) and having the centre at (2, 2) is [UPSEAT 2000] |
| A. | \[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-4x=13\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\] |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-4x=13\] | |
| 5331. |
The equation to a circle whose centre lies at the point (-2, 1) and which touches the line \[3x-2y-6=0\] at (4, 3), is |
| A. | \[{{x}^{2}}+{{y}^{2}}+4x-2y-35=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-4x+2y+35=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+4x+2y+35=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}-4x+2y+35=0\] | |
| 5332. |
Locus of the points from which perpendicular tangent can be drawn to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], is |
| A. | A circle passing through origin |
| B. | A circle of radius 2a |
| C. | A concentric circle of radius \[a\sqrt{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5333. |
The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant, is a circle whose centre is at the |
| A. | Incentre of the triangle |
| B. | Centroid of the triangle |
| C. | Orthocentre of the triangle |
| D. | None of these |
| Answer» C. Orthocentre of the triangle | |
| 5334. |
If the lines \[{{l}_{1}}x+{{m}_{1}}y+{{n}_{1}}=0\] and \[{{l}_{2}}x+{{m}_{2}}y+{{n}_{2}}=0\] cuts the axes at con-cyclic points, then |
| A. | \[{{l}_{1}}{{l}_{2}}={{m}_{1}}{{m}_{2}}\] |
| B. | \[{{l}_{1}}{{m}_{1}}={{l}_{2}}{{m}_{2}}\] |
| C. | \[{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}=0\] |
| D. | \[{{l}_{1}}{{m}_{2}}={{l}_{2}}{{m}_{1}}\] |
| Answer» B. \[{{l}_{1}}{{m}_{1}}={{l}_{2}}{{m}_{2}}\] | |
| 5335. |
The centres of the circles \[{{x}^{2}}+{{y}^{2}}=1\], \[{{x}^{2}}+{{y}^{2}}+6x-2y=1\] and \[{{x}^{2}}+{{y}^{2}}-12x+4y=1\] are [MP PET 1986] |
| A. | Same |
| B. | Collinear |
| C. | Non-collinear |
| D. | None of these |
| Answer» C. Non-collinear | |
| 5336. |
Radius of the circle \[{{x}^{2}}+{{y}^{2}}+2x\cos \theta \] \[+2y\sin \theta -8=0\], is [MNR 1974] |
| A. | 1 |
| B. | 3 |
| C. | \[2\sqrt{3}\] |
| D. | \[\sqrt{10}\] |
| Answer» C. \[2\sqrt{3}\] | |
| 5337. |
Locus of the centre of the circle touching both the co-ordinates axes is |
| A. | \[{{x}^{2}}+{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}=\]a non-zero constant |
| C. | \[{{x}^{2}}-{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}-{{y}^{2}}=\]a non-zero constant |
| Answer» D. \[{{x}^{2}}-{{y}^{2}}=\]a non-zero constant | |
| 5338. |
The equation of the circle concentric with the circle \[{{x}^{2}}+{{y}^{2}}-4x-6y-3=0\] and touching y-axis, is |
| A. | \[{{x}^{2}}+{{y}^{2}}-4x-6y-9=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-4x-6y+9=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-4x-6y+3=0\] | |
| 5339. |
The equation \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] represents [Roorkee 1990] |
| A. | Circle |
| B. | Pair of coincident straight lines |
| C. | Pair of concurrent straight lines |
| D. | Point |
| Answer» E. | |
| 5340. |
The equation of the circumcircle of the triangle formed by the lines \[y+\sqrt{3}x=6,\ y-\sqrt{3}x=6,\] and \[y=0\], is [EAMCET 1982] |
| A. | \[{{x}^{2}}+{{y}^{2}}-4y=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+4x=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-4y=12\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+4x=12\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}+4x=12\] | |
| 5341. |
The radius of a circle which touches y-axis at (0,3) and cuts intercept of 8 units with x-axis, is [IIT 1972] |
| A. | 3 |
| B. | 2 |
| C. | 5 |
| D. | 8 |
| Answer» D. 8 | |
| 5342. |
A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number\[(\ne 1)\]. Then its locus is [IIT 1982] |
| A. | Straight line |
| B. | Circle |
| C. | Parabola |
| D. | A pair of straight lines |
| Answer» C. Parabola | |
| 5343. |
The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is [MNR 1982; IIT 1980; Karnataka CET 1999; MP PET 2002; DCE 2000; Pb. CET 2002] |
| A. | \[5\pi \] |
| B. | \[10\pi \] |
| C. | \[25\pi \] |
| D. | None of these |
| Answer» D. None of these | |
| 5344. |
If the equation \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] represents a circle with x-axis as a diameter and radius a, then |
| A. | \[f=2a,\ g=0,\ c=3{{a}^{2}}\] |
| B. | \[f=0,\ g=a,\ c=3{{a}^{2}}\] |
| C. | \[f=0,\ g=-2a,\ c=3{{a}^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5345. |
A circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] passing through \[(4,\ -2)\] is concentric to the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+20=0\], then the value of c will be [RPET 1984, 86] |
| A. | ? 4 |
| B. | 4 |
| C. | 0 |
| D. | 1 |
| Answer» B. 4 | |
| 5346. |
A circle which passes through origin and cuts intercepts on axes a and b, the equation of circle is [RPET 1991] |
| A. | \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-ax+by=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+ax-by=0\] |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] | |
| 5347. |
If the centre of a circle is (2, 3) and a tangent is \[x+y=1\], then the equation of this circle is [RPET 1985, 89] |
| A. | \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=8\] |
| B. | \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=3\] |
| C. | \[{{(x+2)}^{2}}+{{(y+3)}^{2}}=2\sqrt{2}\] |
| D. | \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=2\sqrt{2}\] |
| Answer» B. \[{{(x-2)}^{2}}+{{(y-3)}^{2}}=3\] | |
| 5348. |
A circle touches the axes at the points (3, 0) and (0, -3). The centre of the circle is [MP PET 1992] |
| A. | (3, -3) |
| B. | (0, 0) |
| C. | (-3, 0) |
| D. | (6, -6) |
| Answer» B. (0, 0) | |
| 5349. |
\[a{{x}^{2}}+2{{y}^{2}}+2bxy+2x-y+c=0\] represents a circle through the origin, if [MP PET 1984] |
| A. | \[a=0,\ b=0,\ c=2\] |
| B. | \[a=1,\ b=0,\ c=0\] |
| C. | \[a=2,\ b=2,\ c=0\] |
| D. | \[a=2,\ b=0,\ c=0\] |
| Answer» E. | |
| 5350. |
The equation \[{{x}^{2}}+{{y}^{2}}=0\] denotes [MP PET 1984] |
| A. | A point |
| B. | A circle |
| C. | x-axis |
| D. | y-axis |
| Answer» B. A circle | |