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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.
| 5551. |
The distance between the foci of an ellipse is 16 and eccentricity is \[\frac{1}{2}\]. Length of the major axis of the ellipse is [Karnataka CET 2001] |
| A. | 8 |
| B. | 64 |
| C. | 16 |
| D. | 32 |
| Answer» E. | |
| 5552. |
What is the equation of the ellipse with foci \[(\pm 2,\ 0)\] and eccentricity \[=\frac{1}{2}\] [DCE 1999] |
| A. | \[3{{x}^{2}}+4{{y}^{2}}=48\] |
| B. | \[4{{x}^{2}}+3{{y}^{2}}=48\] |
| C. | \[3{{x}^{2}}+4{{y}^{2}}=0\] |
| D. | \[4{{x}^{2}}+3{{y}^{2}}=0\] |
| Answer» B. \[4{{x}^{2}}+3{{y}^{2}}=48\] | |
| 5553. |
The eccentricity of the ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\], is [MP PET 2000] |
| A. | \[\frac{1}{2\sqrt{3}}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{\sqrt{5}}{3}\] |
| D. | \[\frac{\sqrt{5}}{6}\] |
| Answer» D. \[\frac{\sqrt{5}}{6}\] | |
| 5554. |
The eccentricity of the ellipse \[25{{x}^{2}}+16{{y}^{2}}=400\] is [MP PET 2001] |
| A. | 3/5 |
| B. | 1/3 |
| C. | 2/5 |
| D. | 1/5 |
| Answer» B. 1/3 | |
| 5555. |
If \[P\equiv (x,\ y)\], \[{{F}_{1}}\equiv (3,\ 0)\], \[{{F}_{2}}\equiv (-3,\ 0)\] and \[16{{x}^{2}}+25{{y}^{2}}=400\], then \[P{{F}_{1}}+P{{F}_{2}}\] equals [IIT 1998] |
| A. | 8 |
| B. | 6 |
| C. | 10 |
| D. | 12 |
| Answer» D. 12 | |
| 5556. |
If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is |
| A. | 39/4 |
| B. | 12 |
| C. | 15 |
| D. | 37/2 |
| Answer» B. 12 | |
| 5557. |
The locus of a variable point whose distance from (?2, 0) is \[\frac{2}{3}\] times its distance from the line \[x=-\frac{9}{2}\], is [IIT 1994] |
| A. | Ellipse |
| B. | Parabola |
| C. | Hyperbola |
| D. | None of these |
| Answer» B. Parabola | |
| 5558. |
The length of the latus rectum of the ellipse \[9{{x}^{2}}+4{{y}^{2}}=1\], is [MP PET 1999] |
| A. | \[\frac{3}{2}\] |
| B. | \[\frac{8}{3}\] |
| C. | \[\frac{4}{9}\] |
| D. | \[\frac{8}{9}\] |
| Answer» D. \[\frac{8}{9}\] | |
| 5559. |
Eccentricity of the ellipse \[9{{x}^{2}}+25{{y}^{2}}=225\] is [Kerala (Engg.) 2002] |
| A. | \[\frac{3}{5}\] |
| B. | \[\frac{4}{5}\] |
| C. | \[\frac{9}{25}\] |
| D. | \[\frac{\sqrt{34}}{5}\] |
| Answer» C. \[\frac{9}{25}\] | |
| 5560. |
The foci of \[16{{x}^{2}}+25{{y}^{2}}=400\] are [BIT Ranchi 1996] |
| A. | \[(\pm 3,\ 0)\] |
| B. | \[(0,\ \pm 3)\] |
| C. | \[(3,\ -3)\] |
| D. | \[(-3,\ 3)\] |
| Answer» B. \[(0,\ \pm 3)\] | |
| 5561. |
The equation of the ellipse whose one focus is at (4, 0) and whose eccentricity is 4/5, is [Karnataka CET 1993] |
| A. | \[\frac{{{x}^{2}}}{{{3}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\] |
| B. | \[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{3}^{2}}}=1\] |
| C. | \[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{4}^{2}}}=1\] |
| D. | \[\frac{{{x}^{2}}}{{{4}^{2}}}+\frac{{{y}^{2}}}{{{5}^{2}}}=1\] |
| Answer» C. \[\frac{{{x}^{2}}}{{{5}^{2}}}+\frac{{{y}^{2}}}{{{4}^{2}}}=1\] | |
| 5562. |
The length of the latus rectum of the ellipse \[\frac{{{x}^{2}}}{36}+\frac{{{y}^{2}}}{49}=1\] [Karnataka CET 1993] |
| A. | 98/6 |
| B. | 72/7 |
| C. | 72/14 |
| D. | 98/12 |
| Answer» C. 72/14 | |
| 5563. |
The locus of the point of intersection of perpendicular tangents to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is [MP PET 1995] |
| A. | \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] |
| B. | \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}-{{b}^{2}}\] |
| C. | \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| D. | \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] |
| Answer» D. \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}+{{b}^{2}}\] | |
| 5564. |
The equation \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0\] represents an ellipse, if [MP PET 1995] |
| A. | \[r>2\] |
| B. | \[2<r<5\] |
| C. | \[r>5\] |
| D. | None of these |
| Answer» C. \[r>5\] | |
| 5565. |
The length of the latus rectum of an ellipse is \[\frac{1}{3}\] of the major axis. Its eccentricity is [EAMCET 1991] |
| A. | \[\frac{2}{3}\] |
| B. | \[\sqrt{\frac{2}{3}}\] |
| C. | \[\frac{5\times 4\times 3}{{{7}^{3}}}\] |
| D. | \[{{\left( \frac{3}{4} \right)}^{4}}\] |
| Answer» C. \[\frac{5\times 4\times 3}{{{7}^{3}}}\] | |
| 5566. |
The equation of the ellipse whose centre is at origin and which passes through the points (?3, 1) and (2, ?2) is |
| A. | \[5{{x}^{2}}+3{{y}^{2}}=32\] |
| B. | \[3{{x}^{2}}+5{{y}^{2}}=32\] |
| C. | \[5{{x}^{2}}-3{{y}^{2}}=32\] |
| D. | \[3{{x}^{2}}+5{{y}^{2}}+32=0\] |
| Answer» C. \[5{{x}^{2}}-3{{y}^{2}}=32\] | |
| 5567. |
If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is [EAMCET 1990] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{2\sqrt{2}}{3}\] |
| Answer» E. | |
| 5568. |
For the ellipse \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{28}=1\], the eccentricity is [MNR 1974] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{4}{3}\] |
| C. | \[\frac{1}{\sqrt{7}}\] |
| D. | \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] |
| Answer» B. \[\frac{4}{3}\] | |
| 5569. |
For the ellipse \[3{{x}^{2}}+4{{y}^{2}}=12\], the length of latus rectum is [MNR 1973] |
| A. | \[\frac{3}{2}\] |
| B. | 3 |
| C. | \[\frac{8}{3}\] |
| D. | \[\sqrt{\frac{3}{2}}\] |
| Answer» C. \[\frac{8}{3}\] | |
| 5570. |
Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is |
| A. | \[\frac{\sqrt{5}+1}{2}\] |
| B. | \[9{{x}^{2}}+5{{y}^{2}}-30y=0\] |
| C. | \[\frac{\sqrt{5}}{2}\] |
| D. | \[\frac{\sqrt{3}}{2}\] |
| Answer» C. \[\frac{\sqrt{5}}{2}\] | |
| 5571. |
The equation of the ellipse whose one of the vertices is (0,7) and the corresponding directrix is \[y=12\], is |
| A. | \[95{{x}^{2}}+144{{y}^{2}}=4655\] |
| B. | \[144{{x}^{2}}+95{{y}^{2}}=4655\] |
| C. | \[95{{x}^{2}}+144{{y}^{2}}=13680\] |
| D. | None of these |
| Answer» C. \[95{{x}^{2}}+144{{y}^{2}}=13680\] | |
| 5572. |
hThe equation of the ellipse whose latus rectum is 8 and whose eccentricity is \[\frac{1}{\sqrt{2}}\], referred to the principal axes of coordinates, is [MP PET 1993] |
| A. | \[\frac{{{x}^{2}}}{18}+\frac{{{y}^{2}}}{32}=1\] |
| B. | \[\frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{9}=1\] |
| C. | \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{32}=1\] |
| D. | \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{24}=1\] |
| Answer» D. \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{24}=1\] | |
| 5573. |
The equation \[2{{x}^{2}}+3{{y}^{2}}=30\] represents [MP PET 1988] |
| A. | A circle |
| B. | An ellipse |
| C. | A hyperbola |
| D. | A parabola |
| Answer» C. A hyperbola | |
| 5574. |
If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5 then its equation is [AMU 1981] |
| A. | \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\] |
| B. | \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] |
| C. | \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{25}=1\] |
| D. | None of these |
| Answer» B. \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] | |
| 5575. |
If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is |
| A. | 1/2 |
| B. | 2/3 |
| C. | \[1/\sqrt{3}\] |
| D. | 4/5 |
| Answer» D. 4/5 | |
| 5576. |
The lengths of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along the y-axis. The equation of the ellipse referred to its centre as origin is [Pb. CET 2003] |
| A. | \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] |
| B. | \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\] |
| C. | \[\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{64}=1\] |
| D. | \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{100}=1\] |
| Answer» C. \[\frac{{{x}^{2}}}{100}+\frac{{{y}^{2}}}{64}=1\] | |
| 5577. |
An ellipse passes through the point (?3, 1) and its eccentricity is \[\sqrt{\frac{2}{5}}\]. The equation of the ellipse is |
| A. | \[3{{x}^{2}}+5{{y}^{2}}=32\] |
| B. | \[3{{x}^{2}}+5{{y}^{2}}=25\] |
| C. | \[3{{x}^{2}}+{{y}^{2}}=4\] |
| D. | \[3{{x}^{2}}+{{y}^{2}}=9\] |
| Answer» B. \[3{{x}^{2}}+5{{y}^{2}}=25\] | |
| 5578. |
If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is |
| A. | 1/2 |
| B. | \[1/\sqrt{2}\] |
| C. | 1/3 |
| D. | \[1/\sqrt{3}\] |
| Answer» C. 1/3 | |
| 5579. |
If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is |
| A. | 3 |
| B. | \[4\sqrt{2}\] |
| C. | 6 |
| D. | None of these |
| Answer» E. | |
| 5580. |
The length of the latus rectum of the ellipse \[5{{x}^{2}}+9{{y}^{2}}=45\] is [MNR 1978, 80, 81] |
| A. | \[\sqrt{5}/4\] |
| B. | \[\sqrt{5}/2\] |
| C. | 5/3 |
| D. | 10/3 |
| Answer» E. | |
| 5581. |
If the eccentricity of an ellipse be \[1/\sqrt{2}\], then its latus rectum is equal to its |
| A. | Minor axis |
| B. | Semi-minor axis |
| C. | Major axis |
| D. | Semi-major axis |
| Answer» E. | |
| 5582. |
The equation of the ellipse whose vertices are \[(\pm 5,\ 0)\] and foci are \[(\pm 4,\ 0)\] is |
| A. | \[9{{x}^{2}}+25{{y}^{2}}=225\] |
| B. | \[25{{x}^{2}}+9{{y}^{2}}=225\] |
| C. | \[3{{x}^{2}}+4{{y}^{2}}=192\] |
| D. | None of these |
| Answer» B. \[25{{x}^{2}}+9{{y}^{2}}=225\] | |
| 5583. |
A point ratio of whose distance from a fixed point and line \[x=9/2\] is always 2 : 3. Then locus of the point will be [DCE 2005] |
| A. | Hyperbola |
| B. | Ellipse |
| C. | Parabola |
| D. | Circle |
| Answer» C. Parabola | |
| 5584. |
The point (4, ?3) with respect to the ellipse \[4{{x}^{2}}+5{{y}^{2}}=1\] [Orissa JEE 2005] |
| A. | Lies on the curve |
| B. | Is inside the curve |
| C. | Is outside the curve |
| D. | Is focus of the curve |
| Answer» D. Is focus of the curve | |
| 5585. |
Minimum area of the triangle by any tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] with the coordinate axes is [IIT Screening 2005] |
| A. | \[\frac{{{a}^{2}}+{{b}^{2}}}{2}\] |
| B. | \[\frac{{{(a+b)}^{2}}}{2}\] |
| C. | ab |
| D. | \[\frac{{{(a-b)}^{2}}}{2}\] |
| Answer» D. \[\frac{{{(a-b)}^{2}}}{2}\] | |
| 5586. |
The eccentricity of the ellipse \[25{{x}^{2}}+16{{y}^{2}}-150x-175=0\] is [Kerala (Engg.) 2005] |
| A. | 2/5 |
| B. | 2/3 |
| C. | 4/5 |
| D. | 3/4 |
| E. | 3/5 |
| Answer» F. | |
| 5587. |
The sum of the focal distances of any point on the conic \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] is [Karnataka CET 2005] |
| A. | 10 |
| B. | 9 |
| C. | 41 |
| D. | 18 |
| Answer» B. 9 | |
| 5588. |
If the foci of an ellipse are \[(\pm \sqrt{5},\,0)\] and its eccentricity is \[\frac{\sqrt{5}}{3}\], then the equation of the ellipse is [J & K 2005] |
| A. | \[9{{x}^{2}}+4{{y}^{2}}=36\] |
| B. | \[4{{x}^{2}}+9{{y}^{2}}=36\] |
| C. | \[36{{x}^{2}}+9{{y}^{2}}=4\] |
| D. | \[9{{x}^{2}}+36{{y}^{2}}=4\] |
| Answer» C. \[36{{x}^{2}}+9{{y}^{2}}=4\] | |
| 5589. |
An ellipse has OB as semi minor axis, F and F¢ its foci and the angle FBF¢ is a right angle. Then the eccentricity of the ellipse is [AIEEE 2005] |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 5590. |
The pole of the straight line \[x+4y=4\] with respect to ellipse \[{{x}^{2}}+4{{y}^{2}}=4\] is [EAMCET 2002] |
| A. | (1, 4) |
| B. | (1, 1) |
| C. | (4, 1) |
| D. | (4, 4) |
| Answer» C. (4, 1) | |
| 5591. |
The distance between the foci of the ellipse \[3{{x}^{2}}+4{{y}^{2}}=48\] is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 5592. |
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is [MP PET 1991, 97; Karnataka CET 2000] |
| A. | 3/2 |
| B. | \[\sqrt{3}/2\] |
| C. | 2/3 |
| D. | \[\sqrt{2}/3\] |
| Answer» C. 2/3 | |
| 5593. |
The perpendicular distance of the straight line \[12x+5y=7\] from the origin is given by [MP PET 1993] |
| A. | \[\frac{7}{13}\] |
| B. | \[\frac{12}{13}\] |
| C. | \[\frac{5}{13}\] |
| D. | \[\frac{1}{13}\] |
| Answer» B. \[\frac{12}{13}\] | |
| 5594. |
If p and \[p'\]be the distances of origin from the lines \[x\sec \alpha +y\text{cosec }\alpha =k\] and \[x\cos \alpha -y\sin \alpha =k\cos 2\alpha \], then \[4{{p}^{2}}+{{{p}'}^{2}}\]= |
| A. | k |
| B. | \[2k\] |
| C. | \[{{k}^{2}}\] |
| D. | \[2{{k}^{2}}\] |
| Answer» D. \[2{{k}^{2}}\] | |
| 5595. |
If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then [Karnataka CET 2003] |
| A. | \[{{a}^{2}}+{{b}^{2}}={{p}^{2}}\] |
| B. | \[{{a}^{2}}+{{b}^{2}}=\frac{1}{{{p}^{2}}}\] |
| C. | \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{{{p}^{2}}}\] |
| D. | \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}\] |
| Answer» E. | |
| 5596. |
The point on the line \[x+y=4\]which lie at a unit distance from the line \[4x+3y=10\], are [IIT 1976] |
| A. | \[(3,\,1),(-7,\,11)\] |
| B. | \[(3,\,1),(7,\,11)\] |
| C. | \[(-3,\,1),(-7,\,11)\] |
| D. | \[(1,\,3),(-7,\,11)\] |
| Answer» B. \[(3,\,1),(7,\,11)\] | |
| 5597. |
The distance of the point of intersection of the lines \[2x-3y+5=0\] and \[3x+4y=0\]from the line \[5x-2y=0\] is |
| A. | \[\frac{130}{17\sqrt{29}}\] |
| B. | \[\frac{13}{7\sqrt{29}}\] |
| C. | \[\frac{130}{17}\] |
| D. | None of these |
| Answer» B. \[\frac{13}{7\sqrt{29}}\] | |
| 5598. |
The position of the points (3, 4) and (2, ?6) with respect to the line \[3x-4y=8\] are [Roorkee 1972; MP PET 1984] |
| A. | On the same side of the line |
| B. | On different side of the line |
| C. | One point on the line and the other outside the line |
| D. | Both point on the line |
| Answer» C. One point on the line and the other outside the line | |
| 5599. |
Let \[\alpha \] be the distance between the lines \[-x+y=2\] and \[x-y=2\], and \[\beta \] be the distance between the lines \[4x-3y=5\] and \[6y-8x=1\], then [J & K 2005] |
| A. | \[20\sqrt{2}\beta =11\alpha \] |
| B. | \[20\sqrt{2}\alpha =11\beta \] |
| C. | \[11\sqrt{2}\beta =20\alpha \] |
| D. | None of these |
| Answer» B. \[20\sqrt{2}\alpha =11\beta \] | |
| 5600. |
Choose the correct statement which describe the position of the point (?6, 2) relative to straight lines \[2x+3y-4=0\] and \[6x+9y+8=0\] [MP PET 1983] |
| A. | Below both the lines |
| B. | Above both the lines |
| C. | In between the lines |
| D. | None of these |
| Answer» B. Above both the lines | |