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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.
| 2451. |
The equation of the parabola whose vertex is (?1, ?2), axis is vertical and which passes through the point (3, 6), is |
| A. | \[{{x}^{2}}+2x-2y-3=0\] |
| B. | \[2{{x}^{2}}=3y\] |
| C. | \[{{x}^{2}}-2x-y+3=0\] |
| D. | None of these |
| Answer» B. \[2{{x}^{2}}=3y\] | |
| 2452. |
If the vertex of a parabola be at origin and directrix be \[x+5=0\], then its latus rectum is [RPET 1991] |
| A. | 5 |
| B. | 10 |
| C. | 20 |
| D. | 40 |
| Answer» D. 40 | |
| 2453. |
The equation of the parabola whose axis is vertical and passes through the points (0, 0), (3, 0) and (?1, 4) is |
| A. | \[{{x}^{2}}-3x-y=0\] |
| B. | \[{{x}^{2}}+3x+y=0\] |
| C. | \[{{x}^{2}}-4x+2y=0\] |
| D. | \[{{x}^{2}}-4x-2y=0\] |
| Answer» B. \[{{x}^{2}}+3x+y=0\] | |
| 2454. |
The equation of the latus rectum of the parabola \[{{x}^{2}}+4x+2y=0\] is [Pb. CET 2004] |
| A. | \[2y+3=0\] |
| B. | \[3y=2\] |
| C. | \[2y=3\] |
| D. | \[3y+2=0\] |
| Answer» D. \[3y+2=0\] | |
| 2455. |
\[x-2={{t}^{2}},\ y=2t\] are the parametric equations of the parabola |
| A. | \[{{y}^{2}}=4x\] |
| B. | \[{{y}^{2}}=-4x\] |
| C. | \[{{x}^{2}}=-4y\] |
| D. | \[{{y}^{2}}=4(x-2)\] |
| Answer» E. | |
| 2456. |
The equation \[{{x}^{2}}-2xy+{{y}^{2}}+3x+2=0\] represents [UPSEAT 2001] |
| A. | A parabola |
| B. | An ellipse |
| C. | A hyperbola |
| D. | A circle |
| Answer» B. An ellipse | |
| 2457. |
Vertex of the parabola \[{{y}^{2}}+2y+x=0\] lies in the quadrant [MP PET 1989] |
| A. | First |
| B. | Second |
| C. | Third |
| D. | Fourth |
| Answer» E. | |
| 2458. |
The equation of latus rectum of a parabola is \[x+y=8\] and the equation of the tangent at the vertex is \[x+y=12\], then length of the latus rectum is [MP PET 2002] |
| A. | \[4\sqrt{2}\] |
| B. | \[2\sqrt{2}\] |
| C. | 8 |
| D. | \[8\sqrt{2}\] |
| Answer» E. | |
| 2459. |
The point on the parabola \[{{y}^{2}}=18x\], for which the ordinate is three times the abscissa, is [MP PET 2003] |
| A. | (6, 2) |
| B. | (?2, ?6) |
| C. | (3, 18) |
| D. | (2, 6) |
| Answer» E. | |
| 2460. |
The parabola \[{{y}^{2}}=x\] is symmetric about [Kerala (Engg.) 2002] |
| A. | x-axis |
| B. | y-axis |
| C. | Both x-axis and y-axis |
| D. | The line \[y=x\] |
| Answer» B. y-axis | |
| 2461. |
PQ is a double ordinate of the parabola\[{{y}^{2}}=4ax\]. The locus of the points of trisection of PQ is |
| A. | \[9{{y}^{2}}=4ax\] |
| B. | \[9{{x}^{2}}=4ay\] |
| C. | \[9{{y}^{2}}+4ax=0\] |
| D. | \[9{{x}^{2}}+4ay=0\] |
| Answer» B. \[9{{x}^{2}}=4ay\] | |
| 2462. |
Focus and directrix of the parabola \[{{x}^{2}}=-8ay\] are [RPET 2001] |
| A. | \[(0,\ -2a)\ \text{and}\ y=2a\] |
| B. | \[(0,\ 2a)\ \text{and}\ y=-2a\] |
| C. | \[(2a,\ 0)\ \text{and}\ x=-2a\] |
| D. | \[(-2a,\ 0)\ \text{and}\ x=2a\] |
| Answer» B. \[(0,\ 2a)\ \text{and}\ y=-2a\] | |
| 2463. |
The normal meet the parabola \[{{y}^{2}}=4ax\] at that point where the abissiae of the point is equal to the ordinate of the point is [DCE 2005] |
| A. | \[(6a,\ -9a)\] |
| B. | \[(-9a,\ 6a)\] |
| C. | \[(-6a,\ 9a)\] |
| D. | \[(9a,\ -6a)\] |
| Answer» E. | |
| 2464. |
The number of parabolas that can be drawn if two ends of the latus rectum are given [DCE 2005] |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 2465. |
The equation of a straight line drawn through the focus of the parabola \[{{y}^{2}}=-4x\] at an angle of 120° to the x-axis is [Orissa JEE 2005] |
| A. | \[y+\sqrt{3}(x-1)=0\] |
| B. | \[y-\sqrt{3}(x-1)=0\] |
| C. | \[y+\sqrt{3}(x+1)=0\] |
| D. | \[y-\sqrt{3}(x+1)=0\] |
| Answer» D. \[y-\sqrt{3}(x+1)=0\] | |
| 2466. |
Let a circle tangent to the directrix of a parabola \[{{y}^{2}}=2ax\] has its centre coinciding with the focus of the parabola. Then the point of intersection of the parabola and circle is [Orissa JEE 2005] |
| A. | (a, ?a) |
| B. | \[(a/2,\ a/2)\] |
| C. | \[(a/2,\ \pm a)\] |
| D. | \[(\pm a,\ a/2)\] |
| Answer» D. \[(\pm a,\ a/2)\] | |
| 2467. |
If the line \[y=2x+k\] is a tangent to the curve \[{{x}^{2}}=4y\], then k is equal to [AMU 2002] |
| A. | 4 |
| B. | 1/2 |
| C. | ?4 |
| D. | ?1/2 |
| Answer» D. ?1/2 | |
| 2468. |
The equation to a parabola which passes through the intersection of a straight line \[x+y=0\] and the circle \[{{x}^{2}}+{{y}^{2}}+4y=0\] is [Orissa JEE 2005] |
| A. | \[{{y}^{2}}=4x\] |
| B. | \[{{y}^{2}}=x\] |
| C. | \[{{y}^{2}}=2x\] |
| D. | None of these |
| Answer» D. None of these | |
| 2469. |
The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6, ?3) is [MP PET 2001] |
| A. | \[{{y}^{2}}=12x+6\] |
| B. | \[{{x}^{2}}=12y\] |
| C. | \[{{x}^{2}}=-12y\] |
| D. | \[{{y}^{2}}=-12x+6\] |
| Answer» D. \[{{y}^{2}}=-12x+6\] | |
| 2470. |
The angle of intersection between the curves \[{{x}^{2}}=8y\] and \[{{y}^{2}}=8x\] at origin is [RPET 1997] |
| A. | p/4 |
| B. | p/3 |
| C. | p/6 |
| D. | p/2 |
| Answer» E. | |
| 2471. |
Tangent to the parabola \[y={{x}^{2}}+6\] at (1, 7) touches the circle \[{{x}^{2}}+{{y}^{2}}+16x+12y+c=0\] at the point [IIT Screening 2005] |
| A. | (?6, ?9) |
| B. | (?13, ?9) |
| C. | (?6, ?7) |
| D. | (13, 7) |
| Answer» D. (13, 7) | |
| 2472. |
From the point (?1, ?60) two tangents are drawn to the parabola \[{{y}^{2}}=4x\]. Then the angle between the two tangents is [J & K 2005] |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» E. | |
| 2473. |
The ends of the latus rectum of the conic \[{{x}^{2}}+10x-16y+25=0\] are [Karnataka CET 2005] |
| A. | (3, ?4), (13, 4) |
| B. | (?3, ?4), (13, ?4) |
| C. | (3, 4), (?13, 4) |
| D. | (5, ?8), (?5, 8) |
| Answer» D. (5, ?8), (?5, 8) | |
| 2474. |
The point on parabola \[2y={{x}^{2}}\], which is nearest to the point (0, 3) is [J & K 2005] |
| A. | (±4, 8) |
| B. | \[(\pm 1,\,1/2)\] |
| C. | (±2, 2) |
| D. | None of these |
| Answer» D. None of these | |
| 2475. |
For the above problem, the area of triangle formed by chord of contact and the tangents is given by [Roorkee 1994] |
| A. | 8 |
| B. | \[8\sqrt{3}\] |
| C. | \[8\sqrt{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2476. |
From the point (?1, 2) tangent lines are drawn to the parabola \[{{y}^{2}}=4x\], then the equation of chord of contact is [Roorkee 1994] |
| A. | \[y=x+1\] |
| B. | \[y=x-1\] |
| C. | \[y+x=1\] |
| D. | None of these |
| Answer» C. \[y+x=1\] | |
| 2477. |
An equilateral triangle is inscribed in the parabola \[{{y}^{2}}=4ax\] whose vertices are at the parabola, then the length of its side is equal to |
| A. | 8a |
| B. | \[8a\sqrt{3}\] |
| C. | \[a\sqrt{2}\] |
| D. | None of these |
| Answer» C. \[a\sqrt{2}\] | |
| 2478. |
The ordinates of the triangle inscribed in parabola \[{{y}^{2}}=4ax\] are \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\], then the area of triangle is |
| A. | \[\frac{1}{8a}({{y}_{1}}+{{y}_{2}})({{y}_{2}}+{{y}_{3}})({{y}_{3}}+{{y}_{1}})\] |
| B. | \[\frac{1}{4a}({{y}_{1}}+{{y}_{2}})({{y}_{2}}+{{y}_{3}})({{y}_{3}}+{{y}_{1}})\] |
| C. | \[\frac{1}{8a}({{y}_{1}}-{{y}_{2}})({{y}_{2}}-{{y}_{3}})({{y}_{3}}-{{y}_{1}})\] |
| D. | \[\frac{1}{4a}({{y}_{1}}-{{y}_{2}})({{y}_{2}}-{{y}_{3}})({{y}_{3}}-{{y}_{1}})\] |
| Answer» C. \[\frac{1}{8a}({{y}_{1}}-{{y}_{2}})({{y}_{2}}-{{y}_{3}})({{y}_{3}}-{{y}_{1}})\] | |
| 2479. |
The end points of latus rectum of the parabola \[{{x}^{2}}=4ay\] are [RPET 1997] |
| A. | \[(a,\ 2a),\ (2a,\ -a)\] |
| B. | \[(-a,\ 2a),\ (2a,\ a)\] |
| C. | \[(a,\ -2a),\ (2a,\ a)\] |
| D. | \[(-2a,\ a),\ (2a,\ a)\] |
| Answer» E. | |
| 2480. |
The area of the triangle formed by the lines joining the vertex of the parabola \[{{x}^{2}}=12y\] to the ends of its latus rectum is |
| A. | 12 sq. unit |
| B. | 16 sq. unit |
| C. | 18 sq. unit |
| D. | 24 sq. unit |
| Answer» D. 24 sq. unit | |
| 2481. |
Equation of diameter of parabola \[{{y}^{2}}=x\] corresponding to the chord \[x-y+1=0\] is [RPET 2003] |
| A. | \[2y=3\] |
| B. | \[2y=1\] |
| C. | \[2y=5\] |
| D. | \[y=1\] |
| Answer» C. \[2y=5\] | |
| 2482. |
The polar of focus of parabola [RPET 1999] |
| A. | x-axis |
| B. | y-axis |
| C. | Directrix |
| D. | Latus rectum |
| Answer» D. Latus rectum | |
| 2483. |
The normal to the parabola \[{{y}^{2}}=8x\] at the point (2, 4) meets the parabola again at the point [Orissa JEE 2003] |
| A. | {?18, ?12} |
| B. | {?18, 12} |
| C. | {18, 12} |
| D. | (18, ?12) |
| Answer» E. | |
| 2484. |
The focal chord to \[{{y}^{2}}=16x\] is tangent to \[{{(x-6)}^{2}}+{{y}^{2}}=2\], then the possible value of the slope of this chord, are [IIT Screening 2003] |
| A. | \[\{-1,\ 1\}\] |
| B. | {?2, 2} |
| C. | {-2, 1/2} |
| D. | {2, ?1/2} |
| Answer» B. {?2, 2} | |
| 2485. |
The normal at the point \[(bt_{1}^{2},\ 2b{{t}_{1}})\] on a parabola meets the parabola again in the point \[(bt_{2}^{2},\ 2b{{t}_{2}})\], then [MNR 1986; RPET 2003; AIEEE 2003] |
| A. | \[{{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}\] |
| B. | \[{{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}\] |
| C. | \[{{t}_{2}}={{t}_{1}}-\frac{2}{{{t}_{1}}}\] |
| D. | \[{{t}_{2}}={{t}_{1}}+\frac{2}{{{t}_{1}}}\] |
| Answer» B. \[{{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}\] | |
| 2486. |
If \[x+y=k\] is a normal to the parabola \[{{y}^{2}}=12x\], then k is [IIT Screening 2000] |
| A. | 3 |
| B. | 9 |
| C. | ?9 |
| D. | ?3 |
| Answer» C. ?9 | |
| 2487. |
If the normal to\[{{y}^{2}}=12x\] at (3, 6) meets the parabola again in (27, ?18) and the circle on the normal chord as diameter is [Kurukshetra CEE 1998] |
| A. | \[{{x}^{2}}+{{y}^{2}}+30x+12y-27=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+30x+12y+27=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-30x-12y-27=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-30x+12y-27=0\] |
| Answer» E. | |
| 2488. |
The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola \[{{y}^{2}}=4ax\], lies on [MP PET 1999] |
| A. | Axis |
| B. | Directrix |
| C. | Latus rectum |
| D. | Tangent at vertex |
| Answer» B. Directrix | |
| 2489. |
At what point on the parabola \[{{y}^{2}}=4x\], the normal makes equal angles with the co-ordinate axes [RPET 1994] |
| A. | (4, 4) |
| B. | (9, 6) |
| C. | (4, ?4) |
| D. | (1, ?2) |
| Answer» E. | |
| 2490. |
If PSQ is the focal chord of the parabola \[{{y}^{2}}=8x\] such that\[SP=6\]. Then the length SQ is |
| A. | 6 |
| B. | 4 |
| C. | 3 |
| D. | None of these |
| Answer» D. None of these | |
| 2491. |
If \[x=my+c\]is a normal to the parabola \[{{x}^{2}}=4ay\], then the value of c is |
| A. | \[-2am-a{{m}^{3}}\] |
| B. | \[2am+a{{m}^{3}}\] |
| C. | \[-\frac{2a}{m}-\frac{a}{{{m}^{3}}}\] |
| D. | \[\frac{2a}{m}+\frac{a}{{{m}^{3}}}\] |
| Answer» B. \[2am+a{{m}^{3}}\] | |
| 2492. |
The equations of the normals at the ends of latus rectum of the parabola \[{{y}^{2}}=4ax\] are given by |
| A. | \[{{x}^{2}}-{{y}^{2}}-6ax+9{{a}^{2}}=0\] |
| B. | \[{{x}^{2}}-{{y}^{2}}-6ax-6ay+9{{a}^{2}}=0\] |
| C. | \[{{x}^{2}}-{{y}^{2}}-6ay+9{{a}^{2}}=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}-{{y}^{2}}-6ax-6ay+9{{a}^{2}}=0\] | |
| 2493. |
If the segment intercepted by the parabola \[{{y}^{2}}=4ax\] with the line \[lx+my+n=0\] subtends a right angle at the vertex, then |
| A. | \[4al+n=0\] |
| B. | \[4al+4am+n=0\] |
| C. | \[4am+n=0\] |
| D. | \[al+n=0\] |
| Answer» B. \[4al+4am+n=0\] | |
| 2494. |
A set of parallel chords of the parabola \[{{y}^{2}}=4ax\] have their mid-point on |
| A. | Any straight line through the vertex |
| B. | Any straight line through the focus |
| C. | Any straight line parallel to the axis |
| D. | Another parabola |
| Answer» D. Another parabola | |
| 2495. |
If ?a? and ?c? are the segments of a focal chord of a parabola and b the semi-latus rectum, then [MP PET 1995] |
| A. | a, b, c are in A.P. |
| B. | a, b, c are in G.P. |
| C. | a, b, c are in H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2496. |
If the parabola \[{{y}^{2}}=4ax\] passes through (?3, 2), then length of its latus rectum is [RPET 1986, 95] |
| A. | 2/3 |
| B. | 1/3 |
| C. | 4/3 |
| D. | 4 |
| Answer» D. 4 | |
| 2497. |
The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola \[{{y}^{2}}=8x\], is [MNR 1976] |
| A. | \[\frac{1}{2}\sqrt{41}\] |
| B. | \[\sqrt{41}\] |
| C. | \[\frac{3}{2}\sqrt{41}\] |
| D. | \[2\sqrt{41}\] |
| Answer» D. \[2\sqrt{41}\] | |
| 2498. |
In the parabola \[{{y}^{2}}=6x\], the equation of the chord through vertex and negative end of latus rectum, is |
| A. | \[y=2x\] |
| B. | \[y+2x=0\] |
| C. | \[x=2y\] |
| D. | \[x+2y=0\] |
| Answer» C. \[x=2y\] | |
| 2499. |
If a normal drawn to the parabola \[{{y}^{2}}=4ax\] at the point \[(a,\ 2a)\] meets parabola again on \[(a{{t}^{2}},\ 2at)\], then the value of t will be [RPET 1990] |
| A. | 1 |
| B. | 3 |
| C. | ?1 |
| D. | ?3 |
| Answer» E. | |
| 2500. |
If the line \[2x+y+k=0\] is normal to the parabola \[{{y}^{2}}=-8x\], then the value of k will be [RPET 1986, 97] |
| A. | \[-16\] |
| B. | \[-8\] |
| C. | \[-24\] |
| D. | 24 |
| Answer» E. | |