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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.
| 2401. |
The locus of a foot of perpendicular drawn to the tangent of parabola \[{{y}^{2}}=4ax\] from focus, is [RPET 1989] |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[{{y}^{2}}=2a(x+a)\] |
| D. | \[{{x}^{2}}+{{y}^{2}}(x+a)=0\] |
| Answer» B. \[y=0\] | |
| 2402. |
The line \[y=mx+1\] is a tangent to the parabola \[{{y}^{2}}=4x\], if [MNR 1990; Kurukshetra CEE 1998; DCE 2000; Pb. CET 2004] |
| A. | \[m=1\] |
| B. | \[m=2\] |
| C. | \[m=4\] |
| D. | \[m=3\] |
| Answer» B. \[m=2\] | |
| 2403. |
The line \[y=2x+c\] is a tangent to the parabola \[{{y}^{2}}=16x\], if c equals [MNR 1988] |
| A. | \[-2\] |
| B. | \[-1\] |
| C. | 0 |
| D. | 2 |
| Answer» E. | |
| 2404. |
The equation of the tangent at a point \[P(t)\] where ?t? is any parameter to the parabola \[{{y}^{2}}=4ax\], is [MNR 1983] |
| A. | \[yt=x+a{{t}^{2}}\] |
| B. | \[y=xt+a{{t}^{2}}\] |
| C. | \[y=xt+\frac{a}{t}\] |
| D. | \[y=tx\] |
| Answer» B. \[y=xt+a{{t}^{2}}\] | |
| 2405. |
The straight line \[y=2x+\lambda \] does not meet the parabola \[{{y}^{2}}=2x\], if [MP PET 1993; MNR 1977] |
| A. | \[\lambda <\frac{1}{4}\] |
| B. | \[\lambda >\frac{1}{4}\] |
| C. | \[\lambda =4\] |
| D. | \[\lambda =1\] |
| Answer» C. \[\lambda =4\] | |
| 2406. |
The point of the contact of the tangent to the parabola \[{{y}^{2}}=4ax\] which makes an angle of \[{{60}^{o}}\]with x-axis, is |
| A. | \[\left( \frac{a}{3},\ \frac{2a}{\sqrt{3}} \right)\] |
| B. | \[\left( \frac{2a}{\sqrt{3}},\ \frac{a}{3} \right)\] |
| C. | \[\left( \frac{a}{\sqrt{3}},\ \frac{2a}{3} \right)\] |
| D. | None of these |
| Answer» B. \[\left( \frac{2a}{\sqrt{3}},\ \frac{a}{3} \right)\] | |
| 2407. |
The focal distance of a point on the parabola \[{{y}^{2}}=16x\] whose ordinate is twice the abscissa, is |
| A. | 6 |
| B. | 8 |
| C. | 10 |
| D. | 12 |
| Answer» C. 10 | |
| 2408. |
The equation of the tangent to the parabola \[{{y}^{2}}=4x+5\] parallel to the line \[y=2x+7\] is [MNR 1979] |
| A. | \[2x-y-3=0\] |
| B. | \[2x-y+3=0\] |
| C. | \[2x+y+3=0\] |
| D. | None of these |
| Answer» C. \[2x+y+3=0\] | |
| 2409. |
The line \[lx+my+n=0\] will touch the parabola \[{{y}^{2}}=4ax\], if [RPET 1988; MNR 1977; MP PET 2003] |
| A. | \[mn=a{{l}^{2}}\] |
| B. | \[lm=a{{n}^{2}}\] |
| C. | \[ln=a{{m}^{2}}\] |
| D. | \[mn=al\] |
| Answer» D. \[mn=al\] | |
| 2410. |
The equation of a tangent to the parabola \[{{y}^{2}}=4ax\] making an angle \[\theta \] with x-axis is |
| A. | \[y=x\cot \theta +a\tan \theta \] |
| B. | \[x=y\tan \theta +a\cot \theta \] |
| C. | \[y=x\tan \theta +a\cot \theta \] |
| D. | None of these |
| Answer» D. None of these | |
| 2411. |
The equation of the common tangent of the parabolas \[{{x}^{2}}=108y\] and \[{{y}^{2}}=32x\], is |
| A. | \[2x+3y=36\] |
| B. | \[2x+3y+36=0\] |
| C. | \[3x+2y=36\] |
| D. | \[3x+2y+36=0\] |
| Answer» C. \[3x+2y=36\] | |
| 2412. |
The point of contact of the tangent \[18x-6y+1=0\] to the parabola \[{{y}^{2}}=2x\]is |
| A. | \[\left( \frac{-1}{18},\ \frac{-1}{3} \right)\] |
| B. | \[\left( \frac{-1}{18},\ \frac{1}{3} \right)\] |
| C. | \[\left( \frac{1}{18},\ \frac{-1}{3} \right)\] |
| D. | \[\left( \frac{1}{18},\ \frac{1}{3} \right)\] |
| Answer» E. | |
| 2413. |
The equation of axis of the parabola \[2{{x}^{2}}+5y-3x+4=0\] is [Pb. CET 2000] |
| A. | \[x=\frac{3}{4}\] |
| B. | \[y=\frac{3}{4}\] |
| C. | \[x=-\frac{1}{2}\] |
| D. | \[x-3y=5\] |
| Answer» B. \[y=\frac{3}{4}\] | |
| 2414. |
If \[{{x}^{2}}+6x+20y-51=0\], then axis of parabola is [Orissa JEE 2004] |
| A. | \[x+3=0\] |
| B. | \[x-3=0\] |
| C. | \[x=1\] |
| D. | \[x+1=0\] |
| Answer» B. \[x-3=0\] | |
| 2415. |
The points on the parabola \[{{y}^{2}}=12x\] whose focal distance is 4, are |
| A. | \[(2,\ \sqrt{3}),\ (2,\ -\sqrt{3})\] |
| B. | \[(1,\ 2\sqrt{3}),\ (1,-2\sqrt{3})\] |
| C. | (1, 2) |
| D. | None of these |
| Answer» C. (1, 2) | |
| 2416. |
If (0, 6) and (0, 3) are respectively the vertex and focus of a parabola, then its equation is [Karnataka CET 2004] |
| A. | \[{{x}^{2}}+12y=72\] |
| B. | \[{{x}^{2}}-12y=72\] |
| C. | \[{{y}^{2}}-12x=72\] |
| D. | \[{{y}^{2}}+12x=72\] |
| Answer» B. \[{{x}^{2}}-12y=72\] | |
| 2417. |
The directrix of the parabola \[{{x}^{2}}-4x-8y+12=0\] is [Karnataka CET 2003] |
| A. | \[x=1\] |
| B. | \[y=0\] |
| C. | \[x=-1\] |
| D. | \[y=-1\] |
| Answer» E. | |
| 2418. |
The equation of the parabola with focus (0, 0) and directrix \[x+y=4\] is [EAMCET 2003] |
| A. | \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y-16=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+8x+8y-16=0\] |
| D. | \[{{x}^{2}}-{{y}^{2}}+8x+8y-16=0\] |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}-2xy+8x+8y=0\] | |
| 2419. |
The equation of the parabola whose vertex is at (2, ?1) and focus at (2, ?3) is [Kerala (Engg.) 2002] |
| A. | \[{{x}^{2}}+4x-8y-12=0\] |
| B. | \[{{x}^{2}}-4x+8y+12=0\] |
| C. | \[{{x}^{2}}+8y=12\] |
| D. | \[{{x}^{2}}-4x+12=0\] |
| Answer» C. \[{{x}^{2}}+8y=12\] | |
| 2420. |
The equation of parabola whose focus is (5, 3) and directrix is \[3x-4y+1=0\], is [MP PET 2002] |
| A. | \[{{(4x+3y)}^{2}}-256x-142y+849=0\] |
| B. | \[{{(4x-3y)}^{2}}-256x-142y+849=0\] |
| C. | \[{{(3x+4y)}^{2}}-142x-256y+849=0\] |
| D. | \[{{(3x-4y)}^{2}}-256x-142y+849=0\] |
| Answer» B. \[{{(4x-3y)}^{2}}-256x-142y+849=0\] | |
| 2421. |
Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is [Karnataka CET 2001, 02] |
| A. | \[{{(x-1)}^{2}}=8(y-1)\] |
| B. | \[{{(y-1)}^{2}}=8(x-3)\] |
| C. | \[{{(y-1)}^{2}}=8(x-1)\] |
| D. | \[{{(x-3)}^{2}}=8(y-1)\] |
| Answer» D. \[{{(x-3)}^{2}}=8(y-1)\] | |
| 2422. |
The vertex of parabola \[{{(y-2)}^{2}}=16(x-1)\] is [Karnataka CET 2001] |
| A. | (2, 1) |
| B. | (1, ?2) |
| C. | (?1, 2) |
| D. | (1, 2) |
| Answer» E. | |
| 2423. |
The focus of the parabola \[{{y}^{2}}-x-2y+2=0\]is [UPSEAT 2000] |
| A. | \[(1/4,\ 0)\] |
| B. | (1, 2) |
| C. | (3/4, 1) |
| D. | (5/4,1) |
| Answer» E. | |
| 2424. |
The points on the parabola \[{{y}^{2}}=36x\] whose ordinate is three times the abscissa are |
| A. | (0, 0), (4, 12) |
| B. | (1, 3),(4, 12) |
| C. | (4, 12) |
| D. | None of these |
| Answer» B. (1, 3),(4, 12) | |
| 2425. |
The focus of the parabola \[y=2{{x}^{2}}+x\] is [MP PET 2000] |
| A. | (0, 0) |
| B. | \[\left( \frac{1}{2},\ \frac{1}{4} \right)\] |
| C. | \[\left( -\frac{1}{4},\ 0 \right)\] |
| D. | \[\left( -\frac{1}{4},\ \frac{1}{8} \right)\] |
| Answer» D. \[\left( -\frac{1}{4},\ \frac{1}{8} \right)\] | |
| 2426. |
The length of the latus rectum of the parabola \[{{x}^{2}}-4x-8y+12=0\] is [MP PET 2000] |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» D. 10 | |
| 2427. |
Focus of the parabola \[{{(y-2)}^{2}}=20(x+3)\] is [Karnataka CET 1999] |
| A. | (3, -2) |
| B. | (2, -3) |
| C. | (2, 2) |
| D. | (3, 3) |
| Answer» D. (3, 3) | |
| 2428. |
The focus of the parabola \[4{{y}^{2}}-6x-4y=5\] is [RPET 1997] |
| A. | (-8/5, 2) |
| B. | (-5/8, 1/2) |
| C. | (1/2, 5/8) |
| D. | (5/8, -1/2) |
| Answer» C. (1/2, 5/8) | |
| 2429. |
The vertex of the parabola \[3x-2{{y}^{2}}-4y+7=0\] is [RPET 1996] |
| A. | (3, 1) |
| B. | (-3, -1) |
| C. | (-3, 1) |
| D. | None of these |
| Answer» C. (-3, 1) | |
| 2430. |
Eccentricity of the parabola \[{{x}^{2}}-4x-4y+4=0\] is [RPET 1996; Pb. CET 2003] |
| A. | \[e=0\] |
| B. | \[e=1\] |
| C. | \[e>4\] |
| D. | \[e=4\] |
| Answer» C. \[e>4\] | |
| 2431. |
The length of latus rectum of the parabola \[4{{y}^{2}}+2x-20y+17=0\] is [MP PET 1999] |
| A. | 3 |
| B. | 6 |
| C. | \[\frac{1}{2}\] |
| D. | 9 |
| Answer» D. 9 | |
| 2432. |
The equation of the lines joining the vertex of the parabola \[{{y}^{2}}=6x\] to the points on it whose abscissa is 24, is |
| A. | \[y\pm 2x=0\] |
| B. | \[2y\pm x=0\] |
| C. | \[x\pm 2y=0\] |
| D. | \[2x\pm y=0\] |
| Answer» D. \[2x\pm y=0\] | |
| 2433. |
Latus rectum of the parabola \[{{y}^{2}}-4y-2x-8=0\] is |
| A. | 2 |
| B. | 4 |
| C. | 8 |
| D. | 1 |
| Answer» B. 4 | |
| 2434. |
The focus of the parabola \[{{x}^{2}}=2x+2y\] is |
| A. | \[\left( \frac{3}{2},\ \frac{-1}{2} \right)\] |
| B. | \[\left( 1,\ \frac{-1}{2} \right)\] |
| C. | (1, 0) |
| D. | (0, 1) |
| Answer» D. (0, 1) | |
| 2435. |
The latus rectum of the parabola \[{{y}^{2}}=5x+4y+1\]is [MP PET 1996] |
| A. | \[\frac{5}{4}\] |
| B. | 10 |
| C. | 5 |
| D. | \[\frac{5}{2}\] |
| Answer» D. \[\frac{5}{2}\] | |
| 2436. |
If the vertex of the parabola \[y={{x}^{2}}-8x+c\] lies on x-axis, then the value of c is |
| A. | -16 |
| B. | -4 |
| C. | 4 |
| D. | 16 |
| Answer» E. | |
| 2437. |
The points of intersection of the curves whose parametric equations are \[x={{t}^{2}}+1,\ y=2t\] and \[x=2s,\ y=\frac{2}{s}\] is given by |
| A. | \[(1,\ -3)\] |
| B. | (2, 2) |
| C. | (?2, 4) |
| D. | (1, 2) |
| Answer» C. (?2, 4) | |
| 2438. |
The vertex of a parabola is the point (a, b) and latus rectum is of length l. If the axis of the parabola is along the positive direction of y-axis, then its equation is |
| A. | \[{{(x+a)}^{2}}=\frac{l}{2}(2y-2b)\] |
| B. | \[{{(x-a)}^{2}}=\frac{l}{2}(2y-2b)\] |
| C. | \[{{(x+a)}^{2}}=\frac{l}{4}(2y-2b)\] |
| D. | \[{{(x-a)}^{2}}=\frac{l}{8}(2y-2b)\] |
| Answer» C. \[{{(x+a)}^{2}}=\frac{l}{4}(2y-2b)\] | |
| 2439. |
The length of the latus rectum of the parabola \[9{{x}^{2}}-6x+36y+19=0\] [MP PET 1994] |
| A. | 36 |
| B. | 9 |
| C. | 6 |
| D. | 4 |
| Answer» E. | |
| 2440. |
Curve \[16{{x}^{2}}+8xy+{{y}^{2}}-74x-78y+212=0\] represents |
| A. | Parabola |
| B. | Hyperbola |
| C. | Ellipse |
| D. | None of these |
| Answer» B. Hyperbola | |
| 2441. |
The equation of parabola whose vertex and focus are (0, 4) and (0, 2) respectively, is [RPET 1987, 89, 90, 91] |
| A. | \[{{y}^{2}}-8x=32\] |
| B. | \[{{y}^{2}}+8x=32\] |
| C. | \[{{x}^{2}}+8y=32\] |
| D. | \[{{x}^{2}}-8y=32\] |
| Answer» D. \[{{x}^{2}}-8y=32\] | |
| 2442. |
The latus rectum of a parabola whose directrix is \[x+y-2=0\] and focus is (3, ? 4), is |
| A. | \[-3\sqrt{2}\] |
| B. | \[3\sqrt{2}\] |
| C. | \[-3/\sqrt{2}\] |
| D. | \[3/\sqrt{2}\] |
| Answer» C. \[-3/\sqrt{2}\] | |
| 2443. |
The equation of the latus rectum of the parabola represented by equation \[{{y}^{2}}+2Ax+2By+C=0\] is |
| A. | \[x=\frac{{{B}^{2}}+{{A}^{2}}-C}{2A}\] |
| B. | \[x=\frac{{{B}^{2}}-{{A}^{2}}+C}{2A}\] |
| C. | \[x=\frac{{{B}^{2}}-{{A}^{2}}-C}{2A}\] |
| D. | \[x=\frac{{{A}^{2}}-{{B}^{2}}-C}{2A}\] |
| Answer» C. \[x=\frac{{{B}^{2}}-{{A}^{2}}-C}{2A}\] | |
| 2444. |
The equations \[x=\frac{t}{4},\ y=\frac{{{t}^{2}}}{4}\] represents |
| A. | A circle |
| B. | A parabola |
| C. | An ellipse |
| D. | A hyperbola |
| Answer» C. An ellipse | |
| 2445. |
The parametric equation of the curve \[{{y}^{2}}=8x\]are |
| A. | \[x={{t}^{2}},\ y=2t\] |
| B. | \[x=2{{t}^{2}},\ y=4t\] |
| C. | \[x=2t,\ y=4{{t}^{2}}\] |
| D. | None of these |
| Answer» C. \[x=2t,\ y=4{{t}^{2}}\] | |
| 2446. |
If the axis of a parabola is horizontal and it passes through the points (0, 0), (0, ?1) and (6, 1), then its equation is |
| A. | \[{{y}^{2}}+3y-x-4=0\] |
| B. | \[{{y}^{2}}-3y+x-4=0\] |
| C. | \[{{y}^{2}}-3y-x-4=0\] |
| D. | None of these |
| Answer» E. | |
| 2447. |
The focus of the parabola \[{{y}^{2}}=4y-4x\] is [MP PET 1991] |
| A. | (0, 2) |
| B. | (1, 2) |
| C. | (2, 0) |
| D. | (2, 1) |
| Answer» B. (1, 2) | |
| 2448. |
The equation of the parabola whose vertex and focus lies on the x-axis at distance a and a? from the origin, is [RPET 2000] |
| A. | |
| B. | \[{{y}^{2}}=4(a'-a)(x+a)\] |
| C. | \[{{y}^{2}}=4(a'+a)(x-a)\] |
| D. | \[{{y}^{2}}=4(a'+a)(x+a)\] |
| Answer» B. \[{{y}^{2}}=4(a'-a)(x+a)\] | |
| 2449. |
The equation of the parabola with (?3, 0) as focus and \[x+5=0\] as directirx, is [RPET 1985, 86, 89; MP PET 1991] |
| A. | \[{{x}^{2}}=4(y+4)\] |
| B. | \[{{x}^{2}}=4(y-4)\] |
| C. | \[{{y}^{2}}=4(x+4)\] |
| D. | \[{{y}^{2}}=4(x-4)\] |
| Answer» D. \[{{y}^{2}}=4(x-4)\] | |
| 2450. |
Equation of the parabola whose directrix is \[y=2x-9\] and focus (?8, ?2) is |
| A. | \[{{x}^{2}}+4{{y}^{2}}+4xy+16x+2y+259=0\] |
| B. | \[{{x}^{2}}+4{{y}^{2}}+4xy+116x+2y+259=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+4xy+116x+2y+259=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}+4xy+116x+2y+259=0\] | |