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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.
| 2501. |
The equation of the normal at the point \[\left( \frac{a}{4},\ a \right)\] to the parabola \[{{y}^{2}}=4ax\], is [RPET 1984] |
| A. | \[4x+8y+9a=0\] |
| B. | \[4x+8y-9a=0\] |
| C. | \[4x+y-a=0\] |
| D. | \[4x-y+a=0\] |
| Answer» C. \[4x+y-a=0\] | |
| 2502. |
The slope of the normal at the point \[(a{{t}^{2}},\ 2at)\] of the parabola \[{{y}^{2}}=4ax\], is [MNR 1991; UPSEAT 2000] |
| A. | \[\frac{1}{t}\] |
| B. | t |
| C. | ?t |
| D. | \[-\frac{1}{t}\] |
| Answer» D. \[-\frac{1}{t}\] | |
| 2503. |
The point on the parabola \[{{y}^{2}}=8x\] at which the normal is inclined at 60o to the x-axis has the co-ordinates [MP PET 1993] |
| A. | \[(6,\ -4\sqrt{3})\] |
| B. | \[(6,\ 4\sqrt{3})\] |
| C. | \[(-6,\ -4\sqrt{3})\] |
| D. | \[(-6,\ 4\sqrt{3})\] |
| Answer» B. \[(6,\ 4\sqrt{3})\] | |
| 2504. |
The maximum number of normal that can be drawn from a point to a parabola is [MP PET 1990] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 2505. |
If (2, 0) is the vertex and y-axis the directrix of a parabola, then its focus is [MNR 1981] |
| A. | (2, 0) |
| B. | (?2, 0) |
| C. | (4, 0) |
| D. | (?4, 0) |
| Answer» D. (?4, 0) | |
| 2506. |
The locus of the middle points of the chords of the parabola \[{{y}^{2}}=4ax\]which passes through the origin [RPET 1997; UPSEAT 1999] |
| A. | \[{{y}^{2}}=ax\] |
| B. | \[{{y}^{2}}=2ax\] |
| C. | \[{{y}^{2}}=4ax\] |
| D. | \[{{x}^{2}}=4ay\] |
| Answer» C. \[{{y}^{2}}=4ax\] | |
| 2507. |
The angle between the tangents drawn from the points (1,4) to the parabola \[{{y}^{2}}=4x\] is [IIT Screening 2004] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{4}\] |
| D. | \[\frac{\pi }{6}\] |
| Answer» C. \[\frac{\pi }{4}\] | |
| 2508. |
The point of intersection of tangents at the ends of the latus-rectum of the parabola \[{{y}^{2}}=4x\] is equal to [Pb. CET 2003] |
| A. | (1, 0) |
| B. | (?1, 0) |
| C. | (0, 1) |
| D. | (0, ?1) |
| Answer» C. (0, 1) | |
| 2509. |
Tangents at the extremities of any focal chord of a parabola intersect |
| A. | At right angles |
| B. | On the directrix |
| C. | On the tangents at vertex |
| D. | None of these |
| Answer» C. On the tangents at vertex | |
| 2510. |
If The tangent to the parabola \[{{y}^{2}}=ax\] makes an angle of 45o with x-axis, then the point of contact is [RPET 1985, 90, 2003] |
| A. | \[\left( \frac{a}{2},\ \frac{a}{2} \right)\] |
| B. | \[\left( \frac{a}{4},\ \frac{a}{4} \right)\] |
| C. | \[\left( \frac{a}{2},\ \frac{a}{4} \right)\] |
| D. | \[\left( \frac{a}{4},\ \frac{a}{2} \right)\] |
| Answer» E. | |
| 2511. |
Angle between two curves \[{{y}^{2}}=4(x+1)\] and \[{{x}^{2}}=4(y+1)\] is [UPSEAT 2002] |
| A. | 0o |
| B. | 90o |
| C. | 60o |
| D. | 30o |
| Answer» C. 60o | |
| 2512. |
. The angle of intersection between the curves \[{{x}^{2}}=4(y+1)\] and \[{{x}^{2}}=-4(y+1)\] is [UPSEAT 2002] |
| A. | \[\frac{\pi }{6}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | 0 |
| D. | \[\frac{\pi }{2}\] |
| Answer» D. \[\frac{\pi }{2}\] | |
| 2513. |
The tangent drawn at any point P to the parabola \[{{y}^{2}}=4ax\] meets the directrix at the point K, then the angle which KP subtends at its focus is [RPET 1996, 2002] |
| A. | 30o |
| B. | 45o |
| C. | 60o |
| D. | 90o |
| Answer» E. | |
| 2514. |
The point at which the line \[y=mx+c\] touches the parabola \[{{y}^{2}}=4ax\] is [RPET 2001] |
| A. | \[\left( \frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\] |
| B. | \[\left( \frac{a}{{{m}^{2}}},\ \frac{-2a}{m} \right)\] |
| C. | \[\left( -\frac{a}{{{m}^{2}}},\ \frac{2a}{m} \right)\] |
| D. | \[\left( -\frac{a}{{{m}^{2}}},\ -\frac{2a}{m} \right)\] |
| Answer» B. \[\left( \frac{a}{{{m}^{2}}},\ \frac{-2a}{m} \right)\] | |
| 2515. |
The focus of the parabola \[{{x}^{2}}=-16y\] is [RPET 1987; MP PET 1988, 92] |
| A. | (4, 0) |
| B. | (0, 4) |
| C. | (?4, 0) |
| D. | (0, ?4) |
| Answer» E. | |
| 2516. |
The equation of the common tangent touching the circle \[{{(x-3)}^{2}}+{{y}^{2}}=9\] and the parabola \[{{y}^{2}}=4x\] above the x-axis, is [IIT Screening 2001] |
| A. | \[\sqrt{3}y=3x+1\] |
| B. | \[\sqrt{3}y=-(x+3)\] |
| C. | \[\sqrt{3}y=x+3\] |
| D. | \[\sqrt{3}y=-(3x+1)\] |
| Answer» D. \[\sqrt{3}y=-(3x+1)\] | |
| 2517. |
. Two perpendicular tangents to \[{{y}^{2}}=4ax\] always intersect on the line, if [Karnataka CET 2000] |
| A. | \[x=a\] |
| B. | \[x+a=0\] |
| C. | \[x+2a=0\] |
| D. | \[x+4a=0\] |
| Answer» C. \[x+2a=0\] | |
| 2518. |
The equation of the tangent to the parabola \[{{y}^{2}}=9x\] which goes through the point (4, 10), is [MP PET 2000] |
| A. | \[x+4y+1=0\] |
| B. | \[9x+4y+4=0\] |
| C. | \[x-4y+36=0\] |
| D. | \[9x-4y+4=0\] |
| Answer» D. \[9x-4y+4=0\] | |
| 2519. |
If \[lx+my+n=0\] is tangent to the parabola \[{{x}^{2}}=y\], then condition of tangency is [RPET 1999] |
| A. | \[{{l}^{2}}=2mn\] |
| B. | \[l=4{{m}^{2}}{{n}^{2}}\] |
| C. | \[{{m}^{2}}=4ln\] |
| D. | \[{{l}^{2}}=4mn\] |
| Answer» E. | |
| 2520. |
The tangent to the parabola \[{{y}^{2}}=4ax\] at the point (a, 2a) makes with x-axis an angle equal to [SCRA 1996] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{\pi }{6}\] |
| Answer» C. \[\frac{\pi }{2}\] | |
| 2521. |
The line \[x-y+2=0\] touches the parabola \[{{y}^{2}}=8x\] at the point [Roorkee 1998] |
| A. | \[(2,\ -4)\] |
| B. | \[(1,\ 2\sqrt{2})\] |
| C. | \[(4,\ -4\sqrt{2})\] |
| D. | (2, 4) |
| Answer» E. | |
| 2522. |
If the line \[lx+my+n=0\] is a tangent to the parabola \[{{y}^{2}}=4ax\], then locus of its point of contact is [RPET 1997] |
| A. | A straight line |
| B. | A circle |
| C. | A parabola |
| D. | Two straight lines |
| Answer» D. Two straight lines | |
| 2523. |
The equation of common tangent to the circle \[{{x}^{2}}+{{y}^{2}}=2\] and parabola \[{{y}^{2}}=8x\] is [RPET 1997] |
| A. | \[y=x+1\] |
| B. | \[y=x+2\] |
| C. | \[y=x-2\] |
| D. | \[y=-x+2\] |
| Answer» C. \[y=x-2\] | |
| 2524. |
The equation of the tangent to the parabola \[{{y}^{2}}=4ax\] at point \[(a/{{t}^{2}},\ 2a/t)\] is [RPET 1996] |
| A. | \[ty=x{{t}^{2}}+a\] |
| B. | \[ty=x+a{{t}^{2}}\] |
| C. | \[y=tx+a{{t}^{2}}\] |
| D. | \[y=tx+(a/{{t}^{2}})\] |
| Answer» B. \[ty=x+a{{t}^{2}}\] | |
| 2525. |
The equation of the tangent to the parabola \[{{y}^{2}}=16x\], which is perpendicular to the line \[y=3x+7\] is [MP PET 1998] |
| A. | \[y-3x+4=0\] |
| B. | \[3y-x+36=0\] |
| C. | \[3y+x-36=0\] |
| D. | \[3y+x+36=0\] |
| Answer» E. | |
| 2526. |
A parabola passing through the point \[(-4,\ -2)\] has its vertex at the origin and y-axis as its axis. The latus rectum of the parabola is |
| A. | 6 |
| B. | 8 |
| C. | 10 |
| D. | 12 |
| Answer» C. 10 | |
| 2527. |
The order of the differential equation \[{{{y\left( \frac{dy}{dx} \right)=x}/{\frac{dy}{dx}+\left( \frac{dy}{dx} \right)}\;}^{3}}\] is [MP PET 1994] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 2528. |
The order and the degree of differential equation \[\frac{{{d}^{4}}y}{d{{x}^{4}}}-4\frac{{{d}^{3}}y}{d{{x}^{3}}}+8\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+4y=0\] are respectively |
| A. | 4, 1 |
| B. | 1, 4 |
| C. | 1, 1 |
| D. | None of these |
| Answer» B. 1, 4 | |
| 2529. |
The order and the degree of the differential equation \[{{\left( \frac{{{d}^{2}}s}{d{{t}^{2}}} \right)}^{2}}+3{{\left( \frac{ds}{dt} \right)}^{3}}+4=0\]are |
| A. | \[2,\,2\] |
| B. | \[2,\,3\] |
| C. | \[3,2\] |
| D. | None of these |
| Answer» B. \[2,\,3\] | |
| 2530. |
The order and degree of the differential equation \[\sqrt{\frac{dy}{dx}}-4\frac{dy}{dx}-7x=0\]are [MP PET 1993] |
| A. | 1 and 1/2 |
| B. | 2 and 1 |
| C. | 1 and 1 |
| D. | 1 and 2 |
| Answer» E. | |
| 2531. |
A differential equation of first order and first degree is |
| A. | \[x{{\left( \frac{dy}{dx} \right)}^{2}}-x+a=0\] |
| B. | \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+xy=0\] |
| C. | \[dy+dx=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 2532. |
The order of differential equations of all parabolas having directrix parallel to x-axis is [Orissa JEE 2004] |
| A. | 3 |
| B. | 1 |
| C. | 4 |
| D. | 2 |
| Answer» B. 1 | |
| 2533. |
The degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\sqrt{\frac{dy}{dx}-3}=x\] is [Orissa JEE 2004] |
| A. | 2 |
| B. | 1 |
| C. | ½ |
| D. | 3 |
| Answer» B. 1 | |
| 2534. |
The order and degree of the differential equation \[x\text{ }{{\left( \frac{dy}{dx} \right)}^{3}}+2\,{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}+3y+x=0\] are respectively [MP PET 2004] |
| A. | 3, 2 |
| B. | 2, 1 |
| C. | 2, 2 |
| D. | 2, 3 |
| Answer» D. 2, 3 | |
| 2535. |
The degree and order of the differential equation of the family of all parabolas whose axis is x?axis, are respectively [AIEEE 2003] |
| A. | 2, 1 |
| B. | 1, 2 |
| C. | 3, 2 |
| D. | 2, 3 |
| Answer» C. 3, 2 | |
| 2536. |
The degree of the differential equation \[{{\left( 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right)}^{3/4}}={{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{1/3}}\] is [Karnataka CET 2004] |
| A. | \[\frac{1}{3}\] |
| B. | 4 |
| C. | 9 |
| D. | \[\frac{3}{4}\] |
| Answer» C. 9 | |
| 2537. |
\[\frac{{{d}^{3}}y}{d{{x}^{3}}}+2\,\left[ 1+\frac{{{d}^{2}}y}{d{{x}^{2}}} \right]=1\] has degree and order as [UPSEAT 2003] |
| A. | 1, 3 |
| B. | 2, 3 |
| C. | 3, 2 |
| D. | 3, 1 |
| Answer» B. 2, 3 | |
| 2538. |
The order and degree of the differential equation \[{{\left[ 4+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{2/3}}=\frac{{{d}^{2}}y}{d{{x}^{2}}}\] are |
| A. | 2, 2 |
| B. | 3, 3 |
| C. | 2, 3 |
| D. | 3, 2 |
| Answer» D. 3, 2 | |
| 2539. |
The order and degree of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{4}}-xy=0\] are respectively [MP PET 2003] |
| A. | 2 and 4 |
| B. | 3 and 2 |
| C. | 4 and 5 |
| D. | 2 and 3 |
| Answer» E. | |
| 2540. |
The degree of differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{3}}+6y=0\] is [Kerala (Engg.) 2002] |
| A. | 1 |
| B. | 3 |
| C. | 2 |
| D. | 5 |
| Answer» B. 3 | |
| 2541. |
Order of the differential equation of the family of all concentric circles centered at (h, k) is [EAMCET 2002] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 2542. |
The order and degree of the differential equation \[\rho =\frac{{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3/2}}}{{{d}^{2}}y/d{{x}^{2}}}\] are respectively [MP PET 2001; UPSEAT 2002] |
| A. | 2, 2 |
| B. | 2, 3 |
| C. | 2, 1 |
| D. | None of these |
| Answer» B. 2, 3 | |
| 2543. |
The order and degree of the differential equation \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}+{{y}^{2}}=0\] are respectively [Karnataka CET 2001] |
| A. | 2 and 2 |
| B. | 1 and 1 |
| C. | 2 and 1 |
| D. | 1 and 2 |
| Answer» D. 1 and 2 | |
| 2544. |
The second order differential equation is [MP PET 2000] |
| A. | \[{{{y}'}^{2}}+x={{y}^{2}}\] |
| B. | \[{y}'{y}''+y=\sin x\] |
| C. | \[{y}'''+{y}''+y=0\] |
| D. | \[{y}'=y\] |
| Answer» C. \[{y}'''+{y}''+y=0\] | |
| 2545. |
The differential equation \[x{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{4}}+y={{x}^{2}}\] is of |
| A. | Degree 3 and order 2 |
| B. | Degree 1 and order 1 |
| C. | Degree 4 and order 3 |
| D. | Degree 4 and order 4 |
| Answer» B. Degree 1 and order 1 | |
| 2546. |
The differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}+\sin y+{{x}^{2}}=0\] is of the following type [Roorkee 1998] |
| A. | Linear |
| B. | Homogeneous |
| C. | Order two |
| D. | Degree one |
| Answer» D. Degree one | |
| 2547. |
Which of the following differential equations has the same order and degree [Kurukshetra CEE 1998] |
| A. | \[\frac{{{d}^{4}}y}{d{{x}^{4}}}+8\text{ }{{\left( \frac{dy}{dx} \right)}^{6}}+5y={{e}^{x}}\] |
| B. | \[5\text{ }{{\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{4}}+8\text{ }{{\left( 1+\frac{dy}{dx} \right)}^{2}}+5y={{x}^{8}}\] |
| C. | \[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{2/3}}=4\frac{{{d}^{3}}y}{d{{x}^{3}}}\] |
| D. | \[y={{x}^{2}}\frac{dy}{dx}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\] |
| Answer» D. \[y={{x}^{2}}\frac{dy}{dx}+\sqrt{1+{{\left( \frac{dy}{dx} \right)}^{2}}}\] | |
| 2548. |
The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | None of these |
| Answer» C. 6 | |
| 2549. |
Family \[y=Ax+{{A}^{3}}\]of curve represented by the differential equation of degree [MP PET 1999] |
| A. | Three |
| B. | Two |
| C. | One |
| D. | None of these |
| Answer» B. Two | |
| 2550. |
The order and degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{\frac{1}{3}}}+{{x}^{\frac{1}{4}}}=0\] are respectively [MP PET 1998] |
| A. | 2, 3 |
| B. | 3, 3 |
| C. | 2, 6 |
| D. | 2, 4 |
| Answer» B. 3, 3 | |