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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.
| 2351. |
A point moves in such a way that the sum of its distance from xy-plane and yz-plane remains equal to its distance from zx-plane. The locus of the point is |
| A. | \[x-y+z=2\] |
| B. | \[x+y-z=0\] |
| C. | \[x-y+z=0\] |
| D. | \[x-y-z=2\] |
| Answer» D. \[x-y-z=2\] | |
| 2352. |
The equation of the plane containing the line of intersection of the planes \[2x-y=0\]and \[y-3z=0\]and perpendicular to the plane \[4x+5y-3z-8=0\]is |
| A. | \[28x-17y+9z=0\] |
| B. | \[28x+17y+9z=0\] |
| C. | \[28x-17y+9x=0\] |
| D. | \[7x-3y+z=0\] |
| Answer» B. \[28x+17y+9z=0\] | |
| 2353. |
Distance of the point (2,3,4) from the plane \[3x-6y+2z+11=0\]is [MP PET 1990, 96] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» B. 2 | |
| 2354. |
If the product of distances of the point (1, 1, 1) from the origin and the plane \[x-y+z+k=0\] be 5, then k = |
| A. | ? 2 |
| B. | ?3 |
| C. | 4 |
| D. | 7 |
| Answer» D. 7 | |
| 2355. |
The period of \[{{\sin }^{4}}x+{{\cos }^{4}}x\]is [RPET 1997] |
| A. | \[\pi /2\] |
| B. | \[\pi \] |
| C. | \[2\pi \] |
| D. | \[3\pi /2\] |
| Answer» B. \[\pi \] | |
| 2356. |
Period of \[|2\sin 3\theta +4\cos 3\theta |\]is |
| A. | \[\frac{2\pi }{3}\] |
| B. | \[\pi \] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{\pi }{3}\] |
| Answer» E. | |
| 2357. |
Period of cot \[3x-\cos (4x+3)\]is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\pi \] |
| D. | \[2\pi \] |
| Answer» D. \[2\pi \] | |
| 2358. |
Period of \[\sin \theta -\sqrt{3}\cos \theta \]is [MP PET 1990] |
| A. | \[\frac{\pi }{4}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\pi \] |
| D. | \[2\pi \] |
| Answer» E. | |
| 2359. |
Period of \[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }\]is |
| A. | \[2\pi \] |
| B. | \[\pi \] |
| C. | \[\frac{2\pi }{3}\] |
| D. | \[\frac{\pi }{3}\] |
| Answer» D. \[\frac{\pi }{3}\] | |
| 2360. |
The period of \[f(x)=\sin \left( \frac{\pi x}{n-1} \right)+\cos \,\left( \frac{\pi x}{n} \right)\,\,,\,n\in Z\], \[n>2\] is [Orissa JEE 2002] |
| A. | \[2\pi n(n-1)\] |
| B. | \[4n\,(n-1)\] |
| C. | \[2n\,(n-1)\] |
| D. | None of these |
| Answer» D. None of these | |
| 2361. |
Period of \[\sin \theta \cos \theta \]is |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\pi \] |
| C. | \[2\pi \] |
| D. | None of these |
| Answer» C. \[2\pi \] | |
| 2362. |
The function \[f(x)=\sin \frac{\pi x}{2}+2\cos \frac{\pi x}{3}-\tan \frac{\pi x}{4}\] is period with period [EAMCET 1992; RPET 2001] |
| A. | 6 |
| B. | 3 |
| C. | 4 |
| D. | 12 |
| Answer» E. | |
| 2363. |
The period of the function \[\sin \left( \frac{\pi x}{2} \right)+\cos \left( \frac{\pi x}{2} \right)\] is [EAMCET 1990] |
| A. | 4 |
| B. | 6 |
| C. | 12 |
| D. | 24 |
| Answer» B. 6 | |
| 2364. |
Let \[f(x)=\cos px+\sin x\] be periodic, then p must be |
| A. | Rational |
| B. | Irrational |
| C. | Positive real number |
| D. | None of these |
| Answer» B. Irrational | |
| 2365. |
The period of the function \[\sin \left( \frac{2x}{3} \right)+\sin \left( \frac{3x}{2} \right)\]is [Orissa JEE 2004] |
| A. | \[2\pi \] |
| B. | \[10\pi \] |
| C. | \[6\pi \] |
| D. | \[12\pi \] |
| Answer» E. | |
| 2366. |
Which of the following functions has period \[2\pi \] [Pb. CET 2004] |
| A. | \[y=\sin \left( 2\pi t+\frac{\pi }{3} \right)+\]\[2\sin \left( 3\pi t+\frac{\pi }{4} \right)+3\sin 5\pi t\] |
| B. | \[y=\sin \frac{\pi }{3}t+\sin \frac{\pi }{4}t\] |
| C. | \[y=\sin t+\cos 2t\] |
| D. | None of these |
| Answer» D. None of these | |
| 2367. |
The period of the function \[y=\sin 2x\]is [Kerala (Engg.) 2002] |
| A. | \[2\pi \] |
| B. | \[\pi \] |
| C. | \[\pi /2\] |
| D. | \[4\pi \] |
| Answer» C. \[\pi /2\] | |
| 2368. |
Period of \[{{\sin }^{2}}x\]is [UPSEAT 2002; AIEEE 2002] |
| A. | \[\pi \] |
| B. | \[2\pi \] |
| C. | \[\frac{\pi }{2}\] |
| D. | None of these\[\] |
| Answer» B. \[2\pi \] | |
| 2369. |
If the period of the function \[f(x)=\sin \left( \frac{x}{n} \right)\]is \[4\pi \], then n is equal to [Pb. CET 2000] |
| A. | 1 |
| B. | 4 |
| C. | 8 |
| D. | 2 |
| Answer» E. | |
| 2370. |
The period of the function \[f(\theta )=\sin \frac{\theta }{3}+\cos \frac{\theta }{2}\]is [EAMCET 2001] |
| A. | \[3\pi \] |
| B. | \[6\pi \] |
| C. | \[9\pi \] |
| D. | \[12\pi \] |
| Answer» E. | |
| 2371. |
If \[u=\log ({{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz)\], then \[\left( \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} \right)\] \[(x+y+z)\] = [EAMCET 1996] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |
| 2372. |
If \[u={{\tan }^{-1}}\left( \frac{{{x}^{3}}+{{y}^{3}}}{x-y} \right)\], then \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=\] [EAMCET 1999] |
| A. | \[\sin 2u\] |
| B. | \[\cos 2u\] |
| C. | \[\tan 2u\] |
| D. | \[\sec 2u\] |
| Answer» B. \[\cos 2u\] | |
| 2373. |
If \[u={{\tan }^{-1}}\frac{y}{x}\], then by Euler?s Theorem the value of x \[\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=\] [Tamilnadu (Engg.) 1993] |
| A. | \[\tan u\] |
| B. | \[\sin u\] |
| C. | \[0\] |
| D. | \[\cos 2u\] |
| Answer» D. \[\cos 2u\] | |
| 2374. |
If \[u={{\sin }^{-1}}\left( \frac{y}{x} \right),\] then \[\frac{\partial u}{\partial x}\] is equal to [Tamilnadu (Engg.) 1992] |
| A. | \[-\frac{y}{{{x}^{2}}+{{y}^{2}}}\] |
| B. | \[\frac{x}{\sqrt{1-{{y}^{2}}}}\] |
| C. | \[\frac{-y}{\sqrt{{{x}^{2}}-{{y}^{2}}}}\] |
| D. | \[\frac{-y}{x\sqrt{{{x}^{2}}-{{y}^{2}}}}\] |
| Answer» E. | |
| 2375. |
If \[u=\frac{x+y}{x-y}\], then \[\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=\] [EAMCET 1991] |
| A. | \[\frac{1}{x-y}\] |
| B. | \[\frac{2}{x-y}\] |
| C. | \[\frac{1}{{{(x-y)}^{2}}}\] |
| D. | \[\frac{2}{{{(x-y)}^{2}}}\] |
| Answer» C. \[\frac{1}{{{(x-y)}^{2}}}\] | |
| 2376. |
If \[u=\log ({{x}^{2}}+{{y}^{2}}),\] then \[\frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}=\] [EAMCET 1994] |
| A. | \[\frac{1}{{{x}^{2}}+{{y}^{2}}}\] |
| B. | 0 |
| C. | \[\frac{{{x}^{2}}-{{y}^{2}}}{{{({{x}^{2}}+{{y}^{2}})}^{2}}}\] |
| D. | \[\frac{{{y}^{2}}-{{x}^{2}}}{{{({{x}^{2}}+{{y}^{2}})}^{2}}}\] |
| Answer» C. \[\frac{{{x}^{2}}-{{y}^{2}}}{{{({{x}^{2}}+{{y}^{2}})}^{2}}}\] | |
| 2377. |
If \[u={{e}^{-{{x}^{2}}-{{y}^{2}}}}\], then [EAMCET 2001] |
| A. | \[x{{u}_{x}}=y{{y}_{y}}\] |
| B. | \[y{{u}_{x}}=x{{u}_{y}}\] |
| C. | \[y{{u}_{x}}+x{{u}_{y}}=0\] |
| D. | \[{{x}^{2}}{{u}_{y}}+{{y}^{2}}{{u}_{x}}=0\] |
| Answer» C. \[y{{u}_{x}}+x{{u}_{y}}=0\] | |
| 2378. |
If \[z=\frac{y}{x}\left[ \sin \frac{x}{y}+\cos \left( 1+\frac{y}{x} \right) \right]\], then \[x\frac{\partial z}{\partial x}=\] [EAMCET 2002] |
| A. | \[y\frac{\partial z}{\partial y}\] |
| B. | \[-y\frac{\partial z}{\partial y}\] |
| C. | \[2y\frac{\partial z}{\partial y}\] |
| D. | \[2y\frac{\partial z}{\partial x}\] |
| Answer» C. \[2y\frac{\partial z}{\partial y}\] | |
| 2379. |
If \[z=\sec \,(y-ax)+\tan (y+ax),\] then \[\frac{{{\partial }^{2}}z}{\partial {{x}^{2}}}-{{a}^{2}}\frac{{{\partial }^{2}}z}{\partial {{y}^{2}}}=\] [EAMCET 2002] |
| A. | z |
| B. | 2z |
| C. | 0 |
| D. | ?z |
| Answer» D. ?z | |
| 2380. |
If \[{{u}^{2}}={{(x-a)}^{2}}+{{(y-b)}^{2}}+{{(z-c)}^{2}}\], then \[\sum \frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}=\] [Tamilnadu (Engg.) 2002] |
| A. | \[\frac{2}{u}\] |
| B. | \[\frac{3}{u}\] |
| C. | 0 |
| D. | \[\frac{1}{u}\] |
| Answer» B. \[\frac{3}{u}\] | |
| 2381. |
If \[u={{x}^{2}}{{\tan }^{-1}}\frac{y}{x}-{{y}^{2}}{{\tan }^{-1}}\frac{x}{y}\], then \[\frac{{{\partial }^{2}}u}{\partial x\,\partial \,y}=\] [Tamilnadu (Engg.) 2002] |
| A. | \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] |
| B. | \[\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] |
| C. | \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] |
| D. | \[-\frac{{{x}^{2}}{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] |
| Answer» C. \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] | |
| 2382. |
If \[u={{({{x}^{2}}+{{y}^{2}}+{{z}^{2}})}^{3/2}}\], then \[{{\left( \frac{\partial u}{\partial x} \right)}^{2}}+{{\left( \frac{\partial u}{\partial y} \right)}^{2}}+{{\left( \frac{\partial u}{\partial z} \right)}^{2}}=\] [EAMCET 1996] |
| A. | 9u |
| B. | \[9{{u}^{4/3}}\] |
| C. | \[9{{u}^{2}}\] |
| D. | \[{{u}^{4/3}}\] |
| Answer» C. \[9{{u}^{2}}\] | |
| 2383. |
If \[u=x{{y}^{2}}{{\tan }^{-1}}\left( \frac{y}{x} \right)\], then \[x{{u}_{x}}+y{{u}_{y}}=\] [EAMCET 2001] |
| A. | 2u |
| B. | u |
| C. | 3u |
| D. | u/3 |
| Answer» D. u/3 | |
| 2384. |
If \[u={{\tan }^{-1}}(x+y),\] then \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=\] [EAMCET 1996] |
| A. | \[\sin 2u\] |
| B. | \[\frac{1}{2}\sin 2u\] |
| C. | \[2\tan u\] |
| D. | \[{{\sec }^{2}}u\] |
| Answer» C. \[2\tan u\] | |
| 2385. |
If \[{{x}^{x}}{{y}^{y}}{{z}^{z}}=c\], then \[\frac{\partial z}{\partial x}=\] [EAMCET 1999] |
| A. | \[\frac{1+\log x}{1+\log z}\] |
| B. | \[-\frac{1+\log x}{1+\log z}\] |
| C. | \[-\frac{1+\log y}{1+\log z}\] |
| D. | None of these |
| Answer» C. \[-\frac{1+\log y}{1+\log z}\] | |
| 2386. |
If \[u={{\log }_{e}}({{x}^{2}}+{{y}^{2}})+{{\tan }^{-1}}\left( \frac{y}{x} \right)\], then \[\frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}=\] [EAMCET 2000] |
| A. | 0 |
| B. | 2u |
| C. | 1/u |
| D. | u |
| Answer» B. 2u | |
| 2387. |
If \[z=\frac{{{({{x}^{4}}+{{y}^{4}})}^{1/3}}}{{{({{x}^{3}}+{{y}^{3}})}^{1/4}}}\], then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=\] |
| A. | \[\frac{1}{12}z\] |
| B. | \[\frac{1}{4}z\] |
| C. | \[\frac{1}{3}z\] |
| D. | \[\frac{7}{12}z\] |
| Answer» E. | |
| 2388. |
If \[z={{\sin }^{-1}}\left( \frac{x+y}{\sqrt{x}+\sqrt{y}} \right)\], then \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}\] is equal to [EAMCET 1998; Orissa JEE 2000] |
| A. | \[\frac{1}{2}\sin z\] |
| B. | \[\frac{1}{2}\tan z\] |
| C. | \[0\] |
| D. | None of these |
| Answer» C. \[0\] | |
| 2389. |
If the parabola \[{{y}^{2}}=4ax\] passes through the point (1, ?2), then the tangent at this point is [MP PET 1998] |
| A. | \[x+y-1=0\] |
| B. | \[x-y-1=0\] |
| C. | \[x+y+1=0\] |
| D. | \[x-y+1=0\] |
| Answer» D. \[x-y+1=0\] | |
| 2390. |
The line \[y=2x+c\] is tangent to the parabola \[{{y}^{2}}=4x\], then \[c=\] [MP PET 1996] |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{3}\] |
| D. | 4 |
| Answer» C. \[\frac{1}{3}\] | |
| 2391. |
The two parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] intersect at a point P, whose abscissa is not zero, such that |
| A. | They both touch each other at P |
| B. | They cut at right angles at P |
| C. | The tangents to each curve at P make complementary angles with the x-axis |
| D. | None of these |
| Answer» D. None of these | |
| 2392. |
If \[{{y}_{1}},\ {{y}_{2}}\] are the ordinates of two points P and Q on the parabola and \[{{y}_{3}}\] is the ordinate of the point of intersection of tangents at P and Q, then |
| A. | \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\] are in A.P. |
| B. | \[{{y}_{1}},\ {{y}_{3}},\ {{y}_{2}}\] are in A.P. |
| C. | \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\] are in G.P. |
| D. | \[{{y}_{1}},\ {{y}_{3}},\ {{y}_{2}}\] are in G.P. |
| Answer» C. \[{{y}_{1}},\ {{y}_{2}},\ {{y}_{3}}\] are in G.P. | |
| 2393. |
The angle between the tangents drawn from the origin to the parabola \[{{y}^{2}}=4a(x-a)\] is [MNR 1994] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{30}^{o}}\] |
| C. | \[{{\tan }^{-1}}\frac{1}{2}\] |
| D. | \[{{45}^{o}}\] |
| Answer» B. \[{{30}^{o}}\] | |
| 2394. |
The locus of the point of intersection of the perpendicular tangents to the parabola \[{{x}^{2}}=4ay\]is [MP PET 1994] |
| A. | Axis of the parabola |
| B. | Directrix of the parabola |
| C. | Focal chord of the parabola |
| D. | Tangent at vertex to the parabola |
| Answer» C. Focal chord of the parabola | |
| 2395. |
The line \[y=mx+c\] touches the parabola \[{{x}^{2}}=4ay\], if [MNR 1973; MP PET 1994, 99] |
| A. | \[c=-am\] |
| B. | \[c=-a/m\] |
| C. | \[c=-a{{m}^{2}}\] |
| D. | \[c=a/{{m}^{2}}\] |
| Answer» D. \[c=a/{{m}^{2}}\] | |
| 2396. |
The angle between the tangents drawn at the end points of the latus rectum of parabola \[{{y}^{2}}=4ax\], is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{2\pi }{3}\] |
| C. | \[\frac{\pi }{4}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» E. | |
| 2397. |
The co-ordinates of the extremities of the latus rectum of the parabola \[5{{y}^{2}}=4x\] are |
| A. | \[(1/5,\ 2/5),\ (-1/5,\ 2/5)\] |
| B. | \[(1/5,\ 2/5),\ (1/5,\ -2/5)\] |
| C. | \[(1/5,\ 4/5),\ (1/5,\ -4/5)\] |
| D. | None of these |
| Answer» C. \[(1/5,\ 4/5),\ (1/5,\ -4/5)\] | |
| 2398. |
A tangent to the parabola \[{{y}^{2}}=8x\] makes an angle of \[{{45}^{o}}\]with the straight line \[y=3x+5\], then the equation of tangent is |
| A. | \[2x+y-1=0\] |
| B. | \[x+2y-1=0\] |
| C. | \[2x+y+1=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 2399. |
If the line \[y=mx+c\] is a tangent to the parabola \[{{y}^{2}}=4a(x+a)\] then \[ma+\frac{a}{m}\] is equal to |
| A. | c |
| B. | 2c |
| C. | ? c |
| D. | 3c |
| Answer» B. 2c | |
| 2400. |
If the straight line \[x+y=1\] touches the parabola \[{{y}^{2}}-y+x=0\], then the co-ordinates of the point of contact are [RPET 1991] |
| A. | (1, 1) |
| B. | \[\left( \frac{1}{2},\ \frac{1}{2} \right)\] |
| C. | (0, 1) |
| D. | (1, 0) |
| Answer» D. (1, 0) | |