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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.
| 2301. |
A line joining the points (1, 2, 0) and (4, 13, 5) is perpendicular to a plane. Then the coefficients of x, y and z in the equation of the plane are respectively [J & K 2005] |
| A. | 5, 15, 5 |
| B. | 3, 11, 5 |
| C. | 3, ?11, 5 |
| D. | ? 5, ? 15, 5 |
| Answer» C. 3, ?11, 5 | |
| 2302. |
The equation of the plane passing through the points (0, 1, 2) and (?1, 0, 3) and perpendicular to the plane \[2x+3y+z=5\] is [J & K 2005] |
| A. | \[3x-4y+18z+32=0\] |
| B. | \[3x+4y-18z+32=0\] |
| C. | \[4x+3y-17z+31=0\] |
| D. | \[4x-3y+z+1=0\] |
| Answer» E. | |
| 2303. |
If O be the origin and the co-ordinates of P be (1, 2, ?3), then the equation of the plane passing through P and perpendicular to OP is |
| A. | \[x-2y+3z+12=0\] |
| B. | \[2x+3y-z-11=0\] |
| C. | \[x+2y-3z-14=0\] |
| D. | \[x+2y-3z=0\] |
| Answer» D. \[x+2y-3z=0\] | |
| 2304. |
If the points \[(1,\,1,\,k)\] and \[(-3,\,0,\,1)\] be equidistant from the plane \[3x+4y-12z+13=0\],then k = |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» C. 2 | |
| 2305. |
Distance between two parallel planes \[2x+y+2z=8\] and \[4x+2y+4z+5=0\] is [AIEEE 2004] |
| A. | \[\frac{9}{2}\] |
| B. | \[\frac{5}{2}\] |
| C. | \[\frac{7}{2}\] |
| D. | \[\frac{3}{2}\] |
| Answer» D. \[\frac{3}{2}\] | |
| 2306. |
The equation of the plane through the intersection of the planes \[x+y+z=1\] and \[2x+3y-z+4=0\] parallel to \[x-\]axis is [Orissa JEE 2003] |
| A. | \[y-3z+6=0\] |
| B. | \[3y-z+6=0\] |
| C. | \[y+3z+6=0\] |
| D. | \[3y-2z+6=0\] |
| Answer» B. \[3y-z+6=0\] | |
| 2307. |
A plane \[\pi \] makes intercepts 3 and 4 respectively on z-axis and x-axis. If \[\pi \] is parallel to y-axis, then its equation is [EAMCET 2003] |
| A. | \[3x+4z=12\] |
| B. | \[3z+4x=12\] |
| C. | \[3y+4z=12\] |
| D. | \[3z+4y=12\] |
| Answer» B. \[3z+4x=12\] | |
| 2308. |
\[XOZ\]plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio [EAMCET 2003] |
| A. | 3 : 7 |
| B. | 2 : 7 |
| C. | ? 3 : 7 |
| D. | ? 2 :7 |
| Answer» D. ? 2 :7 | |
| 2309. |
The equation of the plane passing through (1, 1, 1) and (1, ?1, ?1) and perpendicular to \[2x-y+z+5=0\]is [EAMCET 2003] |
| A. | \[2x+5y+z-8=0\] |
| B. | \[x+y-z-1=0\] |
| C. | \[2x+5y+z+4=0\] |
| D. | \[x-y+z-1=0\] |
| Answer» C. \[2x+5y+z+4=0\] | |
| 2310. |
The value of \[aa'+\,bb'+\,cc'\]being negative the origin will lie in the acute angle between the planes \[an+by+cz+d=0\] and \[a'x+b'y+c'z+d'=0\], if [MP PET 2003] |
| A. | \[a=a'=0\] |
| B. | d and \[d'\]are of same sign |
| C. | d and \[d'\]are of opposite sign |
| D. | None of these |
| Answer» C. d and \[d'\]are of opposite sign | |
| 2311. |
The distance of the plane \[6x-3y+2z-14=0\]from the origin is [MP PET 2003] |
| A. | 2 |
| B. | 1 |
| C. | 14 |
| D. | 8 |
| Answer» B. 1 | |
| 2312. |
The value of k for which the planes \[3x-6y-2z=7\] and \[2x+y-kz=5\] are perpendicular to each other, is [MP PET 1992] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 2313. |
The equation of the plane passing through (2, 3, 4) and parallel to the plane \[5x-6y+7z=3\] [Kerala (Engg.) 2002] |
| A. | \[5x-6y+7z+20=0\] |
| B. | \[5x-6y+7z-20=0\] |
| C. | \[-5x+6y-7z+3=0\] |
| D. | \[5x+6y+7z+3=0\] |
| Answer» C. \[-5x+6y-7z+3=0\] | |
| 2314. |
The equation of the plane passing through the intersection of the planes \[x+2y+3z+4=0\] and \[4x+3y+2z+1=0\] and the origin is [Kerala (Engg.) 2002] |
| A. | \[3x+2y+z+1=0\] |
| B. | \[3x+2y+z=0\] |
| C. | \[2x+3y+z=0\] |
| D. | \[x+y+z=0\] |
| Answer» C. \[2x+3y+z=0\] | |
| 2315. |
The equation of the plane through the point (1, 2, 3 ) and parallel to the plane \[x+2y+5z=0\]is [DCE 2002] |
| A. | \[(x-1)+2(y-2)+5(z-3)=0\] |
| B. | \[x+2y+5z=14\] |
| C. | \[x+2y+5z=6\] |
| D. | None of these |
| Answer» B. \[x+2y+5z=14\] | |
| 2316. |
In the space the equation \[by+cz+d=0\] represents a plane perpendicular to the plane [EAMCET 2002] |
| A. | \[YOZ\] |
| B. | \[Z=k\] |
| C. | \[ZOX\] |
| D. | \[XOY\] |
| Answer» B. \[Z=k\] | |
| 2317. |
The equations \[|x|=p,|y|=p,|z|=p\] in xyz space represent [Orissa JEE 2002] |
| A. | Cube |
| B. | Rhombus |
| C. | Sphere of radius p |
| D. | Point (p, p, p) |
| Answer» B. Rhombus | |
| 2318. |
The points \[A(-1,3,0)\], \[B\,(2,\,2,\,1)\] and \[C\,(1,\,1,\,3)\] determine a plane. The distance from the plane to the point \[D(5,\,7,8)\] is [AMU 2001] |
| A. | \[\sqrt{66}\] |
| B. | \[\sqrt{71}\] |
| C. | \[\sqrt{73}\] |
| D. | \[\sqrt{76}\] |
| Answer» B. \[\sqrt{71}\] | |
| 2319. |
The equation of a plane parallel to x- axis is [DCE 2001] |
| A. | \[ax+by+cz+d=0\] |
| B. | \[ax+by+d=0\] |
| C. | \[by+cz+d=0\] |
| D. | \[ax+cz+d=0\] |
| Answer» D. \[ax+cz+d=0\] | |
| 2320. |
The intercepts of the plane \[5x-3y+6z=60\]on the co-ordinate axes are [Pb. CET 2000 ; MP PET 2001] |
| A. | \[(10,\,20,\,-10)\] |
| B. | (10, ? 20, 12) |
| C. | (12, ? 20, 10) |
| D. | (12, 20, ? 10) |
| Answer» D. (12, 20, ? 10) | |
| 2321. |
The distance of the point (2, 3, ? 5) from the plane \[x+2y-2z=9\]is [MP PET 2001] |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» C. 2 | |
| 2322. |
The equation of the plane which bisects the angle between the planes \[3x-6y+2z+5=0\] and \[4x-12y+3z-3=0\] which contains the origin is |
| A. | \[33x-13y+32z+45=0\] |
| B. | \[x-3y+z-5=0\] |
| C. | \[33x+13y+32z+45=0\] |
| D. | None of these |
| Answer» E. | |
| 2323. |
If P be the point (2, 6, 3), then the equation of the plane through P at right angle to OP, O being the origin, is [MP PET 2000; Pb. CET 2001] |
| A. | \[2x+6y+3z=7\] |
| B. | \[2x-6y+3z=7\] |
| C. | \[2x+6y-3z=49\] |
| D. | \[2x+6y+3z=49\] |
| Answer» E. | |
| 2324. |
The length of the perpendicular from the origin to the plane \[3x+4y+12z=52\]is [MP PET 2000; Pb. CET 2001] |
| A. | 3 |
| B. | ?4 |
| C. | 5 |
| D. | None of these |
| Answer» E. | |
| 2325. |
If two planes intersect , then the shortest distance between the planes is [Kurukshetra CEE 1998] |
| A. | \[\cos \theta \] |
| B. | \[\cos {{90}^{o}}\] |
| C. | \[\sin {{90}^{o}}\] |
| D. | None of these |
| Answer» C. \[\sin {{90}^{o}}\] | |
| 2326. |
If the plane \[x-3y+5z=d\]passes through the point (1,2,4), then the lengths of intercepts cut by it on the axes of x, y, z are respectively [MP PET 1998] |
| A. | 15, ?5, 3 |
| B. | 1, ?5, 3 |
| C. | ?15, 5, ?3 |
| D. | 1, ?6, 20 |
| Answer» B. 1, ?5, 3 | |
| 2327. |
If the length of perpendicular drawn from origin on a plane is 7 units and its direction ratios are ?3, 2, 6, then that plane is [MP PET 1998] |
| A. | \[-3x+2y+6z-7=0\] |
| B. | \[-3x+2y+6z-49=0\] |
| C. | \[3x-2y+6z+7=0\] |
| D. | \[-3x+2y-6z-49=0\] |
| Answer» C. \[3x-2y+6z+7=0\] | |
| 2328. |
The planes \[x=cy+bz,y=az+cx,z=bx+ay\]pass through one line, if |
| A. | \[a+b+c=0\] |
| B. | \[a+b+c=1\] |
| C. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1\] |
| D. | \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\] |
| Answer» E. | |
| 2329. |
The plane \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3\]meets the co-ordinate axes in \[A,B,C\]. The centroid of the triangle ABC is [DCE 2005] |
| A. | \[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\] |
| B. | \[\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)\] |
| C. | \[\left( \frac{1}{a},\frac{1}{b},\frac{1}{c} \right)\] |
| D. | \[(a,b,c)\] |
| Answer» E. | |
| 2330. |
The equation of a plane which cuts equal intercepts of unit length on the axes, is [MP PET 1996] |
| A. | \[x+y+z=0\] |
| B. | \[x+y+z=1\] |
| C. | \[x+y-z=1\] |
| D. | \[\frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1\] |
| Answer» C. \[x+y-z=1\] | |
| 2331. |
The equation of the plane which is parallel to xy-plane and cuts intercept of length 3 from the z-axis is |
| A. | \[x=3\] |
| B. | \[y=3\] |
| C. | \[z=3\] |
| D. | \[x+y+z=3\] |
| Answer» D. \[x+y+z=3\] | |
| 2332. |
The plane \[ax+by+cz=1\]meets the co-ordinate axes in A, B and C. The centroid of the triangle is [CET 1992] |
| A. | \[(3a,3b,3c)\] |
| B. | \[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\] |
| C. | \[\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)\] |
| D. | \[\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)\] |
| Answer» E. | |
| 2333. |
If from a point \[P(a,b,c)\] perpendiculars \[PA\] and \[PB\]are drawn to yz and zx planes, then the equation of the plane \[OAB\] is |
| A. | \[bcx+cay+abz=0\] |
| B. | \[bcx+cay-abz=0\] |
| C. | \[bcx-cay+abz=0\] |
| D. | \[-bcx+cay+abz=0\] |
| Answer» C. \[bcx-cay+abz=0\] | |
| 2334. |
The graph of the equation \[{{y}^{2}}+{{z}^{2}}=0\] in three dimensional space is |
| A. | x-axis |
| B. | z-axis |
| C. | y-axis |
| D. | yz-plane |
| Answer» B. z-axis | |
| 2335. |
If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is [AMU 2005] |
| A. | \[a(x-a)-b(y-b)-c(z-c)=0\] |
| B. | \[a(x+a)+b(y+b)+c(z+c)=0\] |
| C. | \[a(x-a)+b(y-b)+c(z-c)=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 2336. |
If the planes \[3x-2y+2z+17=0\]and \[4x+3y-kz=25\] are mutually perpendicular , then \[k=\] [MP PET 1995] |
| A. | 3 |
| B. | ? 3 |
| C. | 9 |
| D. | ? 6 |
| Answer» B. ? 3 | |
| 2337. |
A point (x, y, z) moves parallel to xy?plane. Which of the three variables x, y, z remain fixed |
| A. | z |
| B. | y |
| C. | x |
| D. | x and y |
| Answer» B. y | |
| 2338. |
The angle between two planes is equal to |
| A. | The angle between the tangents to them from any point |
| B. | The angle between the normals to them from any point |
| C. | The angle between the lines parallel to the planes from any point |
| D. | None of these |
| Answer» C. The angle between the lines parallel to the planes from any point | |
| 2339. |
If a plane cuts off intercepts ?6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is |
| A. | \[\frac{1}{\sqrt{61}}\] |
| B. | \[\frac{13}{\sqrt{61}}\] |
| C. | \[\frac{12}{\sqrt{29}}\] |
| D. | \[\frac{5}{\sqrt{41}}\] |
| Answer» D. \[\frac{5}{\sqrt{41}}\] | |
| 2340. |
Distance between parallel planes \[2x-2y+z+3=0\] and \[4x-4y+2z+5=0\] is [MP PET 1994, 95] |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{6}\] |
| D. | 2 |
| Answer» D. 2 | |
| 2341. |
Image point of \[(1,\,3,4)\] in the plane \[2x-y+z+3=0\] is |
| A. | (? 3, 5, 2) |
| B. | (3, 5, ? 2) |
| C. | (3, ? 5, 3) |
| D. | None of these |
| Answer» B. (3, 5, ? 2) | |
| 2342. |
The ratio in which the plane \[x-2y+3z=17\] divides the line joining the points (?2, 4, 7) and \[(3,-5,\,8)\]is [AISSE 1988] |
| A. | 10 : 3 |
| B. | 3 : 1 |
| C. | 3 : 10 |
| D. | 10 : 1 |
| Answer» D. 10 : 1 | |
| 2343. |
The equation of the plane passing through the intersection of the planes \[x+y+z=6\] and \[2x+3y+4z+5=0\] the point (1, 1, 1), is [AISSE 1983] |
| A. | \[20x+23y+26z-69=0\] |
| B. | \[20x+23y+26z+69=0\] |
| C. | \[23x+20y+26z-69=0\] |
| D. | None of these |
| Answer» B. \[20x+23y+26z+69=0\] | |
| 2344. |
The length and foot of the perpendicular from the point (7, 14, 5) to the plane \[2x+4y-z=2,\]are [AISSE 1987] |
| A. | \[\sqrt{21},(1,\,2,\,8)\] |
| B. | \[3\sqrt{21},(3,\,2,\,8)\] |
| C. | \[21\sqrt{3},(1,\,2,\,8)\] |
| D. | \[3\sqrt{21},(1,\,2,\,8)\] |
| Answer» E. | |
| 2345. |
The equation of a plane which passes through (2, ?3, 1) and is normal to the line joining the points (3, 4, ?1) and (2, ?1, 5) is given by [AI CBSE 1990; MP PET 1993] |
| A. | \[x+5y-6z+19=0\] |
| B. | \[x-5y+6z-19=0\] |
| C. | \[x+5y+6z+19=0\] |
| D. | \[x-5y-6z-19=0\] |
| Answer» B. \[x-5y+6z-19=0\] | |
| 2346. |
The co-ordinates of the foot of the perpendicular drawn from the origin to a plane is (2, 4, ?3). The equation of the plane is |
| A. | \[2x-4y-3z=29\] |
| B. | \[2x-4y+3z=29\] |
| C. | \[2x+4y-3z=29\] |
| D. | None of these |
| Answer» D. None of these | |
| 2347. |
The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is |
| A. | \[3x+2z=1\] |
| B. | \[3x+2z=6\] |
| C. | \[2x+3z=6\] |
| D. | \[3x+2z=0\] |
| Answer» C. \[2x+3z=6\] | |
| 2348. |
The angle between the planes \[2x-y+z=6\] and \[x+y+2z=7\] is [MP PET 1991, 98, 2000, 01, 03; RPET 2001] |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[0{}^\circ \] |
| D. | \[60{}^\circ \] |
| Answer» E. | |
| 2349. |
The equation of yz-plane is [MP PET 1988] |
| A. | \[x=0\] |
| B. | \[y=0\] |
| C. | \[z=0\] |
| D. | \[x+y+z=0\] |
| Answer» B. \[y=0\] | |
| 2350. |
The equation of the perpendicular from the point \[(\alpha ,\beta ,\gamma )\] to the plane \[ax+by+cz+d=0\]is [MP PET 2003] |
| A. | \[a(x-\alpha )+b(y-\beta )+c(z-\gamma )=0\] |
| B. | \[\frac{x-\alpha }{a}=\frac{y-\beta }{b}=\frac{z-\gamma }{c}\] |
| C. | \[a(x-\alpha )+b(y-\beta )+c(z-\gamma )=abc\] |
| D. | None of these |
| Answer» C. \[a(x-\alpha )+b(y-\beta )+c(z-\gamma )=abc\] | |