Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

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.

3551.

The equation to the straight line passing through the points (4, ?5, ?2) and (?1, 5, 3) is [MP PET 2003]

A.                                                               \[\frac{x-4}{1}=\frac{y+5}{-2}=\frac{z+2}{-1}\]
B.                                                               \[\frac{x+1}{1}=\frac{y-5}{2}=\frac{z-3}{-1}\]
C.                                                               \[\frac{x}{-1}=\frac{y}{5}=\frac{z}{3}\]
D.                                                               \[\frac{x}{4}=\frac{y}{-5}=\frac{z}{-2}\]
Answer» B.                                                               \[\frac{x+1}{1}=\frac{y-5}{2}=\frac{z-3}{-1}\]
3552.

If direction cosines of two lines are proportional to (2, 3, ?6) and (3, ?4, 5), then the acute angle between them is                                                                                           [MP PET  2003]

A.                                                               \[{{\cos }^{-1}}\left( \frac{49}{36} \right)\]
B.                                                               \[{{\cos }^{-1}}\left( \frac{18\sqrt{2}}{35} \right)\]
C.                                                               \[96{}^\circ \]
D.                                                               \[{{\cos }^{-1}}\left( \frac{18}{35} \right)\]
Answer» C.                                                               \[96{}^\circ \]
3553.

The line \[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\] and \[\frac{x-1}{k}=\] \[\frac{y-4}{2}=\frac{z-5}{1}\] are coplanar, if [AIEEE 2003]

A.                                                               \[k=0\]or ?1
B.                                                               \[k=0\]or 1
C.                                                               \[k=0\]or ?3
D.                                                               \[k=3\]or ?3
Answer» D.                                                               \[k=3\]or ?3
3554.

The angle between a line with direction ratios 2 : 2 : 1 and a line joining (3, 1, 4) to (7, 2, 12) is                     [DCE 2002]

A.                                                               \[{{\cos }^{-1}}(2/3)\]
B.                                                               \[{{\cos }^{-1}}(-2/3)\]
C.                                                               \[{{\tan }^{-1}}(2/3)\]
D.                                                               None of these
Answer» B.                                                               \[{{\cos }^{-1}}(-2/3)\]
3555.

The straight line \[\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}\]is [RPET 2002]

A.                                                               Parallel to x-axis
B.                                                               Parallel to y-axis
C.                                                               Parallel to z-axis
D.                                                               Perpendicular to z-axis
Answer» E.
3556.

Equation of x-axis is [MP PET 2002]

A.                                                               \[\frac{x}{1}=\frac{y}{1}=\frac{z}{1}\]
B.                                                               \[\frac{x}{0}=\frac{y}{1}=\frac{z}{1}\]
C.                                                               \[\frac{x}{1}=\frac{y}{0}=\frac{z}{0}\]
D.                                                               \[\frac{x}{0}=\frac{y}{0}=\frac{z}{1}\]
Answer» D.                                                               \[\frac{x}{0}=\frac{y}{0}=\frac{z}{1}\]
3557.

The angle between the lines \[\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}\] and \[\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\] is [Pb. CET 2002]

A.                                                               \[{{\cos }^{-1}}\frac{1}{5}\]
B.                                                               \[{{\cos }^{-1}}\frac{1}{3}\]
C.                                                               \[{{\cos }^{-1}}\frac{1}{2}\]
D.                                                               \[{{\cos }^{-1}}\frac{1}{4}\]
Answer» B.                                                               \[{{\cos }^{-1}}\frac{1}{3}\]
3558.

If the direction ratios of two lines are given by \[3lm-4\,ln+mn=0\] and \[l+2m+3n=0\], then the angle between the lines is [EAMCET 2003]

A.                                                               \[\pi /2\]
B.                                                               \[\pi /3\]
C.                                                               \[\pi /4\]
D.                                                               \[\pi /6\]
Answer» B.                                                               \[\pi /3\]
3559.

The shortest distance between the lines \[\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\] and \[\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\] is [RPET 2001; MP PET 2002]

A.                                                               \[\sqrt{30}\]
B.                                                               \[2\sqrt{30}\]
C.                                                               \[5\sqrt{30}\]
D.                                                               \[3\sqrt{30}\]
Answer» E.
3560.

If direction ratios of two lines are \[5,\,\,-12,\,13\] and \[-3,\,4,\,5\] then the angle between them is [RPET 2001]

A.                                                               \[{{\cos }^{-1}}(1/65)\]
B.                                                               \[{{\cos }^{-1}}(2/65)\]
C.                                                               \[{{\cos }^{-1}}(3/65)\]
D.                                                               \[\pi /2\]
Answer» B.                                                               \[{{\cos }^{-1}}(2/65)\]
3561.

The angle between the straight lines \[\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}\] and  \[\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}\] is [MP PET 2000]

A.                                                               \[45{}^\circ \]
B.                                                               \[30{}^\circ \]
C.                                                               \[60{}^\circ \]
D.                                                               \[90{}^\circ \]
Answer» E.
3562.

The acute angle between the line joining the points (2,1,?3), (?3,1,7) and a line parallel to \[\frac{x-1}{3}=\] \[\frac{y}{4}=\frac{z+3}{5}\] through the point (?1, 0, 4) is [MP PET 1998]

A.                                                               \[{{\cos }^{-1}}\left( \frac{7}{5\sqrt{10}} \right)\]
B.                                                               \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{10}} \right)\]
C.                                                               \[{{\cos }^{-1}}\left( \frac{3}{5\sqrt{10}} \right)\]
D.                                                               \[{{\cos }^{-1}}\left( \frac{1}{5\sqrt{10}} \right)\]
Answer» B.                                                               \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{10}} \right)\]
3563.

The angle between the pair of lines with direction ratios       (1, 1, 2) and \[(\sqrt{3}-1,-\sqrt{3}-1,4)\] is       [MP PET 1997, 2000]

A.                                                               \[30{}^\circ \]
B.                                                               \[45{}^\circ \]
C.                                                               \[60{}^\circ \]
D.                                                               \[90{}^\circ \]
Answer» D.                                                               \[90{}^\circ \]
3564.

The equation of the line passing through the points ( 3, 2, 4) and (4, 5, 2) is

A.                                                               \[\frac{x+3}{1}=\frac{y+2}{3}=\frac{z+4}{-2}\]
B.                                                               \[\frac{x-3}{1}=\frac{y-2}{3}=\frac{z-4}{-2}\]
C.                                                               \[\frac{x+3}{7}=\frac{y+2}{7}=\frac{z+4}{6}\]
D.                                                               \[\frac{x-3}{7}=\frac{y-2}{7}=\frac{z-4}{6}\]
Answer» C.                                                               \[\frac{x+3}{7}=\frac{y+2}{7}=\frac{z+4}{6}\]
3565.

The angle between the lines \[\frac{x+4}{1}=\frac{y-3}{2}=\frac{z+2}{3}\] and \[\frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1}\] is

A.                                                               \[{{\sin }^{-1}}\left( \frac{1}{7} \right)\]
B.                                                               \[{{\cos }^{-1}}\left( \frac{2}{7} \right)\]
C.                                                               \[{{\cos }^{-1}}\left( \frac{1}{7} \right)\]
D.                                                               None of these
Answer» D.                                                               None of these
3566.

The straight lines \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}\]                                                                                     and \[\frac{x-1}{2}=\frac{y-2}{2}=\frac{z-3}{-2}\] are

A.                                                               Parallel lines
B.                                                               Intersecting at \[60{}^\circ \]
C.                                                               Skew lines
D.                                                               Intersecting at right angle
Answer» E.
3567.

The angle between two lines \[\frac{x+1}{2}=\]\[\frac{y+3}{2}=\frac{z-4}{-1}\] and \[\frac{x-4}{1}=\frac{y+4}{2}=\frac{z+1}{2}\] is [MP PET 1996]

A.                                                               \[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]
B.                                                               \[{{\cos }^{-1}}\left( \frac{2}{9} \right)\]
C.                                                               \[{{\cos }^{-1}}\left( \frac{3}{9} \right)\]
D.                                                               \[{{\cos }^{-1}}\left( \frac{4}{9} \right)\]
Answer» E.
3568.

If the co-ordinates of the points A, B, C, D be (1, 2, 3),         (4, 5, 7), (?4, 3, ?6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is

A.                                                               \[\frac{\pi }{6}\]
B.                                                               \[\frac{\pi }{4}\]
C.                                                               \[\frac{\pi }{3}\]
D.                                                               None of these
Answer» E.
3569.

The perpendicular distance of the point (2, 4, ?1) from the line \[\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}\] is [Kurukshetra CEE 1996]

A.                                                               3
B.                                                               5
C.                                                               7
D.                                                               9
Answer» D.                                                               9
3570.

The angle between the lines whose direction cosines are connected by the relations \[l+m+n=0\] and \[2lm+2nl-mn=0\],  is

A.                                                               \[\frac{\pi }{3}\]
B.                                                               \[\frac{2\pi }{3}\]
C.                                                               \[\pi \]
D.                                                               None of these
Answer» C.                                                               \[\pi \]
3571.

The length of the perpendicular from point (1, 2, 3) to the line \[\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\]is [MP PET 1997]

A.                                                               5
B.                                                               6
C.                                                               7
D.                                                               8
Answer» D.                                                               8
3572.

The length of the perpendicular drawn from the point            (5, 4, ?1) on the line \[\frac{x-1}{2}=\frac{y}{9}=\frac{z}{5}\] is

A.                                                               \[\sqrt{\frac{110}{2109}}\]
B.                                                               \[\sqrt{\frac{2109}{110}}\]
C.                                                               \[\frac{2109}{110}\]
D.                                                               54
Answer» C.                                                               \[\frac{2109}{110}\]
3573.

The equation of straight line passing through the point (a, b, c) and parallel to z- axis, is         [MP PET 1995; Pb. CET 2000]

A.                                                               \[\frac{x-a}{1}=\frac{y-b}{1}=\frac{z-c}{0}\]
B.                                                               \[\frac{x-a}{0}=\frac{y-b}{1}=\frac{z-c}{1}\]
C.                                                               \[\frac{x-a}{1}=\frac{y-b}{0}=\frac{z-c}{0}\]
D.                                                               \[\frac{x-a}{0}=\frac{y-b}{0}=\frac{z-c}{1}\]
Answer» E.
3574.

The equation of straight line passing through the points          (a, b, c) and (a ? b, b? c, c ? a), is [MP PET 1994]

A.                                                               \[\frac{x-a}{a-b}=\frac{y-b}{b-c}=\frac{z-c}{c-a}\]
B.                                                               \[\frac{x-a}{b}=\frac{y-b}{c}=\frac{z-c}{a}\]
C.                                                               \[\frac{x-a}{a}=\frac{y-b}{b}=\frac{z-c}{c}\]
D.                                                               \[\frac{x-a}{2a-b}=\frac{y-b}{2b-c}=\frac{z-c}{2c-a}\]
Answer» C.                                                               \[\frac{x-a}{a}=\frac{y-b}{b}=\frac{z-c}{c}\]
3575.

The angle between the lines whose direction cosines satisfy the equations \[l+m+n=0\], \[{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\] is given by [MP PET 1993; RPET 2001]

A.                                                               \[\frac{2\pi }{3}\]
B.                                                               \[\frac{\pi }{6}\]
C.                                                               \[\frac{5\pi }{6}\]
D.                                                               \[\frac{\pi }{3}\]
Answer» E.
3576.

The symmetric equation of lines \[3x+2y+z-5=0\] and \[x+y-2z-3=0\], is

A.                                                               \[\frac{x-1}{5}=\frac{y-4}{7}=\frac{z-0}{1}\]
B.                                                               \[\frac{x+1}{5}=\frac{y+4}{7}=\frac{z-0}{1}\]
C.                                                               \[\frac{x+1}{-5}=\frac{y-4}{7}=\frac{z-0}{1}\]
D.                                                               \[\frac{x-1}{-5}=\frac{y-4}{7}=\frac{z-0}{1}\]
Answer» D.                                                               \[\frac{x-1}{-5}=\frac{y-4}{7}=\frac{z-0}{1}\]
3577.

The co-ordinates of the foot of perpendicular drawn from the origin to the line joining the points (?9, 4, 5) and (10, 0, ?1) will be

A.                                                               (? 3, 2, 1)
B.                                                               (1, 2, 2)
C.                                                               (4, 5, 3)
D.                                                               None of these
Answer» E.
3578.

Distance of the point \[({{x}_{1}},{{y}_{1}},{{z}_{1}})\] from the line\[\frac{x-{{x}_{2}}}{l}=\frac{y-{{y}_{2}}}{m}=\frac{z-{{z}_{2}}}{n}\], where \[l,\]m and n are the direction cosines of line is

A.                     \[\sqrt{{{({{x}_{1}}-{{x}_{2}})}^{2}}+{{({{y}_{1}}-{{y}_{2}})}^{2}}+{{({{z}_{1}}-{{z}_{2}})}^{2}}-{{[l({{x}_{1}}-{{x}_{2}})+m({{y}_{1}}-{{y}_{2}})+n({{z}_{1}}-{{z}_{2}})]}^{2}}}\]
B.                                                               \[\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}+{{({{z}_{2}}-{{z}_{1}})}^{2}}}\]
C.                                                               \[\sqrt{({{x}_{2}}-{{x}_{1}})l+({{y}_{2}}-{{y}_{1}})m+({{z}_{2}}-{{z}_{1}})n}\]
D.                                                               None of these
Answer» B.                                                               \[\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}+{{({{z}_{2}}-{{z}_{1}})}^{2}}}\]
3579.

The equation of a line passing through the point  (?3, 2, ? 4) and equally inclined to the axes, are

A.                                                               \[x-3=y+2=z-4\]
B.                                                               \[x+3=y-2=z+4\]
C.                                                               \[\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\]
D.                                                               None of these
Answer» C.                                                               \[\frac{x+3}{1}=\frac{y-2}{2}=\frac{z+4}{3}\]
3580.

The equation of the plane which bisects the line joining the points (?1, 2, 3) and (3, ?5, 6) at right angle, is

A.            \[4x-7y-3z=8\]
B.            \[4x+2y-3z=28\]
C.            \[4x-7y+3z=28\]
D.            \[4x-7y-3z=28\]
Answer» D.            \[4x-7y-3z=28\]
3581.

The equation of the plane passing through the lines \[\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}\]and \[\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}\] is

A.            \[11x-y-3z=35\]
B.            \[11x+y-3z=35\]
C.            \[11x-y+3z=35\]
D.            None of these
Answer» E.
3582.

The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane \[x+2y-5z+9=0\] is                     [MP PET 1991]

A.            \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{-5}\]
B.            \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+5}{3}\]
C.            \[\frac{x+1}{1}=\frac{y+2}{2}=\frac{z+3}{-5}\]
D.            \[\frac{x+1}{1}=\frac{y+2}{2}=\frac{z-5}{3}\]
Answer» B.            \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+5}{3}\]
3583.

The equation of the plane passing through the origin and perpendicular to the line \[x=2y=3z\]is

A.            \[6x+3y+2z=0\]
B.            \[x+2y+3z=0\]
C.            \[3x+2y+z=0\]
D.            None of these
Answer» B.            \[x+2y+3z=0\]
3584.

If the equation of a line and a plane be \[\frac{x+3}{2}=\frac{y-4}{3}=\frac{z+5}{2}\]and\[4x-2y-z=1\]respectively, then

A.            Line is parallel to the plane      
B.            Line is perpendicular to the plane
C.            Line lies in the plane
D.            None of these
Answer» B.            Line is perpendicular to the plane
3585.

The equation of the plane through the point \[(2,-1,-3)\]and parallel to the lines \[\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\] and \[\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\] is [Kerala (Engg.) 2005]

A.  \[8x+14y+13z+37=0\]
B.            \[8x-14y+13z+37=0\]
C.            \[8x+14y-13z+37=0\]
D.            \[8x+14y+13z-37=0\]
E. (e)       \[8x-14y-13z-37=0\]
Answer» B.            \[8x-14y+13z+37=0\]
3586.

The point of intersection of the line \[\frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2}\] and plane \[2x-y+3z-1=0\] is [Orissa JEE 2005]

A.            \[(10,\,\,-10,\,3)\]
B.            \[(10,\,\,10,\,-3)\]
C.            \[(-10,\,\,10,\,3)\]
D.            None of these
Answer» C.            \[(-10,\,\,10,\,3)\]
3587.

The line joining the points (3, 5, ?7) and (?2, 1, 8) meets the yz-plane at point [RPET 2003]

A.            \[\left( 0,\,\frac{13}{5},\,2 \right)\]
B.            \[\left( 2,\,0,\,\frac{13}{5} \right)\]
C.            \[\left( 0,\,2,\,\frac{13}{5} \right)\]
D.            (2, 2, 0)
Answer» B.            \[\left( 2,\,0,\,\frac{13}{5} \right)\]
3588.

A plane which passes through the point (3, 2, 0) and the line \[\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}\]is [AIEEE 2002]

A.            \[x-y+z=1\]
B.            \[x+y+z=5\]
C.            \[x+2y-z=0\]
D.            \[2x-y+z=5\]
Answer» B.            \[x+y+z=5\]
3589.

The ratio in which the line joining the points (2, 4, 5) and  (3, 5, ?4) is divided by the yz-plane is [MP PET 2002; RPET 2002]

A.            \[2:3\]
B.            \[3:2\]
C.            \[-2:3\]
D.            \[4:-3\]
Answer» D.            \[4:-3\]
3590.

The equation of the plane passing through the line \[\frac{x-1}{5}=\frac{y+2}{6}=\frac{z-3}{4}\]and the point (4, 3, 7) is  [MP PET 2001]

A.            \[4x+8y+7z=41\]
B.            \[4x-8y+7z=41\]
C.            \[4x-8y-7z=41\]
D.            \[4x-8y+7z=39\]
Answer» C.            \[4x-8y-7z=41\]
3591.

Under what condition does a straight line \[\frac{x-{{x}_{0}}}{l}=\]\[\frac{y-{{y}_{0}}}{m}=\frac{z-{{z}_{0}}}{n}\] is parallel to the xy-plane [AMU 2000]

A.            \[l=0\]
B.            \[m=0\]
C.            \[n=0\]
D.            \[l=0,m=0\]
Answer» D.            \[l=0,m=0\]
3592.

The xy-plane divides the line joining the points (?1, 3, 4) and (2, ?5, 6) [RPET 2000]

A.            Internally in the ratio 2 : 3        
B.            Internally in the ratio 3 : 2
C.            Externally in the ratio 2 : 3       
D.            Externally in the ratio 3 : 2
Answer» D.            Externally in the ratio 3 : 2
3593.

The equation of the plane containing the line \[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and the point (0, 7, ?7) is [Roorkee 1999]

A.            \[x+y+z=1\]
B.            \[x+y+z=2\]
C.            \[x+y+z=0\]
D.            None of these
Answer» D.            None of these
3594.

The angle between the line \[\frac{x-1}{2}=\] \[\frac{y-2}{1}=\frac{z+3}{-2}\] and the plane \[x+y+4=0\], is [MP PET 1999]

A.            \[0{}^\circ \]
B.            \[30{}^\circ \]
C.            \[45{}^\circ \]
D.            \[90{}^\circ \]
Answer» D.            \[90{}^\circ \]
3595.

The co-ordinates of the point where the line \[\frac{x-6}{-1}=\frac{y+1}{0}=\frac{z+3}{4}\] meets the plane \[x+y-z=3\]are [MP PET 1998; Pb. CET 2002]

A.            (2, 1, 0)
B.            (7, ?1, ?7)
C.            (1, 2, ?6)
D.            (5, ?1, 1)
Answer» E.
3596.

The co-ordinates of the point where the line through \[P(3,\,4,\,1)\]  and \[Q(5,1,6)\] crosses the xy-plane are [MP PET 1997]

A.            \[\frac{3}{5},\frac{13}{5},\frac{23}{5}\]
B.            \[\frac{13}{5},\frac{23}{5},\frac{3}{5}\]
C.            \[\frac{13}{5},\frac{23}{5},0\]
D.            \[\frac{13}{5},0,\,0\]
Answer» D.            \[\frac{13}{5},0,\,0\]
3597.

The line \[\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\] is parallel to the plane

A.            \[2x+3y+4z=29\]
B.            \[3x+4y-5z=10\]
C.            \[3x+4y+5z=38\]
D.            \[x+y+z=0\]
Answer» C.            \[3x+4y+5z=38\]
3598.

The equation of the plane through the origin containing the line \[\frac{x-1}{5}=\frac{y-2}{4}=\frac{z-3}{5}\] is

A.            \[2x+5y-6z=0\]
B.            \[x+5y-5z=0\]
C.            \[x-5y+3z=0\]
D.            \[x+y-z=0\]
Answer» D.            \[x+y-z=0\]
3599.

The point of intersection of the line \[\frac{x}{1}=\frac{y-1}{2}=\frac{z+2}{3}\] and the  plane \[2x+3y+z=0\]is  [MP PET 1989]

A.            (0, 1, ?2)
B.            (1, 2, 3)
C.            (?1, 9, ?25)
D.            \[\left( \frac{-1}{11},\frac{9}{11}\frac{-25}{11} \right)\]
Answer» E.
3600.

The equation of the plane which bisects the line joining      (2, 3, 4) and (6, 7, 8) is [CET 1991, 93]

A.            \[x+y+z-15=0\]
B.            \[x-y+z-15=0\]
C.            \[x-y-z-15=0\]
D.            \[x+y+z+15=0\]
Answer» B.            \[x-y+z-15=0\]