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( 2 )If the plane 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres o
and x2 + y2 + z2 - 10x + 4y - 2z = 8, then a equals

(a) -1 (b) 1 (c) -2 (d) 2

^^^ ^^^
( 3 )The distance between the liner2 i - 2 j + 3k +  ( -i j + 4 k ) and the
 ^^^
planer .( i + 5 j + k ) = 5 s

10 10 3 10
(a) (b) c (d)
9 3 3 10 3

x  1y - 1z - 2
( 1 )If the angle  between the line = = and the plane
1 2 2
2x - y + x + 4 = 0 is such that sin  = 1 , then the value of  is
3

5 - 3 3 4
(a)
3
(b) (c)
4
(d) - 3
5
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( 7 )Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

3 5 7 9
(a) (b) (c) (d)
2 2 2 2

( 8 )A line with direction cosines proportional to 2, 1, 2 meets each o thenes

x = y + a = z and x + a = 2y = 2z. The coordinates of each
x2 of the p ints of intersection are given by
( 5 )The p ane x + 2y - z = 4 cuts the sphere of radius + y2 + z2 - x + z - 2 = 0 in a circle

( a ) ( 3a, 3a, 3a ), ( a, a, a ) ( b ) ( 3a, 2a, 3a ), ( a, a, a )

(ca ) (3 3a, 2a,
( b3a
) ),1 ( a, a,
( c 2a
) 2) (d( d) )2( 2a, 3a, 3a ), ( 2a, a, a )

( 6 ) A line makes the same angle  with each of the X- and Z- axis. If thet ,angle
2  which it makes
( 9 )If the straight lines x = 1 + s, y = - 3 - s, z = 1 + s and x = y = 1 + t,
with parameters s and t respectively, are co-planar, then 
z = 2 - t, equals
2 1 3 2
(a) (b) (c) (d)
3 5 5- 1 5
(a) -2 (b) -1 (c) (d) 0
2

( 10 ) The intersection of the sphe es x2 + y2 + z2 + 7x - 2y - z = 13 and

x2 + y2 + z2 - 3x + 3y + 4z = 8 is the same as the intersection of one of the
spheres and the plane

(a) x - y - z = ( b ) x - 2y - z = 1
( c ) x - y2z = 1 ( d ) 2x - y - z = 1

( 11 ) The ines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ will be perpendicular if and o

( a ) aa’ + cc’ + 1 = 0
( b ) aa’ + cc’ = 0
( c ) aa’ + bb’ = 0and ( d ) aa’ + bb’ + cc’ = 0

x -2 y -3 z -4 x-1k y -4 z -5
( 12 ) The lines = = and = = are coplanar, if
1 1 -k 2 1

( a ) k = 0 or - 1 ( c ) k( b=) 0kor= -13or - 1 ( d ) k = 3 or - 3

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( 14 ) The direction cosines of the normal to the plane x + 2y - 3z4 = 0 are

( a )- 1 2 , 3 1 2 3
, - (b) , ,
14 14 14 14 14 14
1 1 2 3
14 , 2 3 14 , 1 , - 14
( c )- , (d)
14 14

( 13 )Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c

1  1  1  1 11 1  1 - 1  111-=
(a)  = 0( b )
a2b2c2 a'2 b'2c'2 a2b2c2 a'2b'2c'
111  111 1  1  1111
(c) -- -- = 0( d ) --- = 0
a2b2c2 a'2b'2c'2 a2b2c2 a'2b'2 c2

( 15 ) The radius of a circle in which the sphe e x2 + y2 + z2 + 2x - 2y - 4z = 19 is cut by the plane

(a) 1 (b) 2 (c) 3 (d) 4

( 16 ) The shortest distance f om the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y -

( a ) 13 ( b ) 26 ( c ) 39 ( d ) 11
 x y z
line == is
2 3- 6

(a) 1 (b) 7 (c) 3 ( d ) 13 Page 4

( 19)The
( 18 ) The angle between
co-ordinates thepoint
of the planes
in 2x - y +the3z line
which = 6 joining
and x the
+ y points(
+ 2z = 3,7 5,
is - 7 )and ( - 2, 1, 8 ) an
( a ) 0 ( b ) 30 ( c ) 45 ( d ) 60
( a )  0, 13 , 2  ( b )  0, - 13 , - 2 
   
 5   5 
 0, - 13 , 2   0, 13 , 2 
(c)   (d)  
 55x  - 1y - 2z - 3 55  x - 1 3k y - 5 z - 6
( 20 ) If the lines = = and = = are at right
-3 2k is 2 1 -5
angles, then the value of k

- 10 7
(a) (b) - 10 (c) - 10 (d) -7
7


( 21 )A unitvectorperpendiculartotheplaneof a=2 i - 6 j - 3 kand
   
b = 4 i 3 j - k is

 
(a) 4 i  3 j - k (b) 2 i - 6 j - 3k
26 7
 
3 i - 2 j  6k 2 i - 3 j - 6k
(c) (d)
7 7


( 22 ) A unit vector normal tthe plane through the pointsi , 2 jand 3 kis

 
(a) 6 i  3 j  2k ( b )i  2 j  3 k
   
6 i 3 j  2k 6 i 3 j  2k
(c) (d)
7 7

( 23 ) A plane at a unit distance from the origin intersects the coordinate axes at P, Q and
1 1 1
R If the locus of the centroid of PQR satisfies the equation   = k,
x2 y2 z2
then the value of k is

(a) 1 (b) 3 (c) 6 (d) 9

x -1 y  1z - 1 x -3 y-k2 z
( 24 ) Two lines = = and = = intersect at a point, then
2 3 4 1 1
k is

3 9 2
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x - 1y - 2z - k
( 25 ) If the line = = lies exactly on the plane 2x - 4y + z = 7, then the
1 1 2
value of k is

(a) 7 (b) -7 (c) 1 ( d ) no real value

( 26 ) There are infinite planes passing through the points ( 3, 6, 7 ) touching the sphere x2 + y2

( a ) 12 ( b ) 23 ( c ) 67 ( d ) 47

( 27 ) The mid-points of the chords cut off by thlines through the point ( 3, 6, 7 )
intersecting the radius = sphere x2 + y2 + z2 - 2x4y - 6z = 11 lie on a sphere whose

(a) 3 (b) 4 (c) 5 (d) 6

( 28 ) The ratio of magnitudes of tota surface area to volume of a right circular cone with vertex at orig

(a) 1 (b) 2 c) 3 (d) 4

( 29 )The direct on of normal to the plane passing through origin and the line of intersection of the plan

( a ) ( 1, 2, 3 ) ( b ) ( 3, 2, 1 ) ( c ) ( 2, 3, 1 ) ( d ) ( 3, 1, 2 )

( 30 ) The point which is farthest on the sphere x2 + y2 + z2 = 144 from thpoint ( 2, 4, 4 ) is

( a ) ( 3, 6, 6 ) ( b ) ( - 3, - 6, - 6 ) ( c ) ( 4, 8, 8 ) ( d )- 4, - 8, - 8 )
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Answers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
a c b b b c c b a d a c d d c a a a d a

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
c c d b a d a c b b d c d d b c d