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Free download in PDF Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries./p>
1
The distance of point P(3,4, 5) from the yz-plane is
A
3 units
B
4 units
C
5 units
D
550
View Answer
2
Under what condition does the equation x2 + y2 + z2 + 2ux + 2vy + 2wz + d represent a real sphere
A
u2 + v2 + w2 = d2
B
u2 + v2 + w2 > d
C
u2 + v2 + w2 < d
D
u2 + v2 + w2 < d2
View Answer
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3
The coordinate of foot of perpendicular drawn from the point A(1, 0, 3) to the join of the point B(4, 7, 1) and C(3, 5, 3) are
A
(5/3, 7/3, 17/3)
B
(5, 7, 17)
C
(5/3, -7/3, 17/3)
D
(5/7, -7/3, -17/3)
View Answer
4
Three planes x + y = 0 , y + z = 0 , and x + z = 0
A
none of these
B
meet in a line
C
meet in a unique point
D
meet taken two at a time in parallel lines
View Answer
Answer:meet in a unique point
5
The locus of a point which moves so that the difference of the squares of its distances from two given points is constant, is a
A
Straight line
B
Plane
C
Sphere
D
None of these
View Answer
6
The coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the YZ plane is
A
(0, 17/2, 13/2)
B
(0, -17/2, -13/2)
C
(0, 17/2, -13/2)
D
None of these
View Answer
7
The ratio in which the line joining the points(1,2,3) and (-3,4,-5) is divided by the xy-plane is
A
2 : 5
B
3 : 5
C
5 : 2
D
5 :3
View Answer
8
The dirction cosines of a line equally inclined to three mutually perpendicular lines having DCs as l1 ,m1 , n1 , l2 ,m2 , n2 , l3 ,m3 , n3 are
A
l1 + l2 , l3 , m1 + m2 + m3 , n1 + n2 + n3
B
(l1 + l2 , l3 )/3, (m1 + m2 + m3 )/3 , (n1 + n2 + n3 )/3
C
(l1 + l2 , l3 )/√3, (m1 + m2 + m3 )/√3 , (n1 + n2 + n3 )/√3
D
None of these
View Answer
Answer:(l1 + l2 , l3 )/√3, (m1 + m2 + m3 )/√3 , (n1 + n2 + n3 )/√3
9
The points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a
A
Rectangle
B
Square
C
Rhombus
D
None of these
View Answer
10
The equation of plane containing the line of intersection of the plane x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1) is
A
20x + 23y + 26z + 69 = 0
B
20x + 23y - 26z - 69 = 0
C
20x - 23y + 26z - 69 = 0
D
20x + 23y + 26z - 69 = 0
View Answer
Answer:20x + 23y + 26z - 69 = 0
11
There is one and only one sphere through
A
4 points not in the same plane
B
4 points not lie in the same straight line
C
none of these
D
3 points not lie in the same line
View Answer
Answer:4 points not in the same plane
12
If the equation of a plane is lx + my + nz = p is in the normal form, then which is not true
A
l, m and n are the direction cosines of the normal to the plane
B
p is the length of the perpendicular from the origin to the plane
C
The plane passes through the origin for all values of p
D
l2 + m2 + n2 = 1
View Answer
Answer:The plane passes through the origin for all values of p
13
The angle between the planes r . n1 = d1 and r . n2 = d2 is
A
cos θ ={|n1 | * |n2 |}/ (n1 . n2 )
B
cos θ = (n1 . n2 )/{|n1 | * |n2 |}2
C
cos θ = (n1 . n2 )/{|n1 | * |n2 |}
D
cos θ = (n1 . n2 )2 /{|n1 | * |n2 |}
View Answer
Answer:cos θ = (n1 . n2 )/{|n1 | * |n2 |}
14
The centroid of ∆ ABC is at (1, 1, 1). If coordinates of A and B are (3, -5, 7) and (-1, 7, -6) respectively then the coordinates of point C is
A
(1, -1, 2)
B
(1, 1, -2)
C
(1, 1, 2)
D
(-1, 1, 2)
View Answer
15
If the points A(1, 0, –6), B(–5, 9, 6) and C(–3, p, q) are collinear, then the value of p and q are
A
-6 and -2
B
-6 and 2
C
6 and -2
D
6 and 2
View Answer
16
The image of the point P(1,3,4) in the plane 2x - y + z = 0 is
A
(-3, 5, 2)
B
(3, 5, 2)
C
(3, -5, 2)
D
(3, 5, -2)
View Answer
17
The projections of a directed line segment on the coordinate axes are 12, 4, 3. The DCS of the line are
A
12/13, -4/13, 3/13
B
-12/13, -4/13, 3/13
C
12/13, 4/13, 3/13
D
None of these
View Answer
18
The equation of plane passing through the point i + j + k and parallel to the plane r . (2i - j + 2k) = 5 is
A
r . (2i - j + 2k) = 2
B
r . (2i - j + 2k) = 3
C
r . (2i - j + 2k) = 4
D
r . (2i - j + 2k) = 5
View Answer
Answer:r . (2i - j + 2k) = 3
19
The vector equation of a sphere having centre at origin and radius 5 is
A
|r| = 5
B
|r| = 25
C
|r| = √5
D
none of these
View Answer
20
A parallelepiped is formed by planes drawn through the points (2,3,5) and (5,9,7), parallel to the coordinate plane. The length of a diagonal of the parallelopiped is
A
7
B
√38
C
√155
D
none of these
View Answer
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