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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
(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
(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)
(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
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
(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
(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
(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
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
(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
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
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
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 |}
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)
(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
(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)
(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
Answer: 12/13, 4/13, 3/13
(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
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
(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
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