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Free download in PDF Class 12 Maths Chapter 11 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 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
[A]
9 sq. units
[B]
18 sq. units
[C]
27 sq. units
[D]
81 sq. units
(2)
The reflection of the point (a, β, γ) in the xy-plane is
[A]
(α, β, 0)
[B]
(0, 0, γ)
[C]
(- α, – β, γ)
[D]
(α, β, γ)
(3)
The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
[A]
3x – 5y + 2z – 13 = 0
[B]
5x – 3y + 2z + 13 = 0
[C]
3x – 2y + 5z + 13 = 0
[D]
3x – 5y + 2z + 13 = 0
Answer: 3x – 5y + 2z + 13 = 0
(4)
The line x = 1, y = 2 is
[A]
parallel to x-axis
[B]
parallel to y-axis
[C]
parallel to z-axis
[D]
None of these
Answer: parallel to z-axis
(5)
If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
[A]
-2
[B]
-1
[C]
1
[D]
2
(6)
If α, β, γ are the angle which a half ray makes with the positive directions of the axis then sin²α + sin²β + sin²γ =
(7)
The plane x + y = 0
[A]
is parallel to z-axis
[B]
is perpendicular to z-axis
[C]
passes through z-axis
[D]
None of these
Answer: passes through z-axis
(8)
The locus of xy + yz = 0 is
[A]
A pair of st. lines
[B]
A pair of parallel lines
[C]
A pair of parallel planes
[D]
A pair of perpendicular planes
Answer: A pair of perpendicular planes
(9)
The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
[A]
3x – 4y – 5z – 6 = 0
[B]
3x – 4y + 5z + 6 = 0
[C]
3x – 4y + 5z = 0
[D]
3x + 4y – 5z + 6 = 0
(10)
The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
[A]
3, 2, -1
[B]
-3, 7, 5
[C]
1, -1, 2
[D]
– 11, 4, -5
(11)
The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are
[A]
7, 4,-2
[B]
7, 4, 5
[C]
7, 4, 2
[D]
4, -2, 5
(12)
If a line makes angles Q1, Q21 and Q3 respectively with the coordinate axis then the value of cos² Q1 + cos² Q2 + cos² Q3
[A]
2
[B]
1
[C]
4
[D]
3/2
(13)
The distance of the point (-3, 4, 5) from the origin
[A]
50
[B]
5√2
[C]
6
[D]
None of these
(14)
The equation x² – x – 2 = 0 in three dimensional space is represented by
[A]
A pair of parallel planes
[B]
A pair of straight lines
[C]
A pair of perpendicular plane
[D]
None of these
Answer: A pair of parallel planes
(15)
How many lines through the origin in make equal angles with the coordinate axis?
(16)
The direction cosines of any normal to the xy plane are
[A]
1, 0 ,0
[B]
0, 1, 0
[C]
1, 1, 0
[D]
1, 1, 0
(17)
The equation xy = 0 in three dimensional space is represented by
[A]
a plane
[B]
two plane are right angles
[C]
a pair of parallel planes
[D]
a pair of st. line
Answer: two plane are right angles
(18)
(2, – 3, – 1) 2x – 3y + 6z + 7 = 0
[A]
4
[B]
3
[C]
2
[D]
1/5
(19)
If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
[A]
3x + 5y – 6z + 3 = 0
[B]
2x – 5y – 6z + 3 = 0
[C]
2x + 5y – 6z + k = 0
[D]
None of these
Answer: 2x + 5y – 6z + k = 0
(20)
The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is
[A]
4
[B]
3
[C]
2
[D]
1/5
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