NCERT Class 11 Chapter 12 Maths Introduction to Three MCQ

NCERT Class 11 Chapter 12 Maths Introduction to Three MCQ | Questions & Answers: Students who wish to acquire knowledge about NCERT Class 11 Chapter 12 Maths Introduction to Three concepts should go through this article and right away attempt the online quiz that we have accommodated here.

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1. If orthocentre and circumcentre of a triangle are respectively (1, 1, 1) and (3, 2, 2), then the coordinates of its centroid is

A. (-7/3 , 5/3 , 5/3,)

B. (7/3 , 5/3 , 5/3,)

C. (5/3 , 7/3 , 5/3)

D. None of these

2. A plane is parallel xy-plane, so it is perpendicular to

A. z-axis

B. y-axis

C. x-axis

D. None of these

3. The locus of a point for which y = 0, z = 0 is

A. equation of x-axis

B. equation of y-axis

C. equation of z-axis

D. None of these

4. If the vertices of a triangle are A(0, 4, 1), B(2, 3, -1) and C(4, 5, 0), then orthocentre of a ΔABC is

A. (4, 5, 0)

B. (2, 3, – 1)

C. (– 2, 3, – 1)

D. None of the above

5. The points (5, 2, 4), (6, -1, 2) and (8, -7, k) are collinear, if k is equal to

A. -2

B. 2

C. 3

D. -1

6. The point A(1, -1, 3), B(2, -4, 5) and C(5, -13, 11) are

A. collinear

B. non-collinear

C. Do not say anything

D. None of these

7. The distance of point P(3, 4, 5) from the yz-plane is

A. 3 units

B. 4 units

C. 5 units

D. 550 units

8. What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis?

A. √41

B. √34

C. 5

D. None of these

9. If the distance between the points (a, 0, 1) and (0, 1, 2) is √27, then the value of a is

A. 5

B. ±5

C. – 5

D. None of these

10. If x-coordinate of a point P of line joining the points Q(2, 2, 1) and R(5, 2, -2) is 4, then the z-coordinate of P is

A. –2

B. –1

C. 1

D. 2

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11. If A and B be the points (3, 4, 5) and (– 1, 3, – 7) respectively, find the equation of the set of points P such that (PA)2+(PB)2 =0 , where K is a constant.

A. 2(X2+Y2+Z2)+4X+14Y+4Z+109-K2=0

B. 2(X2+Y2+Z2)-4X-14Y+4Z+109-K2=0

C. X2+Y2+Z2+4X+14Y+4Z109-K2=0

D. None of the above

12. Distance of the point (1, 2, 3) from the coordinate axes are

A. 13, 10, 5

B. √13, √10, √5

C. √5, √13, √10

D. 1/√13, 1/√10, 1/√5

13. If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is

A. 6

B. 3√2

C. 2√3

D. None of these

14. The coordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0), (0, b, 0), (0, 0, c) are given by

A. (a/2 , b/2 , c/2,)

B. ( -a/2 , -b/2 , c/2,)

C. (a/2 , -b/2 , c/2,)

D. (-a/2 , b/2 , c/2,)

15. If x2+y2 = 1, then the distance from the point (x, y, 1-x2-y2 ) to the origin is

A. 1

B. – 1

C. 0

D. 2

16. Three vertices of a parallelogram ABCD are A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2). Find the fourth vertex D.

A. (– 4, – 7, – 6)

B. (4, 7, 6)

C. (4, 7, – 6)

D. None of these

17. If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is

A. 2 √3

B. 3√2

C. √2

D. √3

18. The points (5, – 4, 2),(4,– 3, 1), (7, -6, 4) and (8, – 7, 5) are the vertices of

A. a rectangle

B. a square

C. a parallelogram

D. None of these

19. If the coordinates of the vertices of a ΔABC are A(-1, 3, 2), B(2, 3, 5) and C(3, 5, - 2), then ? ∠A is equal to

A. 45°

B. 60°

C. 90°

D. 30°

20. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (– 2, 4, 7) and (3, – 5, 8).

A. externally 2 : 3

B. internally 2 : 3

C. internally 3 : 2

D. externally 3 : 2

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21. ind the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, -4, 6) in the ratio 2 : 3 externally.

A. (– 8, – 17, 3)

B. (– 8, 17, 3)

C. (8, – 17, 3)

D. None of these

22. Find the length of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and C(6, 0, 0).

A. 7, 7, √34

B. 7, 8, √34

C. 7, 9, √34

D. None of these

23. Find the coordinates of the points which trisect the line segment joining the points P(4 , 2, -6) and Q(10, -16, 6)

A. (6, – 4, – 2), (8, – 10, 2)

B. (6, 4, – 2), (8, – 10, 2)

C. (6, – 4, – 2), (8, 10, 2

D. None of these

24. Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E(3, 0, 1) and F (-1, 1, -4).

A. (1, 1, 2)

B. (1, 1, – 2)

C. (– 1, –1, –2)

D. (1, –1, –2)

25. The points A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) are vertices of a

A. square

B. rhombus

C. rectangle

D. None of these