Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Mathematics : Introduction To Three Dimensional Geometry

Match The Following

81.

Match the following columns.


A	The centroid of the triangle formed by (2, 3, - 1), (5, 6, 3), (2, -3 ,1) is	p	(2, 2, 2)
B	The circumcentre of the triangle formed by (1,2, 3) (2, 3, 1), (3, 1, 2) is	q	(3, 1, 4)
C	The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is	r	(1, 1, 0)
D	The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	s	(3, 2, 1)
E	The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is	t	(0, 0, 0)

A. A B C D	(i) s p q r
B. A B C D	(ii) p q r s
C. A B C D	(iii) s r q r
D. A B C D	(iv) s p t r

Multiple Choice Questions

82.

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If $∠$ BAC = 90°, and ar( $∆$ ABC) = 55sq. units, then the abscissa of the vertex C is :

$1 + \sqrt{5}$
$2 + \sqrt{5}$
$1 + 2 \sqrt{5}$
$2 \sqrt{5} - 1$

83.

If the point P on the curve, 4x² + 5y² = 20 is farthest from the point Q(0, – 4), then PQ² is equal to :

Short Answer Type

84.

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD² + MC² is minimums is ___

Multiple Choice Questions

85.

The point dividing the join of (3, - 2, 1) and( - 2, 3 11) in the ratio 2 : 3 is

(1, 1, 4)
(1, 0, 5)
(2, 3, 5)
(0, 6, - 1)