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 triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If $\angle$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 :

• 29

• 48

• 21

• 36

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 ___

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)