CBSE [Delhi]_X_Mathematics_2016_Set_I

For what value of k will k + 9, 2k – 1 and (2k +7) are the consecutive terms of an A.P.?

A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is2.5 m away from the wall, find the length of the ladder.

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability ofgetting neither a red card nor a queen.

If – 5 is a root of the quadratic equation 2x² + px –15 = 0 and the quadratic equation p (x² + x) + k = 0has equal roots, find the value of k.

Let P and Q be the points of trisection of the line segment joining the points A(2, – 2) and B(–7, 4)such that P is nearer to A. Find the coordinates of P and Q.

In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre 0, in such a way that thesides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that.
AB +CD = BC + DA.

     Figure -2
 

Prove that the point (3, 0), (6, 4) and (–1, 3) are the vertices of a right angled isosceles triangle.

The 4^th term of an A.P. is zero. Prove that the 25^th term of the A.P. is three times its 11^th term.

         Figure -3