11.

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

 In a circle of radius 21 cm, an arc subtends an angle of $60°$ at the centre.Find: (i) the length of the arc (ii) area of the sector formed by the arc.
 $\left| \mathrm{Use} \mathrm{\pi } = \frac{22}{7 }\right|$

Find the ratio in which the y-axis divides the line segment joining the points (-4, -6) and (10, 12). Also, find the coordinates of the point of division

Prove that the parallelogram circumscribing a circle is a rhombus.

Two circular pieces of equal radii and maximum area, touching each otherare cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the remaining card board.

[ Use π = 22/7 ]

In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and ACat points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10cm, then find the length of AD, BE and CF.

For what values of k, the roots of the quadratic equation
(k + 4) x2 + (k + 1)x + 1 = 0 are equal?

The sum of first n terms of an AP is 3n² + 4n. Find the 25th term of this AP.

Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right
triangle

Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour