21.

In fig., PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If  $\angle$POQ = 30⁰,  then find the area of the shaded region.

                      

Solve for x:  4x² – 4ax + (a² – b²) = 0

                                   OR

Solve for x:  3x² - $\sqrt{6}$x + 2 = 0

A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60o. Find the length of the string assuming
that there is slack in the string.

Draw a triangle ABC with side BC = 6 cm,  $\angle$C = 30⁰ and  $\angle$A = 105⁰. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of $∆$ABC.

The 16^th term of an AP is 1 more than twice its 8^th term. If the 12^th term of the AP is 47, then find its n^th term.

A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) the queen of diamonds.

A bucket is in the form of a frustum of a cone and its can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. $\left[\mathrm{use} \mathrm{\pi } = \frac{22}{7}\right]$

The angle of elevation of the top of a hill at the foot of a tower is 60⁰ and the angle of depression from the top of the tower of the foot of the hill is 30⁰. If the tower is 50 m high, find the height of the hill.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

                                   OR

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. Find the number of books he bought.

                                            OR

The sum of two number is 9 and the sum of their reciprocals is $\frac{1}{2}$. Find the numbers.