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 POQ = 300, then find the area of the shaded region.
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, C = 300 and A = 1050. Then construct another triangle whose sides are times the corresponding sides of ABC.
The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth 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.
Here, R = 28 cm and r = 21 cm, we need to find h
Volume of frustum = 28.49 L = 28.49 x 1000 cm3 = 28490 cm3
Now, volume of frustum =
Hence the height of bucket is 15 cm.
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 . Find the numbers.