Question - AB + CD = AD + BC
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
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Question - Find the sum of all three digit natural numbers, which are multiples of 7.
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Question - Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th term.
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Question - 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.
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Question - 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. -------
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Question - 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.
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Question - Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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Question - The volume of a hemisphere is ------- cm^3. Find its curved surface area. ---------
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Question - Tangents PA and PB are drawn from an external point P to two concentric circle with centre O and radii 8 cm and 5 cm respectively, as shown in Fig., If AP = 15 cm, then find the length of BP. ------------
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Question - If the vertices of a triangle are (1,-3), (4,p) and (-9,7) and its area is 15 sq. units, find the value (s) of p.
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Question - The angle of elevation of the top of a hill at the foot of a tower is 60^o and the angle of depression from the top of the tower of the foot of the hill is 30^o. If the tower is 50 m high, find the height of the hill.
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Question - A point P divides the line segment joining the points A(3,-5) and B(-4,8) such that ------- If P lies on the line x + y = 0, then find the value of K.
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Question - From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid.
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Question - In fig., OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. ------------
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Question - A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
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Question - 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 60^o. Find the length of the string assuming that there is slack in the string.
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Question - 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 = 30^o, then the area of the shaded region.------------
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Question - The sum of two number is 9 and the sum of their reciprocals is ---- Find the numbers.
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Question - In fig., an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC. ------
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Question - Prove that the parallelogram circumscribing a circle is a rhombus.
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