Question - How many three-digit natural numbers are divisible by 7?
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Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
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Question - 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 - In Figure 3, two concentric circles with centre 0, have radii 21cm and 42 em.
If --- AOB = 60°, find the area of the shaded region. [Use ------]
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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 - The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use -----]
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Question - Prove that the parallelogram circumscribing a circle is a rhombus.
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Question - cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.
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Question - Show that the points (-2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.
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Question - 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 - In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [ -------]
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Question - Find the values (s) of k so that the quadratic equation 3x^2 – 2kx + 12 = 0 has equal roots.
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Question - 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.
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Question - Solve the following quadratic equation for x: ------------
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Question - A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid. ---------
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Question - Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer more?
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Question - Solve for x: -------
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Question - The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30^o. If the height of the second pole is 24 m, find the height of the first pole. [Use ---- 1.732]
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Question - Prove that the parallelogram circumscribing a circle is a rhombus.
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Question - In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the length of AD, BE and CF.
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