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CBSE Class 10 Mathematics Solved Question Paper 2016

Short Answer Type

11.
In Fig. , O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

In the given figure,

Given,
Diameter, AB= 13 cm
therefore,

Radius of the circle, r =13/2 = 6.5 cm
$angle space ACB space is space the space angle space in space the space semi minus circle. therefore space angle ACB space equals space 90 degree Now comma space in space increment ACB comma space using space Phythagoras space theorem comma space we space have AB squared space equals space AC squared plus BC squared left parenthesis 13 right parenthesis squared space equals space left parenthesis 12 right parenthesis squared plus left parenthesis BC right parenthesis squared left parenthesis BC right parenthesis squared space equals space left parenthesis 13 right parenthesis squared minus left parenthesis 12 right parenthesis squared space equals space 169 minus 144 space equals space 25 therefore comma BC space equals space square root of 25 space equals space 5 Now comma space area space of space shaded space region space equals space Area space of space semi space circle space minus Area space of space increment ACB equals 1 half πr squared minus 1 half straight x space BC space straight x space AC equals 1 half space straight x space 3.14 straight x space left parenthesis 6.5 right parenthesis squared space minus 1 half space straight x space 5 space straight x space 12 equals 66.33 minus 30 equals 36.33 space cm squared Thuss comma space the space area space of space the space shaded space region space is space 36.33 space cm squared.$

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12.

In Fig., a tent is in the shape of a cylinder surmounted by a conical top of the same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs. 500/sq. metre. (use π = 22/7)

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13.

If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b,a + b). Prove that bx = ay.

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14.

In Fig. find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use π =22/7)

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15.

If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their m^th terms.

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16.

Solve for x:
$fraction numerator 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis end fraction plus fraction numerator 1 over denominator left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space equals 2 over 3 comma space straight x not equal to 1 comma 2 comma 3$

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17.

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (π = 22/7)

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18.

A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by $3 5 over 9 cm$ . Find the diameter of the cylindrical vessel.

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19.

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of a hill as 30°. Find the distance of the hill from the ship and the height of the hill.

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