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CBSE Class 10 Mathematics Solved Question Paper 2015

Short Answer Type

11.

The 14^th term of an AP is twice its 8^th term. If its 6^th terms is -8, then find the sum of its first 20 terms.

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12.

solve for x:

$square root of 3 straight x squared space minus 2 square root of 2 straight x space minus 2 square root of 3 space equals space 0$

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13. The angle of elevation of an aeroplane from a point A on the ground 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of

1500 space square root of 3 space end root space straight m

, find the speed of the plane in km/hr.

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14.

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.

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15. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

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16.

Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment. [ use π = 22/7 ]

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17.
Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pay. What values are shown by these associations? [ use π = 22/7]

Height of the cylindrical part, H = 4 m

Height of the conical part, h = 2.8 m

Radius of the base, r = 2.1 m

So comma space straight l equals space square root of straight r squared space plus space straight h squared end root rightwards double arrow space straight l space equals space square root of left parenthesis 2.1 right parenthesis squared space plus left parenthesis 2.8 right parenthesis squared end root rightwards double arrow space straight l space equals space square root of 12.25 end root rightwards double arrow space 1 space equals space 3.5 space straight m surface space area space of space canvas space to space be space used space space equals space CSA space of space conical space part space plus space CSA space of space cylindrical space part space equals space πrl space plus space 2 πrH space equals space πr space left parenthesis straight l plus 2 straight H right parenthesis space equals space 22 over 7 space straight x space 2.1 space straight x space left parenthesis 3.5 space plus 8 space right parenthesis equals space 75. space 9 space straight m squared

Cost of the canvas = Rs 100/ m²
So, total cost of the canvas to be used = 75.9 x 100 = Rs 7,590

therefore,

Amount that the association will have to pay for each tent

=50% of Rs 7590

= Rs (50/100) x 7590

= Rs 3,795

Therefore, Amount that the associations will have for 100 tent = Rs 3795 x 100
= Rs 379500

Hence, the amount that the associations will have to pay for 100 tents is Rs 3,79,500
The associations are showing humanity and their helpful nature.

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18. A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of the each bottle, if 10% liquid is wasted in this transfer.

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19. A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq. cm. [Use π =3.14]

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20. 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area. [Use π =22/7]

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