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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]

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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.

Radius space of space the space hemispherical space bowl comma space straight r space equals space 36 over 2 space equals space 18 space cm Volume space of space the space hemispherical space bowl space equals space 2 over 3 πr cubed space equals space 2 over 3 space straight x space straight pi space straight x space 18 space straight x space 18 space straight x space 18 space equals space 3888 space straight pi space cm cubed Volume space of space the space liquid space transferred space space equals space 3888 space straight pi space minus 10 percent sign space of space 3888 space straight pi space equals space 3888 space straight pi space minus space 388.8 space straight pi space equals space 3499.2 space straight pi space cm cubed

Radius of each cylindrical bottle, R = 6/2 = 3 cm

Let the height cylindrical bottle be h

volume of each cylindrical bottle = πR²h

= π x 3 x3 x h

Therefore, Total volume of 72 such cylindrical bottles

= π x 3 x3 x h x 72

= 648 πh² cm³

According to the question,

Total volume of 72 such cylindrical bottles = volume of the liquid transferred

Therefore, 648 πh = 3499.2π

⇒ h = 3499.2/648

⇒ h = 5.4 cm

Hence, the height of each cylindrical bottle is 5.4 cm

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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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