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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.

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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]

Given,

Diameter of the cone = 3.5 cm

∴ Radius of the cone, r= 3.5 /2 cm

Height of the cone, h = 3 cm

Now,

$volume space of space each space cone space equals space fraction numerator 1 over denominator 3 space end fraction πr squared straight h space equals space 1 third space straight x space space 22 over 7 space straight x space open parentheses fraction numerator 3.5 over denominator 2 end fraction close parentheses squared space straight x space 3 9.625 space cm squared Therefore comma space volume space of space 504 space space cone space equals space 504 space straight x space 9.625 space equals space 4851 space cm cubed$

Let the radius of metallic sphere be R

It is given that cones are melted and recast into a metallic sphere.

therefore the volume of the sphere = Volume of 504 cones

$rightwards double arrow space 4 over 3 straight pi space straight R cubed space equals space 4851 rightwards double arrow space 4 over 3 space straight x space 22 over 7 space straight x space straight R cubed space equals space 4851 rightwards double arrow space straight R cubed space equals space fraction numerator 4851 space straight x space 7 space straight x space 3 over denominator 4 space straight x space 22 end fraction rightwards double arrow space straight R cubed space equals space 1157.625 straight R space equals space 10.5 space cm Diameter space of space the space sphere space equals space 2 space straight R space equals space 2 space straight x space 10.5 space cm space space equals space 21 space cm Therefore comma surface space space area space of space the space sphere space space equals space space 4 straight pi space straight R squared space space equals space 4 space straight x space 22 over 7 space straight x space left parenthesis 10.5 right parenthesis squared space equals space 1386 space cm squared$