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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 ]

Radius of the circle, r = 14 cm

The chord AB subtends an angle 60^o at the centre of the circle.
Now,

Area space of space circle space equals space πr squared space equals space 22 over 7 space straight x space left parenthesis 14 right parenthesis squared space equals space 616 space cm squared Area space of space sector space AOB space equals space πr squared space straight x space 60 over 360 space space equals space 616 space space straight x space 1 over 6 space equals space 308 over 3 space equals space 102.67 space cm squared space left parenthesis approx right parenthesis In space increment OAB comma space AO space equals space OB space left parenthesis space radii space of space the space circle right parenthesis therefore space angle OBA space equals space angle OAB space left parenthesis space in space straight a space triangle comma space equal space sides space have space equal space angels space opposite space to space them right parenthesis Now comma angle space OAB space plus space angle OBA space plus space angle AOB space equals space 180 degree space left square bracket Angle space sum space property right square bracket rightwards double arrow space 2 angle space OAB space plus space 60 to the power of straight o space equals space 180 to the power of straight o rightwards double arrow space 2 angle space OAB space equals space 180 degree space minus 60 degree space equals space 120 degree rightwards double arrow space angle OAB space equals space 60 degree Thus comma space increment AOB space thin space is space an space equilateral space triangle. therefore space Area space of space increment AOB space equals space fraction numerator square root of 3 over denominator 4 end fraction left parenthesis OA right parenthesis squared space equals space fraction numerator square root of 3 over denominator 4 end fraction space straight x space left parenthesis 14 right parenthesis squared space equals space fraction numerator 196 square root of 3 over denominator 4 end fraction space equals space 84.87 space cm squared

Area of the minor segment = Area of the sector AOB - Area of ΔAOB

= 102.67 - 84.87
= 17.85 cm²

Now,
Area of the major segment = Area of the circle - Area of the minor segment

=616 - 17.8

= 598.2 cm²

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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]

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