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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.

Let P and Q be the two positions of the plane and A be the point of observation. Let ABC be the horizontal line through A. It is given that angles of elevation of the plane in two positions P and Q from a point A are 60° and 30°, respectively.

∴ ∠PAB = 60^o and ∠QAC = 30^o

Also comma space PB space equals space QC space equals space 1500 square root of 3 space straight m In space increment ABP comma space we space have tan space 60 degree space equals space BP over AB rightwards double arrow space square root of 3 space equals space fraction numerator 1500 square root of 3 over denominator AB end fraction rightwards double arrow space AB space equals space 1500 space straight m In space increment ACQ comma space we space have space tan space 30 degree space equals space QC over AC rightwards double arrow space fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 1500 square root of 3 over denominator AB end fraction rightwards double arrow space AC space equals space 1500 space straight x space 3 space equals space 4500 space straight m therefore space BC space equals space AC space minus space AB space equals space 4500 space straight m space minus space 1500 space straight m space equals space 3000 space straight m Thus comma space the space plane space travels space 3000 space meters space in space 15 space second. therefore space Speed space space of space the space plane equals space 3000 over 15 equals space 20 space straight m divided by straight s space equals space fraction numerator 200 space straight x space 60 space straight x space 60 space over denominator 1000 end fraction equals 720 space km divided by straight h Hence comma space the space speed space of space the space plane space is space 720 space km divided by straight h.

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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]

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