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CBSE Class 10 Mathematics Solved Question Paper 2016

Short Answer Type

21.
Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide the place and the canvas for 1500 tents to be fixed by the governments and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 cm and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (Use π = 22/7)

Given,
Height of conical upper part = 3.5m,
radius = 2.8 m
(slant height of cone)² = (2.1)² +(2.8)² = 4.41+7.84
(Slant height of cone)² = $square root of 12.25 end root space equals space 3.5 straight m$
the canvas used for each tent
= curved surface area of cylinder base+curved surface area of conical upper part

$equals 2 πrh plus πrl equals πr left parenthesis 2 straight h plus straight l right parenthesis equals 22 over 7 space straight x 2.8 space straight x space 10.5 equals 92.4 space straight m squared So comma space the space canvas space used space for space one space tent space is space 92.4 space straight m squared. Thus comma space the space canvas space used space for space 1500 space tents space equals space left parenthesis 92.4 space straight x space 1500 right parenthesis space straight m squared. canvas space used space to space make space the space tents space cost space Rs. space 120 space per space sq space straight m so comma space canvas space used space to space make space 1500 space tents space will cost space Rs. space 92.4 space straight x space 1500 space straight x 120 The space amount space shared space by space each space school space to space set space up space the space tent equals fraction numerator 92.4 space straight x space 1500 space straight x 120 over denominator 50 end fraction space equals space Rs 332640 The space amount space shared space by space each space school space to space set space up space the space tents space is space Rs.332640 The space value space of space help space others space in space times space of space troubles space is space generated space from space the space problem$

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22.

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

1987 Views

23.

Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60^o to each other.

4680 Views

24.

In given Fig. , two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of $DO to the power of apostrophe over CO$

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25.

Solve for x:

$fraction numerator 1 over denominator straight x plus 1 end fraction plus fraction numerator 2 over denominator x plus 2 end fraction plus fraction numerator 4 over denominator x plus 4 end fraction comma space x not equal to negative 1 comma negative 2 comma negative 4$

2246 Views

26.

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o. Find the height of the tower PQ and the distance PX. $Use square root of 3 space equals 1.73$

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27.

The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses preceding the house numbered X is equal to the sum of the numbers of houses following X.

3381 Views

28.

A number x is selected at random from the numbers 1, 2, 3, and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

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29.

In Fig., is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OQ and meets OP produced at B. Prove that the perimeter of shaded region is r $open square brackets tan space theta space plus s e c space theta space plus fraction numerator pi theta over denominator 180 end fraction minus 1 close square brackets$

6794 Views

30.

A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

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