Class-X (2017–18)

Mathematics

Time allowed: 3 Hours

Max. Marks: 80

General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 30 questions divided into four sections A, B, C and D. (iii)Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each. (iv) There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted.

Question numbers 1 to 6 carry 1 mark each.

1.

nor-terminating repeating decimal expansion.

2.

3.

27, 23, 19, ..., –65.

4. Find the coordinates of the point on y-axis which is nearest to the point (–2, 5)

5.

Find the ratio of the area of $$\Delta PST$$ to the area of $$\Delta PRQ$$

6.

11.

A card is drawn at random from the box.

Find the probability that the number on the drawn card is

(i) a square number

(ii) a multiple of 7

12.

If 6 more red balls are put in the box and a ball is drawn at random, the probability

of drawing a red ball doubles than what it was before.

Find the number of red balls in the bag.

Question numbers 13 to 22 carry 3 marks each.

13.

n, n + 2 or n + 4 is divisible by 3.

14.

3x

^{4}+ 6x

^{3}- 2x

^{2}- 10x - 5

if two of its zeroes are

$$\sqrt {{5 \over 3}} {\rm{ }}and - \sqrt {{5 \over 3}} $$

15.

the number obtained by reversing the order of its digits.

If the difference of the digits is 3,

determine the number.

16.

line segment joining the points (–4, –6) and (–1, 7)?

Find the co-ordinates of the point of division.

form a parallelogram. Find the length of the altitude

of the parallelogram on the base AB.

20.

of radius 14 cm and a semicircle is drawn with BC as diameter.

Find the area of the shaded region

21.

is flowing with a speed of 10 km/h.

How much area will it irrigate in 30 minutes,

if 8 cm of standing water is needed?

from a cube of edge 14 cm.

Find the surface area of the remaining solid

after the cone is carved out.

22.

obtained by the students in an examination:

0-20 15

20-40 18

40-60 21

60-80 29

80-100 17

using empirical relationship

estimate the value of its median.

Question numbers 23 to 30 carry 4 marks each.

23.

would have taken 48 minutes less to travel

the same distance if its speed were 5 km/hour more.

Find the original speed of the train.

^{2}– 6x – 2 = 0

has real roots and if it has,

find them by the method of completing the square.

Also verify that roots obtained

satisfy the given equation.

24.

The sum of the three middle most terms is 225

and the sum of the last three terms is 429.

Find the AP.

25.

the square of the hypotenuse is equal to

the sum of the squares of the other two sides.

two similar triangles is equal to

the ratio of the squares of their corresponding sides.

26.

27.

$${{\cos \theta - \sin \theta + 1} \over {\cos \theta + \sin \theta - 1}} = \cos ec\theta + \cot \theta $$

28.

of a building 50 metres high as observed from the

top of a tower are 30° and 60°, respectively.

Find the height of the tower and

also the horizontal distance

between the building and the tower.

29.

flavoured milk filled to capacity in mugs

of negligible thickness,

which are cylindrical in shape

with a raised hemispherical bottom.

The mugs are 14 cm high and

have diameter of 7 cm

as shown in given figure. Both A and B sell flavoured milk

at the rate of Rs.80 per litre.

The dairy owner A uses the formula $$\pi {r^2}h$$ to find the volume of milk in the mug

and charges `Rs. 43.12 for it.

The dairy owner B is of the view

that the price of actual quantity

of milk should be charged.

What according to him should be the

price of one mug of milk?

Which value is exhibited by the

dairy owner B?

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