# CBSE Class 9 Mathematics Sample Paper 2017 (3)

CBSE Class 9 Mathematics Sample Paper 2017 (3). It’s always recommended to practice as mane sample papers as possible before the examinations. Students can download the sample papers and also question papers of previous years to practice and score better marks in examinations. Refer to other links too for more sample papers.

1.

Find the value of k, if the equation of a line 2x – ky = 9 passes through the point (-1, -1).

2.

A box contains 50 bolts and 150 nuts. On checked the box, it was found that half of the bolts and half of the nuts are rusted. If one item is chosen at random, find the probability that it is rusted.

3.

The mean and median of 15 numbers is 8. If 2 is added to every number, what will be the new mean and new median?

4.

If the perimeter of one of the faces of a cube is 40cm then find its volume.

SECTION B ( 2 MARKS EACH)

5.

The class mark of a particular class is 9.5 and its class size is 5. Write the next 3 classes, if they are continuous.

6.

From the graph, answer the following questions: i) Write the equation of a line m. ii) Write the coordinates of any two points lying on the line m.

7.

Find the points where the graph of the equation3x + 2y – 9 = 0 cuts the x-axis and the y-axis.

8.

Construct an angle of 3712 °, using compass and ruler only.

9.

The sum of the radius of the base and height of a cylinder is 37m. If TSA of the solid cylinder is 1628m2 , find the height of the cylinder.

10.

If O is the centre of a circumcircle of a ΔABC and OD ⊥BC, prove that ∠BOD = ∠A.

SECTION C ( 3 MARKS EACH)

11.

A fraction becomes711, if 2 is added to the numerator and 3 is subtracted from the denominator. Write a linear equation in two variables to represent the statement.

12.

Two coins are tossed simultaneously for 360 times. The number of times ‘2 heads’ appeared was three times ‘no head’ appeared and number of times ‘one head’ appeared is double the number of times ‘no head’ appeared. Find the probability of getting one head.

13.

The mean of the following distribution is 50.

X

10

30

50

70

90

f

17

5a +3

32

7a – 11

19

Find the value of ‘a’ and hence find the frequencies of 30 and 70. Also find its mode.

14.

A solid metallic sphere of diameter 28cm is melted and recast into number of smaller cones each of diameter 14/3cm and height 3cm. Find the number of cones so formed.

15.

Two diameters of a circle intersect each other at right angle. Prove that the quadrilateral formed by joining end points is a square.

16.

Construct a ΔABC in which AB = 4.8cm, ∠A = 45° and AC – BC = 2cm.

17.

In the given fig., WZ ll XY and XZ ll YV. Show that ar(ΔWXY) = ar(ΔXVY)

18.

In the fig., points P, Q, R and S lie on a circle. Find the values of x and y and also find all the angles of the cyclic quadrilateral.

SECTION D ( 4 MARKS EACH )

19.

Let x and y be two supplementary angles. Form an equation for this information and draw its graph. Find graphically measure of the other angle, if one of the angles is a) 120° b) 80°

20.

Construct ΔABC in which perimeter is 12.5cm and∠B = 105°, ∠C= 30°.

21.

Draw a histogram and frequency polygon for the data given below:

Class interval

21 - 24

26 - 29

31 - 34

36 - 39

41 - 44

46 - 49

Frequency

30

24

52

28

46

10

22.

Draw the lines x = 4, y = 2 and x = y on the same graph and then identify what type of figure obtained. Also write the coordinates of vertices of the figure so formed.

23.

The marks scored by some students in an exam(out of 1000) are given in the form of a frequency distribution table:

Marks

600 - 650

650 - 700

700 - 750

750 - 800

800 - 850

850 - 900

900 - 950

No. of students

26

55

166

294

182

59

18

If a child is selected at random, find the probability that the child has

i) Scored less than 750 marks

ii) Scored 85% or above

iii) Atleast 75% marks.

24.

A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost of Rs 997.92. If the cost of white washing is 400 paisa per sq. m, find the volume of the air inside the dome.

25.

The internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm respectively. If the cost of painting 1cm2 of the surface area is Rs.0.05, find the cost of painting vessel all over.

26.

Water flows at the rate of 5 m per minute through a cylindrical pipe, whose diameter is 7 cm. How long it will take to fill the conical vessel having base diameter 21 m and depth 12 m.

27.

ABCD is a parallelogram. The circle through A, B and C intersects CD produced at E. If AB = 10 cm, BC = 8 cm, CE = 14 cm. Find AE.

28.

ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. Prove that ar(BDF) = ¼ ar(ABCD). If ar(DFB) = 3 cm2, find the area of the parallelogram ABCD.

**

Questions 29 – 31 are from OTBA which is of 10 marks.

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