Question

Can I get a sample paper for maths class 9​

Answer 1

(Questions 1 to 6 carry 1 mark each)
1. Rationalise the denominator of
1
32
.
2. Is point (2, 1) lie on a line whose equation is 2x + y = 5?
3. In ABC, m A = x, m B = 2x, m C = 3x. Find the value of m C.
4. Point (–2, –5) will lie in which Quadrant?
5. If the range of the data is 28 and number of classes is 7, then find the class size of the
data?
6. O is a center of a Circle and OR  PQ, distance of a chord PQ of a circle from the center
is 12 cm and the length of the chord is 10 cm, what is the length of a radius?
Section B
(Questions 7 to 12 carry 2 marks each)
7. Express 0.975in the form
p
q
, where p and q are integers and q ≠ 0.
8. Factorise: 
2
7 2x10x4 2
9. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular
distance from the y-axis is 5 units. Write the coordinates of such a point if it lies in one
of the following quadrants:
(i) I Quadrant (ii) II Quadrant (iii) III Quadrant (iv) IV Quadrant
10. In the figure, ∠AOC and ∠BOC form a linear pair. If a – b = 80°, then find the values of a
and b.
11. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find
i. Its inner curved surface area,
ii. The cost of plastering this curved surface at the rate of Rs 40 per m2.
12. Find the value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and
3a – 2b = 1.
Section C
(Questions 13 to 22 carry 3 marks each)
13. Simplify:


33
25
435
354
25343
1687

14. If the polynomials x2 – 5x – 3a and ax2 – 5x – 7 leave the same remainder when they
are divided by (x – 1), then what is the value of a?
15. Find the value of x3 – 8y3 – 36xy – 216 when x = 2y + 6.
16. In the figure, PQ is a line segment and O is the mid-point
of PQ. R and S are on the same side of PQ such that
∠PQS = ∠QPR and ∠POS = ∠QOR. Prove that:
(i) ΔPQR ≅ ΔQOS
(ii) PR = QS
17. Show that the line segments joining the mid points of the opposite sides of a
quadrilateral bisect each other.
18. A company selected 2400 families at random and surveyed them to determine
relationship between income level and the number of television sets at home. The
information gathered is listed in the table below:
If one family is choosen at random find the probability of choosing
i. A family whose income is 16,000 or more and has more than 2 TV sets
ii. A family whose income is less than 7,000 and has 2 TV’s
iii. A family whose income is between 10,000 and 13,000 and has 1 TV.
19. In the figure, PQ is the diameter of the circle and XY is chord equal to the radius of the
circle. PX and QY when extended intersect at point E. Prove that m∠PEQ = 60°

20. In the given figure, E is the mid-point of side AD of trapezium ABCD with AB ∥ CD, EF ∥
AB. A line through E parallel to AB meets BC in F. Show that F is the mid-point of BC.
21. Two unbiased dice are tossed 50 times. The sum of integers obtained on the dice is
noted below.
Sum 2 3 4 5 6 7 8 9 10 11 12
Frequency 3 9 8 8 4 5 1 3 7 2 0
Find the probability that:
i. The sum of integers is more than 9.
ii. The sum of integers is exactly 7.
iii. The sum of integers is less than 6.
22. A wooden article was made by scooping out a hemisphere from each end of a solid
cylinder. If the height of the cylinder is 10 cm and its base is 7 cm, find the total
surface area of the article.
(SECTION – D)
(Questions 23 to 30 carry 4 marks each)
23. Simplify:
n 1n
n 2n 2
16 24 2
16 22 2


 
 
24. Find x3 + y3 when x =

1
32 2
and y =

1
32 2
.
25.
(i) Multiply 9x2 + 25y2 + 15xy + 12x – 20y + 16 by 3x – 5y – 4 using suitable
identities.
(ii) Factorise: a2 + b2 – 2(ab – ac + bc).

26. In the figure, PQRS is a square and SRT is an equilateral triangle.
Prove that:
a) PST = QRT
b) PT = QT
27. The cost of painting the complete outside surface of a closed cylindrical oil tank at 60
paise per sq dm is Rs. 237.60. The height of the tank is 6 times the radius of the base
of the tank. Find its volume corrected to two decimal places.
28. AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are
diameters; (ii) ABCD is a rectangle.
29. Construct ∆ABC in which m∠B = 60°, m∠C = 45° and the perimeter of the triangle is
11 cm.
30. The bus fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the
subsequent distance it is Rs. 5 per kilometre. Taking the distance covered as x km and
total fares as Rs. y, write a linear equation for this information and draw its graph.

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