Sample paper maths

Sample Paper
Class 9 Maths
Sample Paper 5 | Class 9 Maths

Time : 3 Hours Maximum Marks : 80

General Instructions:

(i) All questions are compulsory.

(ii) The questions paper consists of 40 questions divided into 4 sections A, B, C and D.

(iii) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each.

(iv) There is no overall choice. However, an internal choices have been provided in two questions of 1 mark each, two questions of 2 marks each, three 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.

SECTION - A

Question 1:

Rational number between √2 and √3 is

(a)

(b)

(c)

(d)

Question 2:

The value of p(2) if p(t) = 2 + t + 2t² – t³is

(a)

(b) 1

(d) 10

Question 3:

If P(x, y) and P’(y, x) are same points then which of the following is true?

(a) x + y = 0

(b) x * y = 0

(d) = 0

Question 4:

In ΔABC, if ∠B < ∠A, then

(a) BC > CA

(b) BC < CA

(d) AB < CA

Question 5:

The degree of the polynomial x³(2 − x³) is

(a) 3

(b) 4

(d) 6

Question 6:

For every line l and for every point P (not on l ), there does not exist a unique line through P

(a) Which is not parallel to l.

(b) Which is perpendicular to l.

(d) None of these

Question 7:

An exterior angle of a triangle is 80° and two interior opposite angles are equal. Measure of each interior angle is

(a) 40°

(b) 60°

(d) 100°

Question 8:

Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, then its height is

(a) 0.5 m

(b) 1 m

(d) 5.5 m

Question 9:

Probability of an event can be any .......... from 0 to 1.

(a) Fraction

(b) Integer

(d) None of these

Question 10:

In the figure, if QT ⊥ PR, ∠ TQR = 40° and ∠ SPR = 30°, then the value of x is

(a) 30°

(b) 50°

(d) 100°

Question 11:

The sum of either pair of opposite angles of a cyclic quadrilateral is ____.

Question 12:

The area of an equilateral triangle having side 6 cm. is _____.

Question 13:

The image of point (−4, 6) under origin is _____.

Question 14:

The relation among class mark, lower limit and upper limit is _____.

Question 15:

A process that has a well-defined collection of outcomes is called a/an ______.

Question 16:

If a point C be the mid-point of a line segment AB, then write the relation among AC, BC and AB.

Question 17:

The base of a right angle triangle is 8 cm and the hypotenuse is 10 cm. Find its area.

Question 18:

Find the coordinates of the point whose abscissa is 2 and which lies on the x -axis.

Question 19:

Find the value of k, if x + k is the factor of the polynomial x³ + kx² − 2x + k + 5.

Question 20:

If two coins are tossed simultaneously, then what is the probability of getting exactly two tails?

Question 21:

Simplify:

Question 22:

Explain Euclid’s fourth axiom.

Question 23:

If ΔABC is congruent to ΔPQR, find the length of QR.

Question 24:

Factorise: 12x² – 7x + 1

Question 25:

A batsman in his 12^th inning makes a score of 63 runs and thereby increases his average score by 2. What is his average after the 12^th inning?

Question 26:

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

SECTION - C

Question 27:

A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Question 28:

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz

Question 29:

Express the linear equation x – – 10 = 0 in the form ax + by + c = 0 and indicate the values of a, b and c.

Question 30:

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Question 31:

In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = .

Question 32:

In a class, number of girls is x and that of boys is y . Also, the number of girls is 10 more than the number of boys. Write the given data in the form of a linear equation in two variables. Also, represent it graphically. Find graphically the number of girls, if the number of boys in 20.

Question 33:

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Question 34:

For a particular year, following is the frequency distribution table of ages (in years) of primary school teachers in a district.

(i) Write the lower limit of the first class interval.

(ii) Determine the class limits of the fourth class interval.

(iii) Find the class mark of the class 45-50.

Age (in years)	Number of teachers
15-20	10
20-25	30
25-30	50
30-35	50
35-40	30
40-45	6
45-50	4

SECTION – D

Question 35:

If a + b + c = 0, then prove that

Question 36:

Use suitable identities to find the following products:

(i) (x + 8)(x – 10)

(ii) 95 * 96

Question 37:

Visualize 4.26 on the number line up to 4 decimal places.

Question 38:

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

Question 39:

Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a number which is a perfect square. The quick brown fox jumps over a little lazy dog.

Question 40:

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

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