Are you a Class 9 CBSE student who has already solved Set 1, Set 2, Set 3, and Set 4 of our Mathematics papers? At Dhingra Classes, we believe that the more varied problems you solve, the more confident you become. This is Question Paper Set 5 — featuring completely new questions with answers and zero duplicates from all our previous papers.

This paper covers nine crucial chapters from your new NCERT Ganita Manjari textbook: Orienting Yourself: The Use of Coordinates, Introduction to Linear Polynomials, Exploring Algebraic Identities, I’m Up and Down, Round and Round, Measuring Space: Perimeter and Area, The Mathematics of Mayhem: Introduction to Probability, Predicting What Comes Next: Exploring Sequences and Progressions, Sets, and Coordinate Geometry.

📋 CBSE Class 9 Mathematics Exam Pattern — 80 Marks (Set 5)

Time Allowed: 3 Hours
Maximum Marks: 80

📝 SECTION A: Multiple Choice Questions (20 × 1 = 20 Marks)

Q1. The x-coordinate of a point is also known as:

(a) Ordinate
(b) Abscissa
(c) Origin
(d) Quadrant

Answer: (b) Abscissa

Q2. If a point lies on the x-axis, its y-coordinate is:

(a) 1
(b) -1
(c) 0
(d) Any number

Answer: (c) 0

Q3. The point (-4, 6) lies in which quadrant?

(a) I
(b) II
(c) III
(d) IV

Answer: (b) II

Q4. Which of the following is a linear polynomial?

(a) x² + 2x + 1
(b) 7x – 3
(c) x³ + 5
(d) 4x² – 9

Answer: (b) 7x – 3

Q5. If f(x) = 2x – 8, then f(5) equals:

(a) 2
(b) 3
(c) 4
(d) 5

Answer: (a) 2

Q6. The zero of the polynomial f(x) = 6x + 18 is:

(a) 3
(b) -3
(c) 6
(d) -6

Answer: (b) -3

Q7. The expansion of (x – y)³ is:

(a) x³ – y³
(b) x³ – 3x²y + 3xy² – y³
(c) x³ + 3x²y + 3xy² + y³
(d) x³ – y³ – 3xy

Answer: (b) x³ – 3x²y + 3xy² – y³

Q8. Using the identity a² – b² = (a + b)(a – b), the value of 68² – 32² is:

(a) 3200
(b) 3400
(c) 3600
(d) 3800

Answer: (c) 3600

Q9. The perpendicular from the centre of a circle to a chord:

(a) Trisects the chord
(b) Bisects the chord
(c) Is parallel to the chord
(d) Is equal to the chord

Answer: (b) Bisects the chord

Q10. The angle in a semicircle is:

(a) 45°
(b) 60°
(c) 90°
(d) 180°

Answer: (c) 90°

Q11. The area of a circle with radius 14 cm is (Take π = 22/7):

(a) 308 cm²
(b) 616 cm²
(c) 1232 cm²
(d) 2464 cm²

Answer: (b) 616 cm²

Q12. The perimeter of a regular pentagon with side 8 cm is:

(a) 32 cm
(b) 40 cm
(c) 48 cm
(d) 56 cm

Answer: (b) 40 cm

Q13. The total surface area of a cube with edge 5 cm is:

(a) 25 cm²
(b) 100 cm²
(c) 125 cm²
(d) 150 cm²

Answer: (d) 150 cm²

Q14. When two dice are rolled simultaneously, the total number of outcomes is:

(a) 6
(b) 12
(c) 24
(d) 36

Answer: (d) 36

Q15. The probability of getting a sum of 7 when two dice are rolled is:

(a) 1/12
(b) 1/9
(c) 1/6
(d) 5/36

Answer: (c) 1/6

Q16. The next term in the sequence 2, 5, 10, 17, 26, … is:

(a) 35
(b) 36
(c) 37
(d) 38

Answer: (c) 37

Q17. The sum of the first 20 natural numbers is:

(a) 190
(b) 200
(c) 210
(d) 220

Answer: (c) 210

Q18. If A = {1, 3, 5, 7} and B = {2, 4, 6, 8}, then A ∪ B is:

(a) {1, 3, 5, 7}
(b) {2, 4, 6, 8}
(c) {1, 2, 3, 4, 5, 6, 7, 8}
(d) Empty set

Answer: (c) {1, 2, 3, 4, 5, 6, 7, 8}

Q19. The power set of a set with 2 elements has how many elements?

(a) 2
(b) 4
(c) 6
(d) 8

Answer: (b) 4

Q20. The distance between the points A(2, 3) and B(5, 7) is:

(a) 3 units
(b) 4 units
(c) 5 units
(d) 7 units

Answer: (c) 5 units

📝 SECTION B: Very Short Answer Questions (5 × 2 = 10 Marks)

Q21. Write the coordinates of a point whose ordinate is -6 and which lies on the y-axis. (2 marks)

Answer:
For a point on the y-axis, the x-coordinate is 0.
Coordinates = (0, -6)

Q22. Find the value of the polynomial f(x) = x² – 6x + 9 at x = 3. (2 marks)

Answer:
f(3) = (3)² – 6(3) + 9
= 9 – 18 + 9
= 0

Q23. Expand (4x – 3)(4x + 5) using a suitable identity. (2 marks)

Answer:
(4x – 3)(4x + 5) = (4x)² + (-3 + 5)(4x) + (-3)(5)
= 16x² + (2)(4x) – 15
= 16x² + 8x – 15

Q24. A card is drawn from a well-shuffled deck of 52 playing cards. Find the probability of getting a red card. (2 marks)

Answer:
Number of red cards = 26 (13 hearts + 13 diamonds)
Total cards = 52
P(red card) = 26/52 = 1/2

Q25. Find the sum of the first 8 terms of the AP: 5, 9, 13, 17, … (2 marks)

Answer:
Given: a = 5, d = 4, n = 8
Sₙ = n/2 [2a + (n – 1)d]
S₈ = 8/2 [2(5) + (8 – 1)(4)]
= 4 [10 + 28]
= 4 × 38
= 152

📝 SECTION C: Short Answer Questions (6 × 3 = 18 Marks)

Q26. Plot the points P(2, 4), Q(-2, 4), R(-2, -4), and S(2, -4) on a Cartesian plane. Name the figure formed and find its perimeter. (3 marks)

Answer:
The figure formed is a rectangle.

Dimensions:

• Length = 4 units (from -2 to 2)

• Breadth = 8 units (from -4 to 4)

Perimeter = 2(Length + Breadth) = 2(4 + 8) = 2 × 12 = 24 units

Q27. If g(x) = 3x² – 5x + 2, find g(0), g(2), and g(-1) . (3 marks)

Answer:
g(0) = 3(0)² – 5(0) + 2 = 2

g(2) = 3(2)² – 5(2) + 2 = 12 – 10 + 2 = 4

g(-1) = 3(-1)² – 5(-1) + 2 = 3 + 5 + 2 = 10

Q28. Using the identity (a + b)³ = a³ + 3a²b + 3ab² + b³, evaluate (102)³. (3 marks)

Answer:
102³ = (100 + 2)³
= (100)³ + 3(100)²(2) + 3(100)(2)² + (2)³
= 1000000 + 60000 + 1200 + 8
= 1061208

Q29. In a circle of radius 26 cm, a chord is at a distance of 10 cm from the centre. Find the length of the chord. (3 marks)

Answer:
Using the formula: Chord length = 2√(r² – d²)
= 2√(26² – 10²)
= 2√(676 – 100)
= 2√576
= 2 × 24
= 48 cm

Q30. Find the circumference and area of a circle with diameter 42 cm. Also find the area of a quadrant of the circle. (Take π = 22/7) (3 marks)

Answer:
Radius = 42/2 = 21 cm

Circumference = 2πr = 2 × (22/7) × 21 = 132 cm

Area = πr² = (22/7) × 21 × 21 = 1386 cm²

Area of quadrant = (1/4) × πr² = (1/4) × 1386 = 346.5 cm²

Q31. A bag contains 9 red, 6 blue, and 5 green balls. One ball is drawn at random. Find the probability of getting:
(a) a blue ball
(b) a red or green ball (3 marks)

Answer:
Total balls = 9 + 6 + 5 = 20

(a) P(blue ball) = 6/20 = 3/10

(b) P(red or green ball) = (9 + 5)/20 = 14/20 = 7/10

📝 SECTION D: Long Answer Questions (4 × 5 = 20 Marks)

Q32. (a) State the identity for a³ – b³.
(b) Using this identity, factorise 8x³ – 27. (5 marks)

Answer:

(a) a³ – b³ = (a – b)(a² + ab + b²)

(b) 8x³ – 27 = (2x)³ – (3)³
= (2x – 3)((2x)² + (2x)(3) + (3)²)
= (2x – 3)(4x² + 6x + 9)

Q33. (a) What is a geometric progression?
(b) Find the 6th term of the GP: 3, 9, 27, 81, … (5 marks)

Answer:

(a) A geometric progression is a sequence in which each term after the first is obtained by multiplying the preceding term by a fixed non-zero number called the common ratio (r).

(b) Given: a = 3, r = 3, n = 6
aₙ = a × r⁽ⁿ⁻¹⁾
a₆ = 3 × 3⁵
= 3 × 243
= 729

Q34. (a) What is the difference between a finite set and an infinite set?
(b) If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, and B = {2, 4, 6, 8, 10}, find A’ and A ∩ B. (5 marks)

Answer:

(a)

• A finite set has a countable number of elements. Example: {1, 2, 3}

• An infinite set has an uncountable or endless number of elements. Example: The set of all natural numbers

(b)
A’ = U – A = {2, 4, 6, 8, 10}
A ∩ B = {1, 3, 5, 7, 9} ∩ {2, 4, 6, 8, 10} = ∅ (empty set)

Q35. A point N(3, -7) is given. (5 marks)
(a) In which quadrant does N lie?
(b) Find its distance from the x-axis and y-axis.
(c) If N is reflected across the origin, find the coordinates of the new point.

Answer:

(a) N(3, -7) lies in Quadrant IV (x is positive, y is negative).

(b) Distance from x-axis = |-7| = 7 units
Distance from y-axis = |3| = 3 units

(c) Reflecting across the origin changes the sign of both coordinates:
New point = (-3, 7)

📝 SECTION E: Case Study Questions (3 × 4 = 12 Marks)

Q36. Read the passage and answer the questions below:

A lottery has 100 tickets numbered 1 to 100. A ticket is drawn at random.

(a) What is the probability of drawing a ticket with a two-digit number? (2 marks)

Answer:
Two-digit numbers from 1 to 100: 10 to 99 = 90 numbers
P(two-digit number) = 90/100 = 9/10 = 0.9

(b) What is the probability of drawing a ticket with a perfect square number? (2 marks)

Answer:
Perfect squares from 1 to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 = 10 numbers
P(perfect square) = 10/100 = 1/10 = 0.1

Q37. Read the passage and answer the questions below:

A circular garden has a radius of 28 m. The gardener wants to build a fence around it and plant grass inside. (Take π = 22/7)

(a) Find the circumference of the garden. (1 mark)

Answer:
Circumference = 2πr = 2 × (22/7) × 28 = 176 m

(b) Find the area of the garden. (1 mark)

Answer:
Area = πr² = (22/7) × 28 × 28 = 2464 m²

(c) If the cost of fencing is ₹30 per metre, find the total cost of fencing. (2 marks)

Answer:
Total cost = Circumference × Rate
= 176 × 30
= ₹5280

Q38. Read the passage and answer the questions below:

A library records the number of books issued each day: 25, 30, 35, 40, … This follows an arithmetic progression.

(a) Find the common difference of this AP. (1 mark)

Answer:
d = 30 – 25 = 5

(b) Find the nth term formula for this AP. (1 mark)

Answer:
aₙ = a + (n – 1)d
aₙ = 25 + (n – 1)(5)
= 25 + 5n – 5
= 5n + 20

(c) How many books will be issued on the 10th day? (2 marks)

Answer:
a₁₀ = 5(10) + 20
= 50 + 20
= 70 books

💡 Why Choose Dhingra Classes, Nashik?

At Dhingra Classes, we specialise in coaching for CBSE, ICSE, and Maharashtra State Board (SSC) students from Class 6 to Class 10. Our experienced teachers provide chapter-wise summaries, practice question papers, and exam-oriented guidance to help students excel with the new NCERT Ganita Manjari textbook.

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🎯 Exam Tips for CBSE Class 9 Mathematics Students

1. Practise MCQs daily — they carry 20 marks in Section A

2. Memorise all algebraic identities — including a³ + b³ and a³ – b³

3. Draw neat diagrams for coordinate geometry and circle problems

4. Show step-by-step calculations in long answer questions

5. Link concepts to real-life examples — case study questions test application