CBSE Class 9 Mathematics — 80 Marks Question Paper (Set 2) with Answers
Are you a Class 9 CBSE student who has already solved our first Mathematics paper? At Dhingra Classes, we believe that the more you practise with fresh questions, the stronger your problem-solving skills become. This is Question Paper Set 2 — featuring completely new questions with answers and zero duplicates from our previous paper.
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.
Q24. A bag contains 4 white balls, 5 black balls, and 6 red balls. One ball is drawn at random. Find the probability of getting a white ball. (2 marks)
Answer: Total balls = 4 + 5 + 6 = 15 Number of white balls = 4 P(white ball) = 4/15
Q25. Find the 15th term of the AP: 10, 13, 16, 19, … (2 marks)
Answer: Given: a = 10, d = 3, n = 15 aₙ = a + (n – 1)d a₁₅ = 10 + (15 – 1)(3) = 10 + 42 = 52
Q31. In a box, there are 8 red marbles, 7 blue marbles, and 5 green marbles. One marble is drawn at random. Find the probability of getting: (a) a red marble (b) a blue or green marble(3 marks)
Answer: Total marbles = 8 + 7 + 5 = 20
(a) P(red marble) = 8/20 = 2/5 = 0.4
(b) P(blue or green marble) = (7 + 5)/20 = 12/20 = 3/5 = 0.6
Q33. (a) Define a geometric progression. (b) Find the 8th term of the GP: 2, 6, 18, 54, … (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 = 2, r = 3, n = 8 aₙ = a × r⁽ⁿ⁻¹⁾ a₈ = 2 × 3⁷ = 2 × 2187 = 4374
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 = {2, 4, 6, 8, 10}, and B = {1, 3, 5, 7, 9}, find A’ and 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 = {1, 3, 5, 7, 9} B’ = U – B = {2, 4, 6, 8, 10}
Q35. A point Q(5, -4) is given. (5 marks) (a) In which quadrant does Q lie? (b) Find its distance from the x-axis and y-axis. (c) If Q is reflected across the x-axis, find the coordinates of the new point.
Answer:
(a) Q(5, -4) lies in Quadrant IV (x is positive, y is negative).
(b) Distance from x-axis = |-4| = 4 units Distance from y-axis = |5| = 5 units
(c) Reflecting across the x-axis changes the sign of the y-coordinate: New point = (5, 4)
📝 SECTION E: Case Study Questions (3 × 4 = 12 Marks)
Q36.Read the passage and answer the questions below:
A cricket match is being played. The probability that Team A wins is 0.6, and the probability that Team B wins is 0.3.
(a) What is the probability that the match ends in a draw? (2 marks)
Answer: Area = πr² = (22/7) × (21)² = (22/7) × 441 = 1386 m²
(c) If the walking track is 3.5 m wide, find the area of the track. (2 marks)
Answer: Outer radius = 21 + 3.5 = 24.5 m Area of track = π(R² – r²) = (22/7) × (24.5² – 21²) = (22/7) × (600.25 – 441) = (22/7) × 159.25 = 500.5 m²
Q38.Read the passage and answer the questions below:
A savings scheme offers increasing deposits each month. The deposit amounts follow the pattern: ₹500, ₹550, ₹600, ₹650, … This follows an arithmetic progression.
(a) Find the common difference of this AP. (1 mark)
Answer: d = 550 – 500 = ₹50
(b) Find the nth term formula for this AP. (1 mark)
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