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CBSE Class 11 Maths starter questions: weeks 1–19

36 short questions to open a lesson for CBSE Class 11 Mathematics, weeks 1–19 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; answers and mark schemes stay with teachers.

Week 1

Question 1: Subsets and intervals
Which of these sets is a subset of every set? (a) 0 (b) φ (c) 1 (d) ℕ
Question 2: Sets and their representations
The set x: x is a prime number less than 12 in roster form is (a) 2, 3, 5, 7, 11 (b) 1, 2, 3, 5, 7, 11 (c) 2, 3, 5, 7, 9, 11 (d) 3, 5, 7, 11
Question 3: Kinds of sets
Which of the following is the empty set? (a) x ∈ ℕ: x < 2 (b) x ∈ ℤ: x² = 4 (c) 0 (d) x ∈ ℝ: x² = -1

Week 2

Question 1: Subsets and intervals
x ∈ ℝ: -3 < x ≤ 5 in interval notation is (a) [-3, 5] (b) (-3, 5) (c) (-3, 5] (d) [-3, 5)
Question 2: Complement
U = 1, 2, …, 10, A = 1, 2, 3, 4, 5, 6, B = 2, 4, 6, 8. Then (A ∪ B)' is (a) 7, 9, 10 (b) 7, 8, 9, 10 (c) 1, 3, 5 (d) 8, 9, 10
Question 3: Ordered pairs and Cartesian products
If (x + 1, y - 2) = (3, 1), then (x, y) is (a) (3, 2) (b) (4, -1) (c) (2, -1) (d) (2, 3)

Week 3

Question 1: Real functions: domain and range
The range of f(x) = (x²)/(1 + x²), x ∈ ℝ, is (a) [0, ∞) (b) [0, 1] (c) (0, 1) (d) [0, 1)
Question 2: Real functions: domain and range
The domain of f(x) = 1/(x - 3) is (a) ℝ (b) ℝ - 3 (c) (3, ∞) (d) ℝ - 0
Question 3: Real functions: domain and range
The range of f(x) = |x - 2|, x ∈ ℝ, is (a) [0, ∞) (b) [2, ∞) (c) ℝ (d) (0, ∞)

Week 4

Question 1: Kinds of sets
Which of the following is the empty set? (a) x ∈ ℕ: x < 2 (b) x ∈ ℤ: x² = 4 (c) 0 (d) x ∈ ℝ: x² = -1
Question 2: Sets and their representations
The set x: x is a prime number less than 12 in roster form is (a) 2, 3, 5, 7, 11 (b) 1, 2, 3, 5, 7, 11 (c) 2, 3, 5, 7, 9, 11 (d) 3, 5, 7, 11
Question 3: Subsets and intervals
Which of these sets is a subset of every set? (a) 0 (b) φ (c) 1 (d) ℕ

Week 5

Question 1: Subsets and intervals
x ∈ ℝ: -3 < x ≤ 5 in interval notation is (a) [-3, 5] (b) (-3, 5) (c) (-3, 5] (d) [-3, 5)
Question 2: Ordered pairs and Cartesian products
If (x + 1, y - 2) = (3, 1), then (x, y) is (a) (3, 2) (b) (4, -1) (c) (2, -1) (d) (2, 3)
Question 3: Complement
U = 1, 2, …, 10, A = 1, 2, 3, 4, 5, 6, B = 2, 4, 6, 8. Then (A ∪ B)' is (a) 7, 9, 10 (b) 7, 8, 9, 10 (c) 1, 3, 5 (d) 8, 9, 10

Week 6

Question 1: Trigonometric functions of any angle
If sin x < 0 and tan x > 0, then x lies in (a) quadrant I (b) quadrant II (c) quadrant III (d) quadrant IV
Question 2: Angles in degrees and radians
240^∘ in radians is (a) (4π)/3 (b) (2π)/3 (c) (5π)/4 (d) (3π)/2
Question 3: Real functions: domain and range
The domain of f(x) = 1/(x - 3) is (a) ℝ (b) ℝ - 3 (c) (3, ∞) (d) ℝ - 0

Week 13

Question 1: Compound angles
The exact value of tan(5π)/12 is (a) 2 + √3 (b) 2 - √3 (c) √3 - 1 (d) (√3 + 1)/2
Question 2: Domains, ranges and graphs
The range of f(x) = 2 - cos x is (a) [1, 2] (b) [-1, 1] (c) [0, 2] (d) [1, 3]
Question 3: Real functions: domain and range
The range of f(x) = |x - 2|, x ∈ ℝ, is (a) [0, ∞) (b) [2, ∞) (c) ℝ (d) (0, ∞)

Week 14

Question 1: Real functions: domain and range
The range of f(x) = (x²)/(1 + x²), x ∈ ℝ, is (a) [0, ∞) (b) [0, 1] (c) (0, 1) (d) [0, 1)
Question 2: Trigonometric functions of any angle
The value of sin(31π)/3 is (a) -(√3)/2 (b) (√3)/2 (c) 12 (d) -12
Question 3: Kinds of sets
Which of the following is the empty set? (a) x ∈ ℕ: x < 2 (b) x ∈ ℤ: x² = 4 (c) 0 (d) x ∈ ℝ: x² = -1

Week 16

Question 1: The number i
The value of i³⁵ is (a) 1 (b) -i (c) i (d) -1
Question 2: Angles in degrees and radians
240^∘ in radians is (a) (4π)/3 (b) (2π)/3 (c) (5π)/4 (d) (3π)/2
Question 3: Ordered pairs and Cartesian products
If (x + 1, y - 2) = (3, 1), then (x, y) is (a) (3, 2) (b) (4, -1) (c) (2, -1) (d) (2, 3)

Week 17

Question 1: Modulus and conjugate
The modulus of 3 - 4i is (a) 7 (b) 25 (c) -1 (d) 5
Question 2: Algebra of complex numbers
(2 + 3i)(1 - i) equals (a) 5 + i (b) -1 + i (c) 5 - i (d) 2 - 3i
Question 3: Trigonometric functions of any angle
If sin x < 0 and tan x > 0, then x lies in (a) quadrant I (b) quadrant II (c) quadrant III (d) quadrant IV

Week 18

Question 1: Systems and double inequalities
The number of integers satisfying both 5x - 3 < 2x + 9 and 3x + 4 ≥ x - 2 is (a) 7 (b) 6 (c) 8 (d) 5
Question 2: Algebra of complex numbers
The multiplicative inverse of 1 + i is (a) 1 - i (b) (1 + i)/2 (c) (1 - i)/2 (d) -1 - i
Question 3: Domains, ranges and graphs
The range of f(x) = 2 - cos x is (a) [1, 2] (b) [-1, 1] (c) [0, 2] (d) [1, 3]

Week 19

Question 1: Factorial
The value of (8!)/(6!) is (a) 2 (b) 48 (c) 56 (d) 43
Question 2: Algebra of complex numbers
The value of ((1 + i)/(1 - i))⁴ is (a) -1 (b) 1 (c) i (d) -i
Question 3: Rules for solving
If -2x ≥ 6, then (a) x ≥ -3 (b) x ≥ 3 (c) x ≤ -3 (d) x ≤ 3

More starter questions

Other weeks: Weeks 1–19 · Weeks 20–34 · Weeks 35–45. Answers and mark schemes are in the teacher tools.