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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; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 1

Question 1: Operations and Venn diagrams
If A = 1, 3, 5, 7 and B = 3, 4, 5, 6, then A ∪ B is (a) 1, 3, 3, 4, 5, 5, 6, 7 (b) 3, 5 (c) 1, 7 (d) 1, 3, 4, 5, 6, 7
Question 2: Sets and their representations
The roster form of x: x ∈ ℕ, x² < 20 is (a) 1, 2, 3, 4, 5 (b) 0, 1, 2, 3, 4 (c) 1, 2, 3, 4 (d) -4, -3, …, 3, 4
Question 3: Kinds of sets
Which pair of sets are equal? (a) the set of letters of FOLLOW and W, O, L, F (b) 1, 2 and 1, 2 (c) 0 and φ (d) x: x² = 9 and 3

Week 2

Question 1: Operations and Venn diagrams
For any two sets A and B, the set A ∩ (A ∪ B) equals (a) A ∪ B (b) B (c) A ∩ B (d) A
Question 2: Sets and their representations
The set 3, 6, 9, 12, 15 in set-builder form is (a) x: x is a multiple of 3, x < 15 (b) x: x = 3n, n ∈ ℕ (c) x: x = n + 3, n ∈ ℕ, n ≤ 5 (d) x: x = 3n, n ∈ ℕ, n ≤ 5
Question 3: Kinds of sets
Which of the following sets is finite? (a) x ∈ ℝ: 0 < x < 1 (b) x ∈ ℕ: x > 100 (c) x: x is a multiple of 5 (d) x ∈ ℕ: x is a divisor of 360

Week 3

Question 1: 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 2: Complement
If U = ℕ and A is the set of even natural numbers, then A' is (a) the set of odd natural numbers (b) φ (c) ℕ (d) the set of prime numbers
Question 3: Algebra of real functions
If f(x) = x² and g(x) = 2x + 1, then (f + g)(2) equals (a) 4 (b) 5 (c) 9 (d) 20

Week 4

Question 1: Functions
Which of these relations from 1, 2, 3 to a, b is a function? (a) (1, a), (1, b), (2, a), (3, b) (b) (1, a), (2, a), (3, b) (c) (1, a), (2, b) (d) (1, a), (2, a), (2, b), (3, a)
Question 2: Ordered pairs and Cartesian products
If A × B = (a, 1), (a, 2), (b, 1), (b, 2), then B is (a) a, b, 1, 2 (b) a, b (c) (1, 2) (d) 1, 2
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 5

Question 1: Algebra of real functions
If f(x) = √x and g(x) = x - 1, the domain of f/g is (a) [0, ∞) (b) [0, 1) ∪ (1, ∞) (c) ℝ - 1 (d) (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: Subsets and intervals
Which of these sets is a subset of every set? (a) 0 (b) φ (c) 1 (d) ℕ

Week 6

Question 1: Trigonometric functions of any angle
The value of cos 1110° is (a) 1/2 (b) (√3)/2 (c) -(√3)/2 (d) -1/2
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: Functions
The domain of the real function f(x) = 1/(√(x - 2)) is (a) ℝ - 2 (b) [2, ∞) (c) (2, ∞) (d) (-∞, 2)

Week 13

Question 1: Compound angles
Writing (5π)/12 = (π)/4 + (π)/6, the exact value of sin(5π)/12 is (a) (√6 - √2)/4 (b) (√6 + √2)/4 (c) (√3 + 1)/2 (d) (1 + √2)/2
Question 2: Domains, ranges and graphs
The range of the sine function is (a) ℝ (b) [-1, 1] (c) [0, 1] (d) (-1, 1)
Question 3: Relations
The range of the relation R = (x, x + 3): x ∈ 1, 2, 3, 4 is (a) 3 (b) 1, 2, 3, 4 (c) 1, 2, 3, 4, 5, 6, 7 (d) 4, 5, 6, 7

Week 14

Question 1: Multiple angles and sum-to-product
If tan x = 1/2, then tan 2x equals (a) 1 (b) 4/3 (c) 3/4 (d) 2/3
Question 2: Compound angles
The value of cos(7π)/18cos(π)/18 + sin(7π)/18sin(π)/18 is (a) (√3)/2 (b) 1/2 (c) 1 (d) 0
Question 3: 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)

Week 16

Question 1: Complex numbers
The real part of (2 + 3i)(1 - i) is (a) 2 (b) -1 (c) 5 (d) 1
Question 2: The number i
The value of i²⁰²⁶ is (a) i (b) 1 (c) -1 (d) -i
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 17

Question 1: The Argand plane
The point representing -2 + 3i in the Argand plane lies in the (a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant
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: Angles in degrees and radians
An angle of (5π)/9 radians, in degrees, is (a) 90° (b) 50° (c) 150° (d) 100°

Week 18

Question 1: Systems and double inequalities
The solution of -3 ≤ 2x - 1 < 5 is (a) (-1, 3] (b) [-1, 3) (c) [-2, 2) (d) [-1, 3]
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: Angles in degrees and radians
In a circle of radius 14 cm, an arc of length 22 cm subtends at the centre an angle of (take π = 22/7) (a) 60° (b) 45° (c) 90° (d) 120°

Week 19

Question 1: Factorial
The value of (8!)/(6!) is (a) 2 (b) 48 (c) 56 (d) 4/3
Question 2: Fundamental principle of counting
A restaurant offers 4 starters and 6 main courses. The number of different meals of one starter and one main course is (a) 6⁴ (b) 10 (c) 4⁶ (d) 24
Question 3: Modulus and conjugate
The modulus of 3 - 4i is (a) 7 (b) 25 (c) -1 (d) 5

More starter questions

Other weeks: Weeks 1–19 · Weeks 20–34 · Weeks 35–45. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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