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CBSE Class 11 Maths starter questions: weeks 20–34

36 short questions to open a lesson for CBSE Class 11 Mathematics, weeks 20–34 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 20

Question 1: Combinations
The number of ways of choosing 3 students from 8 is (a) 336 (b) 24 (c) 512 (d) 56
Question 2: Permutations
The number of 3-digit numbers with distinct digits that can be formed from 1, 2, 3, 4, 5 is (a) 10 (b) 60 (c) 125 (d) 15
Question 3: Inequalities
Which of these numbers satisfies 3x - 7 > 2? (a) 0 (b) 3 (c) 2 (d) 4

Week 21

Question 1: The binomial theorem
The number of terms in the expansion of (a + b)⁷ is (a) 7 (b) 8 (c) 14 (d) 6
Question 2: Permutations
The number of different arrangements of the letters of the word BANANA is (a) 720 (b) 120 (c) 60 (d) 36
Question 3: Rules for solving
The solution of 3x - 5 < 7, x ∈ ℝ, is (a) x < 4 (b) x > 4 (c) x < 2/3 (d) x ≤ 4

Week 22

Question 1: Geometric progressions
The 6th term of the GP 2, 6, 18, … is (a) 486 (b) 1458 (c) 162 (d) 972
Question 2: Special cases
When (1 + x)⁵ is multiplied out, the number in front of x³ is (a) 5 (b) 10 (c) 3 (d) 15
Question 3: Inequalities
Which set lists every natural number x satisfying x + 5 < 9? (a) 0, 1, 2, 3 (b) 1, 2, 3, 4 (c) 1, 2, 3 (d) 4

Week 23

Question 1: Geometric mean and AM ≥ GM
The geometric mean of 4 and 16 is (a) 10 (b) 8 (c) 64 (d) 12
Question 2: Infinite GP
Each term of the series 6 + 3 + 3/2 + … is half the one before. The series adds up to (a) 12 (b) 9 (c) ∞ (d) 10.5
Question 3: Pascal's triangle
The coefficient of a²b³ in (a + b)⁵ is (a) 5 (b) 20 (c) 15 (d) 10

Week 24

Question 1: Slope
The slope of the line through (2, 3) and (6, 11) is (a) 1/2 (b) 2 (c) 8 (d) -2
Question 2: Pascal's triangle
Which row of Pascal's triangle lists the coefficients when (p + q)⁵ is multiplied out? (a) 1 5 5 5 5 1 (b) 1 4 6 4 1 (c) 1 5 10 10 5 1 (d) 1 6 15 20 15 6 1
Question 3: Arithmetic mean
The arithmetic mean of 7 and 19 is (a) 12 (b) √133 (c) 26 (d) 13

Week 27

Question 1: Forms of the equation of a line
The line through (1, -2) with slope 3 is (a) x - 3y - 7 = 0 (b) 3x - y + 5 = 0 (c) 3x - y - 5 = 0 (d) 3x + y - 1 = 0
Question 2: Slope
The slope of a line inclined at 135° to the positive x-axis is (a) -1 (b) 1 (c) √3 (d) -1/(√3)
Question 3: Inequalities
How many integers x satisfy -3 < x ≤ 2? (a) 6 (b) 5 (c) 4 (d) 3

Week 28

Question 1: Distances
The distance of the point (3, -4) from the line 3x + 4y - 3 = 0 is (a) 4 (b) 10 (c) 22/5 (d) 2
Question 2: Distances
The distance between the parallel lines 3x - 4y + 7 = 0 and 6x - 8y - 6 = 0 is (a) 13/5 (b) 2 (c) 13/10 (d) 1
Question 3: The binomial theorem
The sum of the coefficients in the expansion of (1 + x)⁶ is (a) 6 (b) 36 (c) 64 (d) 32

Week 29

Question 1: Parabola
The focus of the parabola y² = 12x is (a) (12, 0) (b) (-3, 0) (c) (0, 3) (d) (3, 0)
Question 2: Circle
The equation of the circle with centre (0, 0) and radius 4 is (a) (x - 4)² + (y - 4)² = 0 (b) x² + y² = 4 (c) x² + y² = 8 (d) x² + y² = 16
Question 3: Infinite GP
The sum to infinity of 1 + 1/3 + 1/9 + … is (a) 4/3 (b) 3 (c) 3/2 (d) 2/3

Week 30

Question 1: Hyperbola
The eccentricity of the hyperbola (x²)/16 - (y²)/9 = 1 is (a) 5/4 (b) 5/3 (c) 3/4 (d) (√7)/4
Question 2: Ellipse
The eccentricity of the ellipse (x²)/25 + (y²)/16 = 1 is (a) 4/5 (b) 3/5 (c) 5/3 (d) (√41)/5
Question 3: Inequalities
The solution set of 2x + 1 > 5 when x is a natural number is (a) 2, 3, 4, … (b) (2, ∞) (c) 1, 2 (d) 3, 4, 5, …

Week 31

Question 1: Using the distance formula
The distance of the point (3, -4, 5) from the x-axis is (a) 3 (b) √41 (c) 5√2 (d) 5
Question 2: Axes, planes and octants
The point (-2, 3, -5) lies in octant (a) II (b) VI (c) III (d) VII
Question 3: Parabola
The length of the latus rectum of x² = -16y is (a) 4 (b) 8 (c) 16 (d) -16

Week 32

Question 1: Polynomial and rational functions
lim_x → 2 (x² - 4)/(x - 2) equals (a) 0 (b) 2 (c) does not exist (d) 4
Question 2: Limits
lim_x → 3(2x + 5) equals (a) 6 (b) 8 (c) 5 (d) 11
Question 3: Coordinates of a point
Every point on the y-axis has coordinates of the form (a) (x, 0, 0) (b) (x, y, 0) (c) (0, 0, z) (d) (0, y, 0)

Week 34

Question 1: The derivative
For f(x) = x² - 3x, the derivative f'(2), found from lim_h → 0(f(2 + h) - f(2))/h, is (a) -1 (b) -2 (c) 4 (d) 1
Question 2: Trigonometric limits
Rewrite (sin 7x)/2x as 7/2 × (sin 7x)/7x. As x → 0, the expression tends to (a) 2/7 (b) 7/2 (c) 1 (d) 14
Question 3: Axes, planes and octants
All the points with x > 0, y < 0 and z > 0 lie in octant (a) V (b) II (c) IV (d) VIII

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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