CBSE Class 11 Maths starter questions: weeks 35–45
33 short questions to open a lesson for CBSE Class 11 Mathematics, weeks 35–45 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 35
Question 1: Rules and standard derivatives
If f(x) = 3x² - 5x + 2, then f'(1) is (a) 1 (b) 0 (c) 6 (d) -5
Question 2: Rules and standard derivatives
The derivative of sin xcos x is (a) -sin 2x (b) cos 2x (c) cos² x (d) -sin xcos x
Question 3: Distance between two points
The distance of (3, 4, 12) from the origin is (a) 13 (b) 19 (c) 5 (d) √19
Week 36
Question 1: Variance and standard deviation
The variance of 1, 2, 3, 4, 5 is (a) 3 (b) √2 (c) 2 (d) 10
Question 2: Dispersion and range
The range of the data 12, 7, 19, 3, 15 is (a) 22 (b) 19 (c) 12 (d) 16
Question 3: Factorial
The value of (8!)/(6!) is (a) 2 (b) 48 (c) 56 (d) 43
Week 37
Question 1: Events
Two dice are thrown. The probability that the sum is 7 or both dice show the same number is (a) 16 (b) 11/36 (c) 13 (d) 5/18
Question 2: Variance and standard deviation
If every observation of a data set is multiplied by 3, its standard deviation is (a) multiplied by 3 (b) unchanged (c) multiplied by 9 (d) increased by 3
Question 3: The binomial theorem
The number of terms in the expansion of (a + b)⁷ is (a) 7 (b) 8 (c) 14 (d) 6
Week 38
Question 1: Random experiments and sample spaces
A coin is tossed three times. The number of outcomes in the sample space is (a) 3 (b) 6 (c) 8 (d) 9
Question 2: Mean deviation
The mean deviation about the mean of 2, 4, 6, 8, 10 is (a) 2 (b) 2.4 (c) 6 (d) 0
Question 3: Geometric progressions
The 6th term of the GP 2, 6, 18, … is (a) 486 (b) 1458 (c) 162 (d) 972
Week 39
Question 1: Axiomatic probability
A sample space has three outcomes. Which of these is NOT a valid assignment of probabilities to them? (a) 0.2, 0.3, 0.5 (b) 13, 13, 13 (c) 0, 0.4, 0.6 (d) 0.6, 0.5, -0.1
Question 2: Variance and standard deviation
Five observations have mean 8 and variance 4. The sum of their squares is (a) 68 (b) 320 (c) 360 (d) 340
Question 3: Slope
The slope of the line through (2, 3) and (6, 11) is (a) 12 (b) 2 (c) 8 (d) -2
Week 40
Question 1: Events
Two dice are thrown. The probability that the sum is 7 or both dice show the same number is (a) 16 (b) 11/36 (c) 13 (d) 5/18
Question 2: Parabola
The focus of the parabola y² = 12x is (a) (12, 0) (b) (-3, 0) (c) (0, 3) (d) (3, 0)
Question 3: Axes, planes and octants
The point (-2, 3, -5) lies in octant (a) II (b) VI (c) III (d) VII
Week 41
Question 1: Random experiments and sample spaces
A coin is tossed three times. The number of outcomes in the sample space is (a) 3 (b) 6 (c) 8 (d) 9
Question 2: Polynomial and rational functions
lim_x → 2 (x² - 4)/(x - 2) equals (a) 0 (b) 2 (c) does not exist (d) 4
Question 3: Dispersion and range
The range of the data 12, 7, 19, 3, 15 is (a) 22 (b) 19 (c) 12 (d) 16
Week 42
Question 1: Axiomatic probability
A sample space has three outcomes. Which of these is NOT a valid assignment of probabilities to them? (a) 0.2, 0.3, 0.5 (b) 13, 13, 13 (c) 0, 0.4, 0.6 (d) 0.6, 0.5, -0.1
Question 2: Modulus and conjugate
The modulus of 3 - 4i is (a) 7 (b) 25 (c) -1 (d) 5
Question 3: Rules for solving
If -2x ≥ 6, then (a) x ≥ -3 (b) x ≥ 3 (c) x ≤ -3 (d) x ≤ 3
Week 43
Question 1: 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 2: Special cases
The value of (√3 + 1)⁴ + (√3 - 1)⁴ is (a) 28 (b) 56 (c) 64 (d) 32√3
Question 3: Geometric mean and AM ≥ GM
The geometric mean of 4 and 16 is (a) 10 (b) 8 (c) 64 (d) 12
Week 44
Question 1: 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 2: Circle
The centre and radius of x² + y² - 6x + 4y - 12 = 0 are (a) (3, -2) and 5 (b) (-3, 2) and 5 (c) (3, -2) and √12 (d) (6, -4) and 5
Question 3: 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
Week 45
Question 1: Polynomial and rational functions
lim_x → 1 (x¹⁰ - 1)/(x⁴ - 1) equals (a) 25 (b) 10 (c) 54 (d) 52
Question 2: Variance and standard deviation
The variance of 1, 2, 3, 4, 5 is (a) 3 (b) √2 (c) 2 (d) 10
Question 3: Events
Two dice are thrown. The probability that the sum is 7 or both dice show the same number is (a) 16 (b) 11/36 (c) 13 (d) 5/18
More starter questions
Other weeks: Weeks 1–19 · Weeks 20–34 · Weeks 35–45. Answers and mark schemes are in the teacher tools.