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CBSE Class 11 Maths Question of the Day: chapters 12–14

30 CBSE Class 11 Mathematics puzzles from the Question of the Day rotation, chapters 12–14. Each puzzle is three board-style questions on one chapter, shown as an image with the question text written out below it; the answers, hints and step-marked solutions are on the daily puzzle page.

Chapter 12: Limits and Derivatives

Chapter 12: Limits and Derivatives
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. lim_x → 2 (x² - 4)/(x - 2) equals Options: A) 0; B) 2; C) does not exist; D) 4
2. If f(x) = 3x² - 5x + 2, then f'(1) is Options: A) 1; B) 0; C) 6; D) -5
3. lim_x → 0 (sin 3x)/x equals Options: A) 1; B) 13; C) 3; D) 0
Chapter 12: Limits and Derivatives · Trigonometric limits
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. lim_x → 0 (sin x + sin 3x)/2x equals Options: A) 2; B) 1; C) 4; D) 3/2
2. lim_x → 0 (sin 4x)/(sin 2x) equals Options: A) 1; B) 4; C) 2; D) 1/2
3. lim_x → 0 (1 - cos 2x)/(x²) equals Options: A) 4; B) 0; C) 2; D) 1
Chapter 12: Limits and Derivatives · Product and quotient rules
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. d/dx(x² sin x) equals Options: A) 2xcos x; B) 2xsin x - x²cos x; C) x²cos x; D) 2xsin x + x²cos x
2. d/dx(x/(x + 1)) equals Options: A) 1/((x + 1)²); B) (-1)/((x + 1)²); C) (2x + 1)/((x + 1)²); D) 1
3. The derivative of tan x at x = (π)/4 is Options: A) 1/2; B) 2; C) 1; D) √2
Chapter 12: Limits and Derivatives · The derivative from first principles
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator. Let f(x) = x² + 3x.
1. f(x + h) - f(x) equals Options: A) 2xh + 3h; B) x² + 2xh + h²; C) 2xh + h² + 3h; D) h² + 3h
2. lim_h → 0 (f(x + h) - f(x))/h equals Options: A) 2x + h + 3; B) x² + 3; C) 2x; D) 2x + 3
3. lim_h → 0 (f(2 + h) - f(2))/h equals Options: A) 10; B) 4; C) 5; D) 7
Chapter 12: Limits and Derivatives · One-sided limits
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator. Let f(x) = 2x + 1 for x < 1 and f(x) = x² + k for x ≥ 1.
1. The left-hand limit of f at x = 1 is Options: A) k + 1; B) 3; C) 1; D) 2
2. lim_x → 1 f(x) exists when k equals Options: A) 2; B) 3; C) 1; D) 0
3. With this value of k, lim_x → 2 f(x) equals Options: A) 6; B) 5; C) 4; D) 8
Chapter 12: Limits and Derivatives · Derivatives of trigonometric functions
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. d/dx(sin² x) equals Options: A) 2sin x; B) 2cos x; C) cos 2x; D) sin 2x
2. d/dx(sec x) equals Options: A) sec² x; B) -sec xtan x; C) tan² x; D) sec xtan x
3. d/dx((sin x)/(1 + cos x)) equals Options: A) 1/(1 + cos x); B) (cos x)/(1 + cos x); C) (-1)/(1 + cos x); D) (cos x)/((1 + cos x)²)
Chapter 12: Limits and Derivatives · Slopes of tangents and a limit that fails
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. The point on y = x² - 4x + 5 where the tangent is parallel to the x-axis is Options: A) (4, 5); B) (2, 1); C) (1, 2); D) (2, 5)
2. The values of x at which the curve y = x³ - 3x has slope 9 are Options: A) ± 2; B) ± √3; C) 2 only; D) ± 3
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): lim_x → 0 (|x|)/x does not exist. Reason (R): The left-hand limit of (|x|)/x at 0 is -1 and the right-hand limit is 1. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 12: Limits and Derivatives · Limits by substitution and factorising
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. lim_x → 2 (x³ - 3x + 1) equals Options: A) 3; B) 1; C) 15; D) -1
2. lim_x → -1 (2x² + x) equals Options: A) 3; B) -3; C) -1; D) 1
3. lim_x → 3 (x² - 9)/(x - 3) equals Options: A) 9; B) 6; C) 0; D) 3
Chapter 12: Limits and Derivatives · Differentiating a polynomial
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator. Let f(x) = x⁴ - 3x² + 5x.
1. f'(x) equals Options: A) 4x³ - 6x; B) 4x³ - 6x + 5; C) 4x³ - 3x + 5; D) x³ - 6x + 5
2. f'(1) equals Options: A) 3; B) 1; C) 5; D) 15
3. The slope of the tangent to y = f(x) at x = -1 is Options: A) 3; B) 15; C) 7; D) -7
Chapter 12: Limits and Derivatives · Limits of rational functions
Three board-style questions on Limits and Derivatives (CBSE Class 11 Mathematics). No calculator.
1. lim_x → 1 (x³ - 1)/(x - 1) equals Options: A) 1; B) 0; C) 2; D) 3
2. lim_x → 2 (x² - 5x + 6)/(x² - 4) equals Options: A) 1/4; B) -1; C) 0; D) - 1/4
3. lim_x → 3 (x⁴ - 81)/(x - 3) equals Options: A) 81; B) 324; C) 108; D) 27

Chapter 13: Statistics

Chapter 13: Statistics
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator.
1. The range of the data 12, 7, 19, 3, 15 is Options: A) 22; B) 19; C) 12; D) 16
2. The mean deviation about the mean of 2, 4, 6, 8, 10 is Options: A) 2; B) 2.4; C) 6; D) 0
3. The variance of 1, 2, 3, 4, 5 is Options: A) 3; B) √2; C) 2; D) 10
Chapter 13: Statistics · Grouped data
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. Use the mid-points of the classes. Class0-1010-2020-3030-40Frequency3773
1. The mean is Options: A) 15; B) 10; C) 20; D) 25
2. The mean deviation about the mean is Options: A) 5; B) 160; C) 8; D) 10
3. The variance is Options: A) 85; B) 64; C) 125; D) 100
Chapter 13: Statistics · Using sums
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. For 10 observations, Σ x_i = 60 and Σ x_i² = 400.
1. The mean is Options: A) 6; B) 40; C) 10; D) 4
2. The variance is Options: A) 40; B) 34; C) 2; D) 4
3. The standard deviation is Options: A) √34; B) 2; C) 4; D) 16
Chapter 13: Statistics · Changing every value
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. A set of observations has mean 20 and standard deviation 4.
1. If 5 is added to every observation, the new standard deviation is Options: A) 20; B) 4/5; C) 4; D) 9
2. If every observation is multiplied by -2, the new standard deviation is Options: A) 8; B) -8; C) 4; D) 16
3. If every observation x is replaced by 3x - 1, the new variance is Options: A) 143; B) 36; C) 144; D) 48
Chapter 13: Statistics · Correcting a recording error
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. Ten observations have mean 12 and variance 9. Later it is found that one observation, 15, was recorded as 5.
1. The correct mean is Options: A) 27/2; B) 13; C) 12; D) 11
2. The correct value of Σ x_i² is Options: A) 1730; B) 1530; C) 1630; D) 1330
3. The correct variance is Options: A) 13; B) 4; C) 9; D) 173
Chapter 13: Statistics · Comparing spread
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. Data set P is 5, 6, 7, 8, 9 and data set Q is 1, 4, 7, 10, 13.
1. The variance of P is Options: A) 10; B) √2; C) 1; D) 2
2. The standard deviation of Q is Options: A) 6; B) √6; C) 3 √2; D) 18
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): Adding 10 to every value of a data set does not change its variance. Reason (R): Adding a constant to every value adds the same constant to the mean, so every deviation from the mean is unchanged. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 13: Statistics · Range, mean and mean deviation
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. The data are 4, 7, 9, 12, 18.
1. The range is Options: A) 9; B) 14; C) 18; D) 5
2. The mean is Options: A) 10; B) 9; C) 12; D) 50
3. The mean deviation about the mean is Options: A) 4; B) 0; C) 20; D) 5
Chapter 13: Statistics · Mean deviation about the median
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. The data are 3, 5, 6, 9, 12, 14, 16.
1. The median is Options: A) 9; B) 6; C) 12; D) 65
2. Σ |x_i - M|, where M is the median, equals Options: A) 28; B) 0; C) 30; D) 4
3. The mean deviation about the median is Options: A) 4; B) 14/3; C) 9; D) 7/2
Chapter 13: Statistics · Variance and standard deviation
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. The data are 2, 4, 6, 8, 10.
1. The variance is Options: A) 2 √2; B) 8; C) 10; D) 40
2. The standard deviation is Options: A) 4; B) √10; C) 2 √2; D) 8
3. If every value is multiplied by 3, the new variance is Options: A) 24; B) 8; C) 11; D) 72
Chapter 13: Statistics · A frequency table
Three board-style questions on Statistics (CBSE Class 11 Mathematics). No calculator. The table shows values x_i with frequencies f_i. x_i12345f_i23532
1. The mean is Options: A) 15/2; B) 3; C) 9; D) 5/2
2. The mean deviation about the mean is Options: A) 6/5; B) 2/3; C) 22/15; D) 14/15
3. The variance is Options: A) 14/15; B) 2; C) 11/15; D) 22/15

Chapter 14: Probability

Chapter 14: Probability
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator.
1. A coin is tossed three times. The number of outcomes in the sample space is Options: A) 3; B) 6; C) 8; D) 9
2. If P(A) = 0.35, then P(not A) is Options: A) 0.65; B) 0.35; C) 0.75; D) 1.35
3. If P(A) = 0.5, P(B) = 0.3 and P(A ∩ B) = 0.1, then P(A ∪ B) is Options: A) 0.8; B) 0.7; C) 0.9; D) 0.6
Chapter 14: Probability · Drawing two balls
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. A bag has 4 red and 6 blue balls. Two balls are drawn at random together.
1. The probability that both are red is Options: A) 4/25; B) 1/15; C) 4/15; D) 2/15
2. The probability of one red and one blue is Options: A) 12/25; B) 8/15; C) 6/25; D) 4/15
3. The probability of at least one red ball is Options: A) 2/3; B) 1/3; C) 8/15; D) 2/15
Chapter 14: Probability · Two cards
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. Two cards are drawn together at random from a well-shuffled pack of 52 cards.
1. The probability that both are aces is Options: A) 1/169; B) 1/13; C) 2/221; D) 1/221
2. The probability that both are hearts is Options: A) 1/13; B) 1/17; C) 1/16; D) 1/4
3. The probability of one king and one queen is Options: A) 16/221; B) 8/663; C) 4/663; D) 1/169
Chapter 14: Probability · Axiomatic probability
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. A sample space is S = ω_1, ω_2, ω_3, ω_4 with P(ω_1) = 18, P(ω_2) = 14 and P(ω_3) = 38.
1. P(ω_4) equals Options: A) 1/4; B) 1/8; C) 3/8; D) 3/4
2. Which of these is a valid assignment of probabilities to ω_1, ω_2, ω_3, ω_4 (in that order)? Options: A) 12, 14, 18, 18; B) 12, 12, 12, -12; C) 13, 13, 13, 13; D) 0.4, 0.3, 0.2, 0.2
3. P(ω_1, ω_3) equals Options: A) 1/4; B) 3/64; C) 1/2; D) 3/8
Chapter 14: Probability · Random arrangements of letters
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. The letters of the word TRIANGLE are arranged in a row at random.
1. The probability that the arrangement begins with a vowel is Options: A) 5/8; B) 1/8; C) 3/5; D) 3/8
2. The probability that it begins and ends with a consonant is Options: A) 3/28; B) 5/8; C) 5/14; D) 25/64
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The events 'the arrangement begins with T' and 'the arrangement ends with T' are mutually exclusive. Reason (R): The letter T occurs only once in TRIANGLE. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 14: Probability · A die and a coin
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. A fair coin is tossed and a fair die is rolled.
1. The number of outcomes in the sample space is Options: A) 12; B) 8; C) 36; D) 6
2. The probability of a head and an even number is Options: A) 1/2; B) 1/3; C) 3/4; D) 1/4
3. The probability of a tail or a number greater than 4 is Options: A) 5/6; B) 1/2; C) 1/6; D) 2/3
Chapter 14: Probability · The complement of an event
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator.
1. If P(A) = 0.35, then P(not A) equals Options: A) 0.35; B) 0.75; C) 1.35; D) 0.65
2. A card is drawn at random from a well-shuffled pack of 52 cards. The probability that it is not a king is Options: A) 1/13; B) 4/13; C) 48/13; D) 12/13
3. A letter is chosen at random from the word PROBABILITY (each of its 11 letters equally likely). The probability that it is not a vowel is Options: A) 8/11; B) 7/11; C) 4/11; D) 6/11
Chapter 14: Probability · Two dice
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. Two fair dice are rolled.
1. The probability that the sum is 8 is Options: A) 1/9; B) 7/36; C) 5/36; D) 1/6
2. The probability of a doublet (both numbers the same) is Options: A) 1/3; B) 1/6; C) 1/36; D) 1/12
3. The probability that the product of the numbers is 12 is Options: A) 1/9; B) 1/18; C) 1/12; D) 1/6
Chapter 14: Probability · The addition rule
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2.
1. P(A ∪ B) equals Options: A) 0.1; B) 0.5; C) 0.7; D) 0.9
2. P(A ∩ B'), the probability of A but not B, equals Options: A) 0.1; B) 0.2; C) 0.3; D) 0.5
3. The probability that exactly one of A, B happens is Options: A) 0.7; B) 0.3; C) 0.9; D) 0.5
Chapter 14: Probability · Mutually exclusive and exhaustive events
Three board-style questions on Probability (CBSE Class 11 Mathematics). No calculator. A die is rolled. A = 2, 4, 6, B = 1, 3 and C = 3, 5, 6.
1. Which two events are mutually exclusive? Options: A) A and B; B) A and C; C) B and C; D) no two of them
2. Which statement about A, B and C is true? Options: A) they are neither mutually exclusive nor exhaustive; B) they are exhaustive but not mutually exclusive; C) they are mutually exclusive and exhaustive; D) they are mutually exclusive but not exhaustive
3. P(A ∪ C) equals Options: A) 1; B) 2/3; C) 1/2; D) 5/6

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Other chapters: Chapters 1–4 · Chapters 5–8 · Chapters 9–11 · Chapters 12–14. See all CBSE Maths daily and weekly questions.