the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12 Solution: Given data is 6, 7, 10, 12, 13, 4, 8, 12 xi (xi - x) (xi - x)2 6 -3 9 7 -2 4 10 -1 1 12 3 9 13 4 16 4 -5 25 8 -1 1… Continue reading Statistics – Exercise 15.2 – Class XI

# Category: 11th mathematics exercise questions with answers

## Limits and derivatives – Exercise 13.1 – Class XI

## Straight Lines – Exercise 10.2 – Class XI

Write the equations for the x and y-axes. Solution: The y-coordinate of every point on the x-axis is 0. Therefore, the equation of the x-axis is y = 0. The x-coordinate of every point on the y-axis is 0. Therefore, the equation of the y-axis is y = 0. Find the equation of the line… Continue reading Straight Lines – Exercise 10.2 – Class XI

## Straight Lines – Exercise 10.1 – Class XI

Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area. Solution: Let ABCD be the given quadrilateral with vertices A (–4, 5), B (0, 7), C (5, –5), and D (–4, –2). Now let us plot A, B, C, and D on… Continue reading Straight Lines – Exercise 10.1 – Class XI

## Probability – Exercise 16.3 – Class XI

Which of the following cannot be valid assignment of probabilities for outcomes of sample space? S = {ω1, ω2, ω3, ω4, ω5, ω6, ω7} Assignment ω1 ω2 ω3 ω4 ω5 ω6 ω7 (a) 0.1 0.001 0.05 0.03 0.01 0.2 0.6 (b) 1/7 1/7 1/7 1/7 1/7 1/7 1/7 (c) 0.1 0.2 0.3 0.4 0.5 0.6… Continue reading Probability – Exercise 16.3 – Class XI

## Probability – Exercise 16.2 – Class XI

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive? Solution: When a die is rolled, the sample space is given by S = {1, 2, 3, 4, 5, 6} Then, E = {4} and F = {2,… Continue reading Probability – Exercise 16.2 – Class XI

## Probability – Exercise 16.1 – Class XI

Describe the sample space for the indicated experiment: A coin is tossed three times. Solution: A coin has two faces: head (H) and tail (T). It is given that, a coin is tossed three times, then the total number of possible outcomes is 23= 8 Thus, when a coin is tossed three times, the sample… Continue reading Probability – Exercise 16.1 – Class XI

## Mathematical Reasoning – Exercise 14.5 – Class XI

Show that the statement p: “If x is a real number such that x3+ 4x = 0, then x is 0” is true by (i) direct method (ii) method of contradiction (iii)method of contrapositive Solution: p: “If x is a real number such that x3 + 4x = 0, then x is 0”. q: x… Continue reading Mathematical Reasoning – Exercise 14.5 – Class XI

## Mathematical Reasoning – Exercise 14.4 – Class XI

Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd. Solution: The given statement can be written in five different ways as follows. (i) A natural number is odd implies that its square is odd. (ii) A natural number… Continue reading Mathematical Reasoning – Exercise 14.4 – Class XI

## Mathematical Reasoning – Exercise 14.3 – Class XI

For each of the following compound statements first identify the connecting words and then break it into component statements. (i) All rational numbers are real and all real numbers are not complex. (ii) Square of an integer is positive or negative. (iii) The sand heats up quickly in the Sun and does not cool down… Continue reading Mathematical Reasoning – Exercise 14.3 – Class XI