Mathematics Part-1

Probability (Ex – 16.3) Question 1.Which of the following cannot be valid assignment of probabilities for outcomes of sample spaceS = {⍵1, ⍵2, ⍵3, ⍵4, ⍵5, ⍵6, ⍵7} Solution:(a) Sum of probabilities = 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1.00∴ Assignment of probabilities is valid.(b) Sum of […]

Probability (Ex – 16.2) Question 1.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:An experiment consists of rolling a die.∴ S = {1, 2, 3, 4, 5, 6}E: die shows 4 = {4}F : die shows

Probability (Ex – 16.1) In each of the following Exercises 1 to 7, describe the sample space for the indicated experiment. Question 1.A coin is tossed three times. Solution:When one coin is tossed three times, The sample space of the experiment is given by S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. Question

Statistics (Ex – 15.3) Question 1.From the data given below state which group is more variable, A or B? Solution:For Group A : Question 2.From the prices of shares X and Y below, find out which is more stable in value: Solution: Question 3.An analysis of monthly wages paid to workers in two firms A

Statistics (Ex – 15.2) Find the mean and variance for each of the data in Exercises 1 to 5. Question 1.6, 7, 10, 12, 13, 4, 8, 12 Solution:Here xi = 6, 7, 10, 12, 13, 4, 8, 12∴ Σxi = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 =

Statistics (Ex – 15.1) Find the mean deviation about the mean for the data in Exercises 1 and 2. Question 1.4, 7, 8, 9, 10, 12, 13, 17 Solution:Mean of the given data is Question 2.38, 70, 48, 40, 42, 55, 63, 46, 54, 44 Solution:Mean of the given data is Question 3.13, 17, 16,

Mathematical Reasoning (Ex – 14.5) Question 1.Show that the statementp: “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:The given compound statement is of the form “if p then q”p: x ϵ R such that x3 + 4x = 0q:

Mathematical Reasoning (Ex – 14.4) Question 1.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:(i) A natural number is odd implies that its square is odd.(ii) A natural number is odd only if its square is odd.(iii) For a natural

Mathematical Reasoning (Ex – 14.3) Question 1.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

Mathematical Reasoning (Ex – 14.2) Question 1.Write the negation of the following statements:(i) Chennai is the capital of Tamil Nadu.(ii) √2 is not a complex number.(iii) All triangles are not equilateral triangle.(iv) The number 2 is greater than 7.(v) Every natural number is an integer. Solution:(i) Negation of statement is: Chennai is not the capital of Tamil Nadu.(ii) Negation of statement is: √2 is a