HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Heramb requires at most 400 calories from his breakfast. Every morning he likes to take oats and milk. If each bowl of oats and a glass of milk provides him 80 calories and 50 calories respectively, then as a constraint this information can be expressed as ______

Ganesh owns a godown used to store electronic gadgets like refrigerator (x) and microwave (y). If the godown can accommodate at most 75 gadgets, then this can be expressed as a constraint by ______

Ms. Mohana want to invest at least ₹ 55000 in Mutual funds and fixed deposits. Mathematically this information can be written as ______

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The assignment problem is generally defined as a problem of ______

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Assignment Problem is special case of ______

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When an assignment problem has more than one solution, then it is ______

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The assignment problem is said to be balanced if ______

If the given matrix is ______ matrix, the assignment problem is called balanced problem

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

State whether the following statement is True or False:

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

State whether the following statement is True or False: 

In assignment problem each worker or machine is assigned only one job

X : is number obtained on upper most face when a fair die is thrown then E(X) = ______

The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.

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For the Poisson distribution ______

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A distance random variable X is said to have the Poisson distribution with parameter m if its p.m.f. is given by P(x) = `("e"^(-"m")"m"^"x")/("x"!)` the condition for m is ______

State whether the following statement is True or False:

X is the number obtained on upper most face when a die is thrown, then E(x) = 3.5

State whether the following statement is True or False:  

A discrete random variable X is said to follow the Poisson distribution with parameter m ≥ 0 if its p.m.f. is given by P(X = x) = `("e"^(-"m")"m"^"x")/"x"`, x = 0, 1, 2, .....

State whether the following statement is True or False:

If n is very large and p is very small then X follows Poisson distribution with n = mp

The probability that a bomb will hit the target is 0.8. Using the following activity, find the probability that, out of 5 bombs, exactly 2 will miss the target

Solution: Let p = probability that bomb miss the target

∴ q = `square`, p = `square`, n = 5.

X ~ B`(5, square)`, P(x) = `""^"n""C"_x"P"^x"q"^("n" - x)`

P(X = 2) =  `""^5"C"_2  square = square`