HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Choose the correct alternative:

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 ______.

Choose the correct alternative:

For the Poisson distribution ______

Choose the correct alternative:

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`

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, using the following activity find the value of m.

Solution: X : Follows Poisson distribution

∴ P(X) = `("e"^-"m" "m"^x)/(x!)`, P(X = 1) = 0.4 and P(X = 2) = 0.2

∴ P(X = 1) = `square` P(X = 2).

`("e"^-"m" "m"^x)/(1!) = square ("e"^-"m" "m"^2)/(2!)`,

`"e"^-"m" = square  "e"^-"m" "m"/2`, m ≠ 0

∴ m = `square`

A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

If ax² + 2hxy + by² = 0, then prove that `(d^2y)/(dx^2)` = 0.

State whether the following statement is true or false:

lf X ∼ P(m) with P(X = 1) = P(X = 2) then m = 1.

State whether the following statement is true or false:

Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.

If P₀₁ (L) = 121, P₀₁ (P) = 100, then P₀₁ (F) = ______.