HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The number of complaints which a bank manager receives per day is a Poisson random variable with parameter m = 4. Find the probability that the manager will receive -

(a) only two complaints on any given day.

(b) at most two complaints on any given day

[Use e^-4 =0.0183]

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

 How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Solve the following minimal assignment problem and hence find the minimum value : 

Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.
                                             Service Time ( in hrs.)

 If a random variable X follows Poisson distribution such that P(X = l) =P(X = 2), then find P(X ≥ 1).  [Use e^-2 = 0.1353] 

 If X has Poisson distribution with parameter m = 1, find P[X ≤ 1]  [Use `e^-1 = 0.367879`]

If X has a Poisson distribution with variance 2, find P (X = 4) 

[Use e^-2 = 0.1353] 

If X has a Poisson distribution with variance 2, find P(X ≤ 4) 

[Use e^-2 = 0.1353] 

If X has a Poisson distribution with variance 2, find 

Mean of X [Use e^-2 = 0.1353] 

Solve the following minimal assignment problem : 

Determine `l_92 and l_93, "given that"  l_91 = 97, d_91 = 38 and q_92 = 27/59`

Solve the following minimal assignment problem and hence find minimum time where  '- ' indicates that job cannot be assigned to the machine : 

Solve the following maximal assignment problem :

A departmental head has three jobs and four subordinates. The subordinates differ in their capabilities and the jobs differ in their work
contents. With the help of the performance matrix given below, find out which of the four subordinates should be assigned which jobs ?

In a factory there are six jobs to be performed each of which should go through two machines A and B in the order A - B. The processing timing (in hours) for the jobs arc given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T. What is the value of T? Also find the idle time for machines · A and B.

Feasible region is the set of points which satisfy ______.

Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

A triangle has ‘n’ sides.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The sum of interior angles of a triangle is 180°

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

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