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

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

State whether the following is True or False :

In assignment problem, each facility is capable of performing each task.

State whether the following is True or False :

It is not necessary to express an assignment problem into n x n matrix.

Solve the following problem :

A plant manager has four subordinates, and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This estimate of the time each man would take to perform each task is given in the effectiveness matrix below.

How should the tasks be allocated, one to a man, as to minimize the total man hours?

Solve the following problem :

A dairy plant has five milk tankers, I, II, III, IV and V. These 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 X has Poisson distribution with m = 1, then find P(X ≤ 1) given e⁻¹ = 0.3678

If X~P(0.5), then find P(X = 3) given e^−0.5 = 0.6065.

If X has Poisson distribution with parameter m and P(X = 2) = P(X = 3), then find P(X ≥ 2). Use e⁻³ = 0.0497

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives a) only two complaints on a given day, b) at most two complaints on a given day. Use e⁻⁴ = 0.0183.

A car firm has 2 cars, which are hired out day by day. The number of cars hired on a day follows Poisson distribution with mean 1.5. Find the probability that (i) no car is used on a given day, (ii) some demand is refused on a given day, given e^−1.5 = 0.2231.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has exactly 5 rats inclusive. Given e^-5  = 0.0067.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has more than 5 rats inclusive. Given e^-5  = 0.0067.

It is known that, in a certain area of a large city, the average number of rats per bungalow is five. Assuming that the number of rats follows Poisson distribution, find the probability that a randomly selected bungalow has between 5 and 7 rats inclusive. Given e⁻⁵ = 0.0067.

If E(X) = m and Var(X) = m then X follows ______.

Solve the following problem :

If X follows Poisson distribution such that P(X = 1) = 0.4 and P(X = 2) = 0.2, find variance of X.

Solve the following problem :

If X follows Poisson distribution with parameter m such that
`("P"("X" = x + 1))/("P"("X" = x)) = (2)/(x + 1)`
Find mean and variance of X.

If y = sec (tan⁻¹x), then `dy/dx` at x = 1 is ______.

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`