HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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?

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) = ______.

A job production unit has four jobs P, Q, R, and S which can be manufactured on each of the four machines I, II, III, and IV. The processing cost of each job for each machine is given in the following table:

Find the optimal assignment to minimize the total processing cost.

Slope of the tangent to the curve y = 6 – x² at (2, 2) is ______.

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.

P[X = x] = `square`

Since P[X = 2] = P[X = 3]

`square` = `square`

`m^2/2 = m^3/6` 

∴ m = `square`

Now, P[X ≥ 2] = 1 – P[x < 2]

= 1 – {P[X = 0] + P[X = 1]

= `1 - {square/(0!) + square/(1!)}`

= 1 – e^–3[1 + 3]

= 1 – `square` = `square`

`sqrt((sump_1q_0)/(sump_0q_0)) xx sqrt((sump_1q_1)/(sump_0q_1)) xx 100`

Conditions under which the object function is to be maximum or minimum are called ______.

A department store has four workers to pack goods. The times (in minutes) required for each worker to complete the packings per item sold is given below. How should the manager of the store assign the jobs to the workers, so as to minimize the total time of packing?

If X – P(m) with P(X = 1) = P(X = 2), then find the mean and P(X = 2) given that e^–2 = 0.1353

Solution: Since P(X = 1) = P(X = 2)

`(e^-mm^1)/(1!) = square`

∴ m = `square`

∴ mean = `square` = `square`

Then P(X = 2) = `square` = `square`

Find the equation of tangent and normal to the curve y = x² + 5 where the tangent is parallel to the line 4x – y + 1 = 0.

Laspeyre’s Price Index Number uses current year’s quantities as weights.

An agent places insurance for ₹ 4,00,000 on life of a person. The premium is to be paid annually at the rate of ₹ 35 per thousand per annum. Find the agent’s commission at 15% on the premium.

An agent was paid ₹ 88,000 as a commission on the sales of computers at the rate of 12.5%. If the price of each computer was ₹ 32,000, how many computers did he sell?

Calculate Marshall – Edgeworth’s price index number for the following data:

Evaluate `int1/(x(x-1)) dx`

Evaluate `int 1/(x(x-1))dx`

Evaluate `int(5x^2 - 6x+3)/(2x- 3 )dx`