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

Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`

A random variable X has the following probability distribution:

then E(X)=....................

If `int_0^alpha3x^2dx=8` then the value of α is :

(a) 0

(b) -2

(c) 2 

(d) ±2

Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`

Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) ,  "for " x != 0 `

`=k`,            for x=0

is continuos at x=0

Price P for demand D is given as P = 183 +120D - 3D² Find D for which the price is increasing

Examine the continuity of the following function :

`{:(,,f(x)= x^2 -x+9,"for",x≤3),(,,=4x+3,"for",x>3):}}"at "x=3`

 If 'f' is continuous at x = 0, then find f(0).

`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`

The ratio of number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, find the percentage of students who are not scholarship holders.

An agent charges 12% commission on the sales. What does he earn if the total sale amounts to Rs. 36,000? What does the seller get?     

The present worth of the sum of Rs. 5,830, due 9 months hence, is Rs. 5,500. Find the rate of interest.

Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?

From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -

(a) exactly 1 defective bulb.

(b) at least 1 defective bulb.

 You are given the following information about advertising expenditure and sales:

Correlation coefficient between X and Y = 0.8.

(a) Obtain the two regression equations.

(b) What is the likely sales when the advertising budget is ? 15 lakh?

(c) What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.

Find:

(a) Correlation coefficient

(b) `sigma_x/sigma_y`

A warehouse valued at Rs. 10,000 contained goods worth Rs. 60,000. The warehouse was insured against fire for Rs. 4,000 and the goods to the extent of 90% of their value. A fire broke out and goods worth Rs. 20,000 were completely destroyed, while the remainder was damaged and reduced to 80% of its value. The damage to the warehouse was to the extent of Rs. 2,000. Find the total amount that can be claimed.

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?

Evaluate : `intlogx/(1+logx)^2dx`

For the bivariate data r = 0.3, cov(X, Y) = 18, σ_x = 3, find σ_y .