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

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

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

A random variable X has the following probability distribution:

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

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

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

(a) 0

(b) -2

(c) 2 

(d) ±2

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

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

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

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

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) ,  "for " x != 0 `

`=k`,            for x=0

is continuos at x=0

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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

[0.05] Applications of Derivative
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions

Examine the continuity of the following function :

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

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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

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

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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.

[0.08] Ratio, Proportion and Partnership
Chapter: [0.08] Ratio, Proportion and Partnership
Concept: Ratio, Proportion and Partnership

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?     

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

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

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

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?

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

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.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

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

 

 

 

 

 

                          Advertisement

Expenditure (Rs. in lakh)

            (X)

Sales (Rs. in lakh)

           (Y)

Arithmetic mean

10

90

Standard deviation

3

12

 

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?

[0.13] Regression Analysis Introduction
Chapter: [0.13] Regression Analysis Introduction
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

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`

[0.13] Regression Analysis Introduction
Chapter: [0.13] Regression Analysis Introduction
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

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.

[0.1] Insurance and Annuity
Chapter: [0.1] Insurance and Annuity
Concept: Insurance and Annuity

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:

         Jobs

 

 

                          Machines

P

Q

R

S

                Processing Cost (Rs.)

 

A

31

25

33

29

B

25

24

23

21

C

19

21

23

24

D

38

36

34

40

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

[0.027000000000000003] Assignment Problem and Sequencing
Chapter: [0.027000000000000003] Assignment Problem and Sequencing
Concept: Assignment Problem
 
 

Evaluate : `intlogx/(1+logx)^2dx`

 
 
[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

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

[0.12] Bivariate Data and Correlation
Chapter: [0.12] Bivariate Data and Correlation
Concept: Statistics > Bivariate Frequency Distribution
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