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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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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Question Bank Solutions for HSC Commerce 12th Board Exam Maharashtra State Board Mathematics and Statistics. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for Maharashtra State Board can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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