HSC Commerce 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Mathematics and Statistics 2014-2015 HSC Commerce 12th Board Exam Question Paper Solution

Login
Create free account


      Forgot password?
Mathematics and Statistics
2014-2015 March
Marks: 80

[12]1 | Attempt any SIX of the following
[2]1.1

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "

Concept: Mathematical Logic - Statement Patterns and Logical Equivalence
Chapter: [1] Mathematical Logic
[2]1.2
 

Find the values of x and y, if 

`2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]]`

 

 
Concept: Solution of Equations
Chapter: [2] Matrices
[2]1.3

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) , `

`=k`,            for x=0

is continuos at x=0

 

Concept: Continuous Function of Point
Chapter: [3] Continuity
[2]1.4

Find dy/dx if `y=cos^-1(sqrt(x))`

Concept: Derivative - Derivative of Inverse Function
Chapter: [4] Differentiation
[2]1.5

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

Concept: Increasing and Decreasing Functions
Chapter: [5] Applications of Derivative
[2]1.6

Evaluate : `int1/(x(3+logx))dx`

 

Concept: Indefinite Integration - Methods of Integration
Chapter: [6] Indefinite Integration
[2]1.7

If   `a=[[2,1],[1,1]] " then show taht " A^2-3A+I=0`

 

Concept: Solution of Equations
Chapter: [2] Matrices
[2]1.8

evaluate : `int xcosxdx`

Concept: Indefinite Integration - Integration by Parts
Chapter: [6] Indefinite Integration
[14]2
[6]2.1 | Attempt any TWO of the following
[3]2.1.1

Prove that the following statement pattern is equivalent :

(p ∨ q)  r and (p → r) ∧ (q → r)

Concept: Mathematical Logic - Statement Patterns and Logical Equivalence
Chapter: [1] Mathematical Logic
[3]2.1.2

Examine the continuity of the following function : 

`f(x)=x^2-x+9` , for x ≤ 3

        `=4x+3`          for x > 3`

 

Concept: Continuous Function of Point
Chapter: [3] Continuity
[3]2.1.3

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

Concept: Derivative - Derivative of Inverse Function
Chapter: [4] Differentiation
[8]2.2 | Attempt any TWO of the following :
[4]2.2.1

 Find the inverse of the following matrix by elementary row transformations if it exists. `A=[[1,2,-2],[0,-2,1],[-1,3,0]]`

Concept: Inverse of Matrix
Chapter: [2] Matrices
[4]2.2.2

Find the area of elipse `x^2/a^2+y^2/b^2=1`

Concept: Applications of Definite Integrals
Chapter: [7] Definite Integrals
[4]2.2.3

The expenditure Ec of a person with income I is given by Ec = (0.000035) I2 + (0.045) I. Find marginal propensity to consume (MPC) and marginal propensity to save (MPS) when I = 5000. Also find A (average) PC and A (average)

PS.

Concept: Maxima and Minima
Chapter: [5] Applications of Derivative
[14]3
[6]3.1 | Attempt any TWO of the following :
[3]3.1.1

Express the truth of each of the following statements by Venn diagram:

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

 

Concept: Venn Diagrams
Chapter: [1] Mathematical Logic
[3]3.1.2

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

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

Concept: Continuous Function of Point
Chapter: [3] Continuity
[3]3.1.3

find dy/dx if x=e2t , y=`e^sqrtt`

Concept: Derivatives of Functions in Parametric Forms
Chapter: [4] Differentiation
[8]3.2 | Attempt any TWO of the following :
[4]3.2.1

Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`

Concept: Indefinite Integration - Methods of Integration
Chapter: [6] Indefinite Integration
[4]3.2.2

Evaluate :`int_0^(pi/2)dx/(1+cotx)`

Concept: Indefinite Integration - Integration by Parts
Chapter: [6] Indefinite Integration
[4]3.2.3

A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q2. Find the output for which profit is maximum and also find the profit amount at this output.

Concept: Maxima and Minima
Chapter: [5] Applications of Derivative
[12]4 | Attempt any SIX of the following :
[2]4.1

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.

Concept: Ratio, Proportion and Partnership
Chapter: [8] Ratio, Proportion and Partnership
[2]4.2

Obtain crude death rates (C. D. R.) for city A and city B from the data given below :

Age groups (in years)

City A

City B

Population

No. of deaths

Population

No. of deaths

Below 15

800

32

900

12

15-25

3000

12

1500

8

25-65

4800

48

4500

38

65 and above

1400

42

600

30

Concept: Measurements of Mortality
Chapter: [11] Demography
[2]4.3

Coefficient of rank correlation between x and y is 0.5 and `sumd_i^2`= 42. Assuming that no ranks are repeated, find the number of pairs of observations.

Concept: Rank Correlation
Chapter: [12] Bivariate Data and Correlation
[2]4.4

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?     

Concept: Commission, Brokerage and Discount
Chapter: [9] Commission, Brokerage and Discount
[2]4.5

     Find the age standard death rate (S. D. R.) for the following  data:

Age groups (in years)

Population (in '000)

No. of deaths

0-10

11

240

10-20

12

150

20-60

9

125

60 and above

2

90

 

Concept: Life Tables
Chapter: [11] Demography
[2]4.6

Following table gives the age of husbands and wives

Age of wives (in years)

Age of husbands (in years)

20-30

30-40

40-50

50-60

15-25

5

9

 -

25-35

10

25

2

35-45

1

12

2

45-55

4

16

55-65

4

 

Find:

(a)The marginal frequency distribution of the age of husbands.

(b)The conditional distribution of the age of husbands

 

Concept: Uses of Vital Statistics in Demography
Chapter: [11] Demography
[2]4.7

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

Concept: Commission, Brokerage and Discount
Chapter: [9] Commission, Brokerage and Discount
[2]4.8

For a binomial distribution mean is 6 and variance is 2. Find n and p.

Concept: Binomial Theorem and Binomial Distribution
Chapter: [14] Random Variable and Probability Distribution
[14]5
[6]5.1 | Attempt any TWO of the following :
[3]5.1.1

For the following problem, find the sequence that minimizes total elapsed time (in hours) required to complete jobs on two machines M1 and M2 in the order M1-M2 Also find the minimum elapsed time T.

Jobs

A

B

C

D

E

Machine M1

5

1

9

3

10

Machine M2

2

6

7

8

4

Concept: Sequencing in Management Mathematics
Chapter: [15] Management Mathematics
[3]5.1.2

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?

Concept: Commission, Brokerage and Discount
Chapter: [9] Commission, Brokerage and Discount
[3]5.1.3

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.

Concept: Random Variables and Its Probability Distributions
Chapter: [14] Random Variable and Probability Distribution
[8]5.2 | Attempt any TWO of the following :
[4]5.2.1

Given the following table which relates to the number of parrots at age x, complete the life table for parrots.

X

0

1

2

3

4

5

 lx

1000

940

780

590

25

0

Concept: Life Tables
Chapter: [11] Demography
[4]5.2.2

 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

 

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Chapter: [13] Regression Analysis Introduction
[4]5.2.3

Electro Corp. Co. manufactures two electrical products :Air conditioners and Fans. The assembly process for each is similar in which both require a certain amount of wiring and drilling. Each air conditioner takes 4 hours for wiring and 2 hours for drilling. Each fan also takes 2 hours for wiring and 1 hour for drilling. During the next production period, 240 hours of wiring time are available and upto 100 hours of drilling time may be used. Each air-conditioner assembled may be sold for Rs. 2,000 profit and each fan assembled may be sold for Rs. 1,000 profit. Formulate this problem as an L.P.P. in order to maximize the profit.

Concept: Commission, Brokerage and Discount
Chapter: [9] Commission, Brokerage and Discount
[14]6
[6]6.1 | Attempt any TWO of the following :
[3]6.1.1

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`

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Chapter: [13] Regression Analysis Introduction
[3]6.1.2

Find graphical solution for the following system of linear inequations:

2x + 3y ≥ 2, -x + y ≤ 3,  x ≤ 4, y ≥ 3

 

Concept: Linear Programming Problem in Management Mathematics
Chapter: [15] Management Mathematics
[3]6.1.3

The number of complaints which a bank manager receives per day is a Poisson random variable with parameter m = 4. Find the probability that the manager will receive -

(a) only two complaints on any given day.

(b) at most two complaints on any given day

[Use e-4 =0.0183]

Concept: Poisson Distribution
Chapter: [14] Random Variable and Probability Distribution
[8]6.2 | Attempt any TWO of the following :
[4]6.2.1

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.

Concept: Insurance and Annuity
Chapter: [10] Insurance and Annuity
[4]6.2.2

In the following data, one of the values of Y is missing. Arithmetic means of X and Y series are 6 and 8

X

6

2

10

4

8

Y

9

11

?

8

7

 (a) Estimate the missing observation.

 (b) Calculate correlation coefficient.

Concept: Statistics - Karl Pearson’s Coefficient of Correlation
Chapter: [12] Bivariate Data and Correlation
[4]6.2.3

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?

Concept: Assignment Problem
Chapter: [15] Management Mathematics

Request Question Paper

If you dont find a question paper, kindly write to us





      View All Requests

Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help students




only jpg, png and pdf files

Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2014 - 2015

     Maharashtra State Board 12th Board Exam Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our Maharashtra State Board 12th Board Exam Maths question paper 2015 serve as a catalyst to prepare for your Mathematics and Statistics board examination.
     Previous year Question paper for Maharashtra State Board 12th Board Exam Maths-2015 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
     By referring the question paper Solutions for Mathematics and Statistics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of Maharashtra State Board 12th Board Exam.

How Maharashtra State Board 12th Board Exam Question Paper solutions Help Students ?
• Question paper solutions for Mathematics and Statistics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
S
View in app×