HSC Commerce (Marketing and Salesmanship) 12th Board ExamMaharashtra State Board
Share

Books Shortlist

# Mathematics and Statistics 2017-2018 HSC Commerce (Marketing and Salesmanship) 12th Board Exam Question Paper Solution

SubjectMathematics and Statistics
Year2017 - 2018 (March)
Mathematics and Statistics
2017-2018 March
Marks: 80

[12]1 | Attempt any six of the following
[2]1.1
[2]1.1.1

(i) Draw Venn diagram for the truth of the following statements :

All rational number are real numbers.

Chapter: [1] Mathematical Logic
Concept: Venn Diagrams
[2]1.1.2

Draw Venn diagram for the truth of the following statements :

Some rectangles are squares.

Chapter: [1] Mathematical Logic
Concept: Venn Diagrams
[2]1.2

Find the inverse of the matrix A=[[1,2],[1,3]] using elementry transformations.

Chapter: [2] Matrices
Concept: Introduction of Matrices
[2]1.3

Examine the continuity of f(x)=x^2-x+9  "for"  x-<=3

=4x+3  "for"  x>3,  at  x=3

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

find dy/dx, if y= cos ^-1 (sin 5x)

Chapter: [11] Demography
Concept: Concept of Demography
[2]1.5

The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.

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

Evaluateint (1)/(x(3+log x))dx

Chapter: [7] Definite Integrals
Concept: Properties of Definite Integrals
[2]1.7

Find cofactors of the elements of the matrix A = [[-1,2],[-3,4]]

Chapter: [2] Matrices
Concept: Introduction of Matrices
[2]1.8

Evaluate : int 1/(9x^2+49) dx

Chapter: [6] Indefinite Integration
Concept: Indefinite Integration - Integral of Standard Functions
[14]2
[6]2.1 | Attempt any two of the following
[3]2.1.1

Find k, if f(x) =log (1+3x)/(5x) "for" x≠0

=  k  "for" x=0

is continuous at x = 0.

Chapter: [3] Continuity
Concept: Continuous Function of Point
[3]2.1.2

Examine whether the following statement pattern is tautology, contradiction or contingency :
p ∨ – (p ∧ q)

Chapter: [13] Regression Analysis Introduction
Concept: Regression Coefficient of X on Y and Y on X
[3]2.1.3

If x = cos2 θ and y = cot θ then find dy/dx  at  θ=pi/4

Chapter: [5] Applications of Derivative
Concept: Increasing and Decreasing Functions
[8]2.2 | Attempt any two of the following
[4]2.2.1

The sum of three numbers is 6. If we multiply the third number by 3 and add it to the second number we
get 11. By adding first and third numbers we get a number, which is double than the second number. Use
this information and find a system of linear equations. Find these three numbers using matrices.

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

Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.

Chapter: [2] Matrices
Concept: Inverse of Matrix
[4]2.2.3

The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x
Find MPC, MPS, APC and APS when the income x = 200.

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

Discuss continuity of f(x) =x^3-64/(sqrtx^2+9-5)For x≠4

= 10 for x = 4  at x = 4

Chapter: [3] Continuity
Concept: Continuous Function of Point
[3]3.1.2

Find dy/dx,if e^x+e^y=e^(x-y)

Chapter: [5] Applications of Derivative
Concept: Increasing and Decreasing Functions
[3]3.1.3

Using truth table show that – (p → – q) ≡ p ∧ q

Chapter: [5] Applications of Derivative
Concept: Increasing and Decreasing Functions
[8]3.2 | Attempt any TWO of the following :
[4]3.2.1

Evaluate :int Sinx/(sqrtCos^2 x-2 cos x-3)  dx

Chapter: [3] Continuity
Concept: Continuous Function of Point
[4]3.2.2

The total cost function of a firm is C = x^2 + 75x + 1600 for output x. Find the output (x) for which average
cost is minimum. Is C_A = C_M at this output?

Chapter: [5] Applications of Derivative
Concept: Maxima and Minima
[4]3.2.3

Evaluate : int_1^2 1/((x+1)(x+3)) dx

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

A shop valued at  2,40,000 is insured for 75% of its value. If the rate of premium is 90 paise percent, find the
premium paid by the owner of the shop.

Chapter: [10] Insurance and Annuity
Concept: Insurance and Annuity
[2]4.2

Find the Age-Specific Death Rate (Age-SDR) for the following data :

 Age groups(in years) Population(in '000) Number of deaths 1 - 10 11 240 10 - 20 12 150 20 -60 9 125 60 and above 2 90
Chapter: [10] Insurance and Annuity
Concept: Insurance and Annuity
[2]4.3

If Σdi^2 = 25, n = 6 find rank correlation coefficient where di, is the difference between the ranks of ith values.

Chapter: [12] Bivariate Data and Correlation
Concept: Statistics - Bivariate Frequency Distribution
[2]4.4

The following table gives the ages 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 3 - 25-35 - 10 25 2 35-45 - 1 12 2 45-55 - - 4 16 55-65 - - - 4

Find : (i) The marginal frequency distribution of the age of husbands.
(ii) The conditional frequency distribution of the age of husbands when the age of wives lies between
25 - 35.

Chapter: [12] Bivariate Data and Correlation
Concept: Statistics - Bivariate Frequency Distribution
[2]4.5

The regression equation of Y on X is y = 2/9 xand the regression equation of X on Y is x=y/2+7/6

Find : (i) Correlation coefficient between X and Y.

(ii) σ_y^2 if σ _x^2=4

Chapter: [12] Bivariate Data and Correlation
Concept: Statistics - Bivariate Frequency Distribution
[2]4.6

Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0

Chapter: [13] Regression Analysis Introduction
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
[2]4.7

If X has Poisson distribution with parameter m = 1, find P[X ≤ 1]. (Use e–1 = 0.3679)

Chapter: [13] Regression Analysis Introduction
Concept: Regression Propertise
[2]4.8

Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution
of X.

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

Ramesh, Vivek and Sunil started a business by investing capitals in the ratio 4 : 5 : 6. After 3 months Vivek withdrew all his capital and after 6 months Sunil withdrew all his capital from the business. At the end
of the year Ramesh received  6,400 as profit. Find the profit earned by Vivek.

Chapter: [9] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount
[13]5.1.2

Solve the following minimal assignment problem and hence find the minimum value :

 I II III IV A 2 10 9 7 B 13 2 12 2 C 3 4 6 1 D 4 15 4 9

Chapter: [15] Management Mathematics
Concept: Assignment Problem
[3]5.1.3

Calculate from e_0^0,e_1^0,e_2^0 from the following data :

 Age x 0 1 2 l_x 1000 900 700 T_x - - 11500
Chapter: [12] Bivariate Data and Correlation
Concept: Statistics - Karl Pearson’s Coefficient of Correlation
[8]5.2 | Attempt any TWO of the following :
[4]5.2.1

A bill was drawn on 12th April for  3,500 and was discounted on 4th July at 5% p.a. If the banker paid  3,465 for the bill. Find period of the bill.

Chapter: [9] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount
[4]5.2.2

Find Karl Pearson's correlation coefficient for the following data :

 X 3 2 1 5 4 Y 8 4 10 2 6
Chapter: [12] Bivariate Data and Correlation
Concept: Statistics - Karl Pearson’s Coefficient of Correlation
[4]5.2.3

Solve the following using graphical method :

Minimize :Z=3x+5y

2x+3x>=12

-x+y<=3

x<=4,y>=3,x>=0,y>=0

Chapter: [15] Management Mathematics
Concept: Linear Programming Problem in Management Mathematics
[14]6
[6]6.1 | Attempt any TWO of the following :
[3]6.1.1

Given the following information :

 Age groups(in years) Population Number of deaths 0 - 20 40,000 350 20 - 65 65,000 650 65 and above 15,000 x

Find X, if the CDR = 13.4 per thousand.

Chapter: [14] Random Variable and Probability Distribution
Concept: Probability Distribution of a Discrete Random Variable
[3]6.1.2

The manager of a company wants to find a measure which he can use to fix the monthly wages of persons applying for a job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years of service and their monthly income :

 Years of service 11 7 9 5 8 6 10 Income ( in thousands) 10 8 6 5 9 7 11

Find regression equation of income on the years of service.

Chapter: [15] Management Mathematics
Concept: Sequencing in Management Mathematics
[3]6.1.3

Solve the following inequation :
– 8 < – (3x – 5) < 13.

Chapter: [15] Management Mathematics
Concept: Inequations in Management Mathematics
[8]6.2
[4]6.2.1

Find the probability of guessing correctly at most three of the seven answers in a True or False objective test.

Chapter: [14] Random Variable and Probability Distribution
Concept: Probability Distribution of a Discrete Random Variable
[4]6.2.2

A person bought a television set paying  20,000 in cash and promised to pay  1,000 at the end of every month for the next 2 years. If the money is worth 12% p.a. converted monthly, what is the cash price of the television set?

Chapter: [9] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount
[4]6.2.3

The given problem is of n jobs and three machines. We change the problem in of n jobs and two machines.
For this either Min M1 ≤ M3 × M2 or min M3 ≤ max M2 Here min M3 = 7 = M1 × M2 Hence we write M1+ M2 = G and M2 + M3 = H the problem will be as follows

Chapter: [15] Management Mathematics
Concept: Linear Programming Problem in 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 2017 - 2018

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 2018 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-2018 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