(i) Draw Venn diagram for the truth of the following statements :
All rational number are real numbers.
Concept: Venn Diagrams
Draw Venn diagram for the truth of the following statements :
Some rectangles are squares.
Concept: Venn Diagrams
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
Concept: Introduction of Matrices
Examine the continuity of f(x)=`x^2-x+9 "for" x-<=3`
=`4x+3 "for" x>3, at x=3`
Concept: Continuous Function of Point
find `dy/dx, if y= cos ^-1 (sin 5x)`
Concept: Concept of Demography
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
Concept: Increasing and Decreasing Functions
Evaluate`int (1)/(x(3+log x))dx`
Concept: Properties of Definite Integrals
Find cofactors of the elements of the matrix A = `[[-1,2],[-3,4]]`
Concept: Introduction of Matrices
Evaluate : `int 1/(9x^2+49) dx`
Concept: Indefinite Integration - Integral of Standard Functions
Find k, if f(x) =`log (1+3x)/(5x) "for" x≠0`
= `k "for" x=0`
is continuous at x = 0.
Concept: Continuous Function of Point
Examine whether the following statement pattern is tautology, contradiction or contingency :
p ∨ – (p ∧ q)
Concept: Regression Coefficient of X on Y and Y on X
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Concept: Increasing and Decreasing Functions
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.
Concept: Inverse of Matrix
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Concept: Inverse of Matrix
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.
Concept: Increasing and Decreasing Functions
Discuss continuity of f(x) =`x^3-64/(sqrtx^2+9-5)`For x≠4
= 10 for x = 4 at x = 4
Concept: Continuous Function of Point
Find dy/dx,if `e^x+e^y=e^(x-y)`
Concept: Increasing and Decreasing Functions
Using truth table show that – (p → – q) ≡ p ∧ q
Concept: Increasing and Decreasing Functions
Evaluate :`int Sinx/(sqrtCos^2 x-2 cos x-3) dx`
Concept: Continuous Function of Point
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?
Concept: Maxima and Minima
Evaluate : `int_1^2 1/((x+1)(x+3)) dx`
Concept: Maxima and Minima
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.
Concept: Insurance and Annuity
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 |
Concept: Insurance and Annuity
If `Σdi^2 = 25`, n = 6 find rank correlation coefficient where di, is the difference between the ranks of ith values.
Concept: Statistics - Bivariate Frequency Distribution
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.
Concept: Statistics - Bivariate Frequency Distribution
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`
Concept: Statistics - Bivariate Frequency Distribution
Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
If X has Poisson distribution with parameter m = 1, find P[X ≤ 1]. (Use e–1 = 0.3679)
Concept: Regression Propertise
Three fair coins are tossed simultaneously. If X denotes the number of heads, find the probability distribution
of X.
Concept: Random Variables and Its Probability Distributions
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.
Concept: Commission, Brokerage and Discount
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 |
Concept: Assignment Problem
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 |
Concept: Statistics - Karl Pearsonâ€™s Coefficient of Correlation
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.
Concept: Commission, Brokerage and Discount
Find Karl Pearson's correlation coefficient for the following data :
X | 3 | 2 | 1 | 5 | 4 |
Y | 8 | 4 | 10 | 2 | 6 |
Concept: Statistics - Karl Pearsonâ€™s Coefficient of Correlation
Solve the following using graphical method :
Minimize :Z=3x+5y
`2x+3x>=12`
`-x+y<=3`
`x<=4,y>=3,x>=0,y>=0`
Concept: Linear Programming Problem in Management Mathematics
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.
Concept: Probability Distribution of a Discrete Random Variable
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.
Concept: Sequencing in Management Mathematics
Solve the following inequation :
– 8 < – (3x – 5) < 13.
Concept: Inequations in Management Mathematics
Find the probability of guessing correctly at most three of the seven answers in a True or False objective test.
Concept: Probability Distribution of a Discrete Random Variable
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?
Concept: Commission, Brokerage and Discount
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
Concept: Linear Programming Problem in Management Mathematics
Submit Question Paper
Help us maintain new question papers on shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files
Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2017 - 2018
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.