Date: March 2018
Draw a Venn diagram for the truth of the following statement :
All rational number are real numbers.
Chapter: [1] Mathematical Logic
Draw Venn diagram for the truth of the following statements :
Some rectangles are squares.
Chapter: [1] Mathematical Logic
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
Chapter: [2] Matrices
Examine the continuity of f(x)=`x^2-x+9 "for" x<=3`
=`4x+3 "for" x>3, "at" x=3`
Chapter: [3] Continuity
find `dy/dx, if y= cos ^-1 (sin 5x)`
Chapter: [11] Demography
The price P for demand D is given as P = 183 + 120 D – 3D^{2}.
Find D for which the price is increasing.
Chapter: [5] Applications of Derivative
Evaluate`int (1)/(x(3+log x))dx`
Chapter: [7] Definite Integrals
Find cofactors of the elements of the matrix A = `[[-1,2],[-3,4]]`
Chapter: [2] Matrices
Evaluate : `int 1/(9x^2+49) dx`
Chapter: [6] Indefinite Integration
Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0
= k for x = 0
is continuous at x = 0.
Chapter: [3] Continuity
Examine whether the following statement pattern is tautology, contradiction or contingency :
p ∨ – (p ∧ q)
Chapter: [13] Regression Analysis Introduction
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Chapter: [5] Applications of Derivative
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
Find the area of the region bounded by the parabola y^{2} = 16x and the line x = 4.
Chapter: [2] Matrices
The consumption expenditure E_{c} of a person with the income x. is given by E_{c} = 0.0006x^{2} + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.
Chapter: [5] Applications of Derivative
Discuss continuity of f(x) =`(x^3-64)/(sqrt(x^2+9)-5)` For x ≠ 4
= 10 for x = 4 at x = 4
Chapter: [3] Continuity
Find `dy/dx,if e^x+e^y=e^(x-y)`
Chapter: [5] Applications of Derivative
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Chapter: [5] Applications of Derivative
Evaluate :`int Sinx/(sqrt(cos^2 x-2 cos x-3)) dx`
Chapter: [3] Continuity
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
Evaluate : `int_1^2 1/((x+1)(x+3)) dx`
Chapter: [5] Applications of Derivative
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
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: [11] Demography
If `Σd_i^2` = 25, n = 6 find rank correlation coefficient where d_{i}, is the difference between the ranks of i^{th} values.
Chapter: [12] Bivariate Data and Correlation
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
The regression equation of Y on X is y = `2/9` x and the regression equation of X on Y is `x=y/2+7/6`
Find:
- The correlation coefficient between X and Y.
- `σ_y^2 if σ _x^2=4`
Chapter: [12] Bivariate Data and Correlation
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
If X has Poisson distribution with parameter m = 1, find P[X ≤ 1]. (Use e–1 = 0.3679)
Chapter: [13] Regression Analysis Introduction
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
Ramesh, Vivek, and Sunil started a business by investing capital 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
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
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
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
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
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
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
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
Solve the following inequation :
– 8 < – (3x – 5) < 13.
Chapter: [15] Management Mathematics
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
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?
[(1.01)^{-24} = 0.7884]
Chapter: [9] Commission, Brokerage and Discount
There are found jobs to be completed. Each job must go through machines M_{1} , M_{2} , M_{3} in the order M_{1} - M_{2} - M_{3}. Processing time in hours is given below. Determine the optimal sequesnce and idle time for machine M_{1} .
Jobs | A | B | C | D |
M_{1} | 5 | 8 | 7 | 3 |
M_{2} | 6 | 7 | 2 | 5 |
M_{3} | 7 | 8 | 10 | 9 |
Chapter: [15] Management Mathematics
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Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2017 - 2018
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