Date: March 2014
- All questions are compulsory.
- Answer to every question must be written on a new page.
- L.P.P. problem should be solved on a graph paper
- Log table will be provided on demand.
- Write answers of Section - I and Section - II in one answer book.
If `"A" = [(1,2,-3),(5,4,0)] , "B" = [(1,4,3),(-2,5,0)]`, then find 2A + 3B.
Chapter: [0.02] Matrices
If the function f is continuous at x = I, then find f(1), where f(x) = `(x^2 - 3x + 2)/(x - 1),` for x ≠ 1
Chapter: [0.03] Continuity
If x = tan^{-1}t and y = t^{3} , find `(dy)/(dx)`.
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Evaluate : `∫sin^2x` dx
Chapter: [0.06] Indefinite Integration
Write the negation of the following statements :
(a) Chetan has black hair and blue eyes.
(b) ∃ x ∈ R such that x^{2} + 3 > 0.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
If A = `[(1,1),(2,2)] , "B" = [(1,2),(3,4)]` then find |AB|.
Chapter: [0.02] Matrices
Evaluate : `∫dx/(4 - 9x^2)`
Chapter: [0.06] Indefinite Integration
If the function f is continuous at x = 2, then find 'k' where
f(x) = `(x^2 + 5)/(x - 1),` for 1< x ≤ 2
= kx + 1 , for x > 2
Chapter: [0.03] Continuity
If `x^y = e^(x - y)` , show that `(dy)/(dx) = logx/(1 + logx)^2`
Chapter: [0.04] Differentiation
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
Chapter:
Discuss extreme values of the function f(x) = x.logx
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Discuss the continuity of the function f at x = 0, where
f(x) = `(5^x + 5^-x - 2)/(cos2x - cos6x),` for x ≠ 0
= `1/8(log 5)^2,` for x = 0
Chapter: [0.03] Continuity
The expenditure E_{c} of a person with income I is given by E_{c }= (0.000035) I^{2} + (0. 045) I. Find marginal propensity to consume (MPC) and average propensity to consume (APC) when I = 5000.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Evaluate : `∫x cot^-1x` dx
Chapter: [0.06] Indefinite Integration
If p : It is a day time , q : It is warm
Give the verbal statements for the following symbolic statements :
(a) p ∧ ∼ q (b) p v q (c) p ↔ q
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Using the truth table statement, examine whether the statement pattern (p → q) ↔ (∼ p v q) is a tautology, a contradiction or a contingency.
Chapter: [0.02] Matrices
The cost C of producing x articles is given as C = x^{3}-16x^{2 }+ 47x. For what values of x, with the average cost is decreasing'?
Chapter: [0.04] Differentiation
If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A^{-1} by using elementary transformation .
Chapter: [0.02] Matrices
Evaluate : `∫_0^3dx/(x + sqrt(9 - x^2))`
Chapter: [0.06] Indefinite Integration
Find the volume of a solid obtained by the complete revolution of the ellipse `x^2/36 + y^2/25 = 1` about X-axis.
Chapter: [0.07] Definite Integrals
Alex spends 20% of his income on food items and 12% on conveyance. If for the month of June 2010, he spent ₹900 on conveyance, find his expenditure on food items during the same month.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Find the premium on a property worth ₹12,50,000 at 3% if the property is fully insured.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
The following table gives the age of the husbands and of the 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 the marginal frequency distribution of the age of husbands.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
For a bivariate data,
`bar x = 53 , bar y = 28 , "b"_"xy" = - 0.2` , `"b"_"yx" = -1.5` Find
Estimate of Y , When X = 50.
Chapter: [0.13] Regression Analysis Introduction
Values of two regression coefficients between the variables X and Y are `b_"yx" = - 0.4` and `b_"xy"` = - 2.025 respectively. Obtain the value of correlation coefficient.
Chapter: [0.13] Regression Analysis Introduction
Verify whether the following function can be regarded as probability mass function (p.m.f.) for the given values of X :
X | -1 | 0 | 1 |
P(X = x) | -0.2 | 1 | 0.2 |
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
The p.m.f. of a random variable X is
`"P"(x) = 1/5` , for x = I, 2, 3, 4, 5
= 0 , otherwise.
Find E(X).
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
The time (in hours) required to perform the printing and binding operations (in that order) for each book is given in the following table :
Books | I | II | III | IV | V |
Printing Machine M_{1} | 3 | 7 | 4 | 5 | 7 |
Binding Machine M_{2} |
6 | 2 | 7 | 3 | 4 |
Find the sequence that minimizes the total elapsed time (in hours) to complete the work .
Chapter: [0.15] Management Mathematics
Find the present value of an annuity immediate.of ₹18,000. p.a. for 3 years at 9% p.a. compounded annually. [Given `(1.09)^-3 = 0.7722`]
Chapter: [0.1] Insurance and Annuity
Compute rank correlation coefficient for the following data :
R_{x} | 1 | 2 | 3 | 4 | 5 | 6 |
R_{y} | 6 | 3 | 2 | 1 | 4 | 5 |
Chapter: [0.12] Bivariate Data and Correlation
If the rank correlation coefficient is `2/3` and `Σ"d"_1^2` = 55` , then find the number of pairs of observations. (Assume that no rank is repeated.)
Chapter: [0.12] Bivariate Data and Correlation
From the following data, find the crude death rates (C.D.R.) for Town I and Town II, and comment on the results :
Age Group (in years) | Town I | Town II | ||
Population | No. of deaths | Population | No. of deaths | |
0-10 | 1500 | 45 | 6000 | 150 |
10-25 | 5000 | 30 | 6000 | 40 |
25 - 45 | 3000 | 15 | 5000 | 20 |
45 & above | 500 | 22 | 3000 | 54 |
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Calculate quantities indicated by'?' for the following part of a life table :
x | l_{x} | d_{x} | q_{x} | L_{x} | T_{x} | `e_x^0` |
4 | 9100 | 60 | ? | . ? | 510000 | ? |
5 | ? | 45 |
Chapter: [0.11] Demography
The probability that a bomb dropped from an aeroplane will strike a target is `1/5`, If four bombs are dropped, find the probability that :
(a) exactly two will strike the target,
(b) at least one will strike the target.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Amit and Rohit started a business by investing ₹20,000 each. After 3 months Amit withdrew ₹5,000 and Rohit put in ₹5,000 additionally. How should a profit of ₹12,800 be divided between them at the end of the year?
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
A bill of Rs.7,500 was discounted for Rs. 7,290 at a bank on 28^{th} October 2006. If the rate of interest was 14% p.a., what is the legal due date ?
Chapter: [0.09] Commission, Brokerage and Discount
Let X be the number of matches played by the player and Y he the number of matches in which he scored more thun 50 runs. The following data is obtained for 5 players :
No. of Matches Played (X) | Data of matches of 5 players | ||||
21 | 25 | 26 | 24 | 19 | |
Scored more than 50 in a match (Y) | 19 | 20 | 24 | 21 | 16 |
Find the regression line of X on Y.
Chapter: [0.13] Regression Analysis Introduction
Find the sequence that minimizes total elapsed time (in hours) required to complete the following jobs on two machines M_{1} and M_{2} in order M_{1}-M_{2}. Also, find the minimum elapsed time T and idle time for the two machines.
Jobs | |||||
Machines | A | B | C | D | E |
M_{1} | 5 | 1 | 9 | 3 | 10 |
M_{2} | 2 | 6 | 7 | 8 | 4 |
Chapter: [0.15] Management Mathematics
Solve the following L.P.P. :
Minimize : Z = 4x+ 2y
Subject to: 3x+ y ≥ 27 , x + y ≥ 21,
x + 2y ≥ 30, x ≥ 0 , y ≥ 0
Chapter: [0.15] Management Mathematics
Solve the following L.P.P. :
Minimize : Z = 4x + 10y,
Subject to : 2x + 5y ≤10 , 5x + 3y ≤ 15,
x + 2y ≥ 30, x ≥ 0, y ≥ 0.
Chapter: [0.15] Management Mathematics
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Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2013 - 2014
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