March 2018
Time : 3 Hours
Max. Marks. 80
Note: (1) All questions are compulsory.
(2) Answer to every question must be written on a new page.
(3) Log table will be provided on demand.
(4) Answer to Section  I and Section  II should be written in two separate answer books.
(5) Questions from Section  I attempted in the answer book of Section  II and vice versa will not be assessed / not given any credit.
(6) Graph paper is necessary for L.P.P.
Section  I
Q. 1. Attempt any SIX of the following: [12]
(i) Draw Venn diagram for the truth of the following statements.
(ii) Some rectangles are squares. (Ans: Click Here)
(ii) Find the inverse of the matrix A = using elementary transformation. (Ans: Click Here)
(Iii) Examine the continuity of (Ans: Click Here)
(Iv) Find dy/dx, if y = cos1 (sin 5x) (Ans: Click Here)
(V) The price P for demand D is given as P = 183 + 120 D  3D2 . Find D for which the price is increasing. (Ans: Click Here)
(Vi) Evaluate : (Ans: Click Here)
(Vii) Find cofactors of the elements of the matrix A = (Ans: Click Here)
(Viii) Evaluate : (Ans: Click Here)
Q. 2. A. Attempt any Two of the following: [6]
(I) Find k, if
Is continuous at x = 0. (Ans: Click Here)
(Ii) Examine whether the following statement pattern is tautology, contradiction or contingency: (Ans: Click Here)
(Iii) If and then find dy/dx at . (Ans: Click Here)
Q. 2. B. Attempt any Two of the following. [8]
(I) 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. (Ans: Click Here)
(Ii) Find the area of the region bounded by the parabola y2 = 16x and the line x = 4. (Ans: Click Here)
(Iii) 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. (Ans: Click Here)
Q. 3. A. Attempt any Two of the following: [6]
(I) Discuss the continuity of
(Ans: Click Here)
(Ii) Find dy/dx, if ex + ey = ex  y. (Ans: Click Here)
(Iii) Using truth table show that : (Ans: Click Here)
Q. 3. B. Attempt any Two of the following: [8]
(I) Evaluate : (Ans: Click Here)
(Ii) The total cost function of a firm is C = x2 + 75 x + 1600 for output x. Find the output (x) for which average cost is minimum. Is CA = CM at this output? (Ans: Click Here)
(iii) Evaluate: (Ans: Click Here)
Section  II
Q. 4. A. Attempt any SIX of the following.
(I) A shop valued at Rs. 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.
(Ii) Find the Age  Specific Death Rate (Age  SDR) for the following data:
Age groups
(In years)

Population
(In ‘000)

Number of deaths

0  10

11

240

10  20

12

150

20  60

9

125

60 and above

2

90

(Iii) If n = 6 find rank correlation coefficient where d, is the difference between the ranks ith values.
(Iv) The following table gives the ages of husbands and wives:
Age of husband in years

20  30

30  40

40  50

50  60

Age of Wives
(In years)
 
15  25

5

9

3



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 frequency distribution of the age of husbands when the age of wives lies between 25  35.
(V) The regression equation of Y on X is and he regression equation of X on Y is
Find (a) Correlation coefficient between X and Y.