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)
using elementary transformation. (Ans: Click Here)
(Iii) Examine the continuity of 
(Ans: Click Here)
(Ans: Click Here)
(Iv) Find dy/dx, if y = cos-1 (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)
(Ans: Click Here)
(Vii) Find cofactors of the elements of the matrix A = 
(Ans: Click Here)
(Ans: Click Here)
(Viii) Evaluate : 
(Ans: Click Here)
(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)
(Ans: Click Here)
(Iii) If 
and 
then find dy/dx at 
. (Ans: Click Here)
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)
(Ans: Click Here)
Q. 3. B. Attempt any Two of the following: [8]
(I) Evaluate : 
(Ans: Click Here)
(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)
(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.
