### March 2018 HSC Commerce Maths paper Solution

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) Find the inverse of the matrix A = using elementary transformation. (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)

(Vii) Find cofactors of the elements of the matrix A = (Ans: Click Here)

Q. 2. A. Attempt any Two of the following: [6]

(I) Find k, if

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

(Ii) Find dy/dx, if ex + ey = ex - y. (Ans: Click Here)

Q. 3. B. Attempt any Two of the following: [8]

(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)

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.