HSC Commerce (English Medium)
HSC Commerce: Marketing and Salesmanship
Academic Year: 2016-2017
Date & Time: 6th March 2017, 11:00 am
Duration: 3h
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(I) All questions are compulsory.
(2) Answer lo every question must be written on a new page .
(3) Log table will be provided on demand .
(4) Write answers of section - I and Section - II in two separate answer books .
Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`
Chapter: [0.012] Matrices [0.02] Matrices
Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
Find the points of discontinuity , if any for the function : f(x) = `(x^2 - 9)/(sinx - 9)`
Chapter: [0.03] Continuity
Write negation of the following statements :
(a) The number 6 is an even number or the number 25 is a perfect square.
(b) If x ∈ A ∩ B , then x ∈ A and x ∈ B.
Chapter: [0.01] Mathematical Logic
Evaluate : ∫ `cos^2`x dx
Chapter: [0.06] Indefinite Integration
Find `(d^2y)/(dx^2)` , if y = log x
Chapter: [0.04] Differentiation
Evaluate : `∫(e^x + 1)/(e^x + x)` dx
Chapter: [0.06] Indefinite Integration
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Chapter: [0.012] Matrices [0.02] Matrices
If f(x) = `(e^(2x) - 1)/(ax)` . for x < 0 , a ≠ 0
= 1. for x = 0
= `(log(1 + 7x))/(bx)`. for x > 0 , b ≠ 0
is continuous at x = 0 . then find a and b
Chapter: [0.03] Continuity
Demand function x, for a certain commodity is given as x = 200 - 4p where p is the unit price. Find :
(a) elasticity of demand as function of p.
(b) elasticity of demand when p = 10 , interpret your result.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Using the truth table verify that p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r).
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
If the demand function is D = 150 - p^{2} - 3p, find marginal revenue, average revenue and elasticity of demand for price p = 3.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Chapter: [0.06] Indefinite Integration
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Solve the following equations by reduclion method
x+3y+3z= 16 , x+4y+4z=21 , x+3y+4z = 19
Chapter: [0.012] Matrices [0.02] Matrices
If the function f (x) = `(15^x - 3^x - 5^x + 1)/(x tanx)`, x ≠ 0 is continuous at x = 0 , then find f(0).
Chapter: [0.03] Continuity
Examine the function f(x) = `x + 25/x ` for maxima and minima
Chapter: [0.05] Applications of Derivative
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
If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Evaluate : `∫((1 + logx))/(x(2 + logx)(3 + logx)`dx
Chapter: [0.06] Indefinite Integration
The ratio of number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, find the percentage of students who are not scholarship holders.
Chapter: [0.08] Ratio, Proportion and Partnership
Calculate crude death rates (CDR) for district A.
Age group (in years) | Number or persons (in thousands) | Number of deaths |
0 - 15 | 1 | 20 |
15 - 60 | 3 | 30 |
60 and above | 2 | 40 |
Chapter: [0.14] Random Variable and Probability Distribution
What is the sum due of ₹5,000, due 4 months, hence at 12.5% p.a. simple interest?
Chapter: [0.09] Commission, Brokerage and Discount
The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class :
(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
A wholesaler allows 25% trade discount and 5% cash discount, what will be the net price of an article marked at ₹1,600?
Chapter: [0.09] Commission, Brokerage and Discount
Verify the following function, which can be regarded as p.m.f. for the given values of X :
X = x | -1 | 0 | 1 |
P(x) | -0.2 | 1 | 0.2 |
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Solve the following minimal assignment problem :
Machines | Jobs | ||
I | II | III | |
M_{1} | 1 | 4 | 5 |
M_{2} | 4 | 2 | 7 |
M_{3} | 7 | 8 | 3 |
Chapter: [0.02] Matrices
If X has Poisson distribution with parameter m = 1, find P[X ≤ 1] [Use `e^-1 = 0.367879`]
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
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Find the present value of annuity immediate of ₹ 18000 p.a. for 3 years at 9% p.a. compounded annually. [(Given : `(1.09)^-3 = 0.7722`]
Chapter: [0.1] Insurance and Annuity
Complete the following life table :
x | l_{x} | d_{x} | q_{x} | p_{x} |
L_{x} |
4 | 9100 | 60 | ? | ? | ? |
5 | ? | 45 | ? | ? |
Chapter: [0.11] Demography
Given that r = 0.4 , `Σ(x - barx)(y - bary) = 108 , σ_y = 3 and Σ(x - barx)^2 = 900` . Find the number of pairs of observations.
Chapter: [0.12] Bivariate Data and Correlation
Find mean and standard deviation of the continuous random variable X whose p.d.f. is given by f(x) = 6x(1 - x);= (0); 0 < x < 1(otherwise)
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Solve the following L.P.P. graphically Minimize Z = 3x + 5y Subject to 2x + 3y ≥ 12
-x + y ≤ 3
x ≤ 4
y ≥ 3
Chapter: [0.15] Management Mathematics
We have seven jobs each of which has to go through two machines M_{1} and M_{2} in the order M_{1 }- M_{2 . }Processing times (in hours) are given as :
Jobs | A | B | C | D | E | F | G |
Machine M_{1 } | 3 | 12 | 15 | 6 | 10 | 11 | 9 |
Machine M_{2} | 8 | 10 | 10 | 6 | 12 | 1 | 3 |
Determine a sequence of these jobs that Will minimize the total elapsed time 'T', and idle time for each machine .
Chapter: [0.15] Management Mathematics
Compute the age specific death rate for the following data :
Age group (years) | Population (in thousands) | Number of deaths |
Below 5 | 15 | 360 |
5-30 | 20 | 400 |
Above 30 | 10 | 280 |
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
If the rank correlation coefficient is 0.6 and the sum of squares of differences of ranks is 66, then find the number of pairs of observations.
Chapter: [0.12] Bivariate Data and Correlation
The equations of the two regression lines are 2x + 3g - 6 = 0 and 5x + 7g - 12 = 0
Find: (a) Correlation coefficient.
(b) `sigma_x/sigma_y`
Chapter: [0.12] Bivariate Data and Correlation
John and Mathew started a business with their capitals in the ratio 8 : 5. After 8 months, john added 25% of his earlier capital as further investment. At the same time, Mathew withdrew 20% of bis earlier capital. At the end of the year, they earned ₹ 52000 as profit. How should they divide the profit between them?
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
A departmental store gives trafnfng to the salesmen in service followed by a test. It is experienced that the performance regarding sales of any salesman is linearly related to the scores secured by him. The following data gives the test scores and sales made by nine (9) salesmen during a fixed period.
Test scores (X) | 16 | 22 | 28 | 24 | 29 | 25 | 16 | 23 | 24 |
Sales (Y) (₹ in hundreds) | 35 | 42 | 57 | 40 | 54 | 51 | 34 | 47 | 45 |
(a) Obtain the line of regression of Y on X.
(b) Estimate Y when X = 17.
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Three different aeroplanes are to be assigned to carry three cargo consignments with a view to maximize profit. The profit matrix (in lakhs of ₹) is as follows :
Aeroplanes | Cargo consignments | ||
C_{1} | C_{2} | C_{3} | |
A_{1} | 1 | 4 | 5 |
A_{2} | 2 | 3 | 3 |
A_{3} | 3 | 1 | 2 |
How should the cargo consignments be assigned to the aeroplanes to maximize the profit?
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
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