Mathematics and Statistics [Set 1]
Marks: 80 Maharashtra State Board
HSC Commerce (English Medium)
HSC Commerce: Marketing and Salesmanship
Academic Year: 2016-2017
Date: जुलै 2017
Advertisements
(1) All questions are compulsory.
(2) Figure to the right tndtcate full marks.
(3) Answer to every question must be .written on a new page.
(4) Graph paper is necessaryJor L.P.P.
(5) Log table will be provided on demand.
(6) Answer to Section-I and Section-II should be written In two separate answer books.
(7) Question from Section-I attempted in the answer book of Section-II and vice versa wil not be assessed/not given any credit.
vice versa will not be assessed/not given any credit.
SECTION - I
[12]1|Attempt any Six
[2]1.A
[2]1.A.i
Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) `∃x cc` R such that x + 3 ≥ 10.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.02] Matrices
[2]1.A.ii
If A = `[(1,2), (1,3)]`, find A2 - 3A
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.02] Matrices
[2]1.A.iii
Discuss the continuity of the function f at x = 0
If f(x) = `(2^(3x) - 1)/tanx`, for x ≠ 0
= 1, for x = 0
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.03] Continuity
[2]1.A.iv
Evaluate : `int ("x" + 1)/("x"("x" + log"x")`dx
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.06] Indefinite Integration
[2]1.A.v
Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.02] Matrices
[2]1.A.vi
If the function f is continuous at = 2, then find f(2) where f(x) = `(x^5 - 32)/(x - 2)`, for ≠ 2.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.03] Continuity
[2]1.A.vii
Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.013999999999999999] Applications of Derivatives
[2]1.A.viii
Differentiate
log (1 + x2) w.r.t. tan-1(x)
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.04] Differentiation
[14]2|Attempt any Two
[6]2.A|Attempt any two
[3]2.A.i
If p : It is raining
q : It is humid
Write the following statements in symbolic form:
(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
[3]2.A.ii
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
[3]2.A.iii
Evaluate ; `int x^2/(x^6 - 4x^3 + 13)` dx
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.06] Indefinite Integration
[8]2.B|Attempt any two
[4]2.B.i
If the function f is continuous at x = 0
Where f(x) = 2`sqrt(x^3 + 1)` + a, for x < 0,
= `x^3 + a + b, for x > 0
and f (1) = 2, then find a and b.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.03] Continuity
[4]2.B.ii
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.013999999999999999] Applications of Derivatives [0.05] Applications of Derivative
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.013999999999999999] Applications of Derivatives [0.05] Applications of Derivative
Advertisements
[4]2.B.iii
The total cost C for producing x units is Rs (x2 + 60x + 50) and the price is Rs (180 - x) per unit. For how many units the profit is maximum.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.03] Continuity
[14]3|Attempt any Two
[6]3.A
[3]3.A.i
If y = sin -1`((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.04] Differentiation
[3]3.A.ii
If y = 5x+ xx,Find `(dy)/(dx)`.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.07] Definite Integrals
[3]3.A.iii
`int (2x + 1)/((x + 1) ( x - 2))` dx
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.06] Indefinite Integration
[8]3.B|Attempt any Two
[4]3.B.i
Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.012] Matrices [0.02] Matrices
[4]3.B.ii
Find the area of the region bounded by the curve (parabola) y2 = 4x and the line
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.06] Indefinite Integration
[4]3.B.iii
Evaluate `int_0^1 (x(sin^-1 x)^2)/sqrt(1 - x^2)` dx
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.07] Definite Integrals
SECTION - II
[12]4|Attempt any six
[2]4.A
[2]4.A.i
In a class 60% students arc boys and 40% are girls. By admitting 16 boys and 8 girls, the ratio of boys to girls becomes 8 : 5. Find the original number of boys and girls in the class.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.01] Mathematical Logic
[2]4.A.ii
An agent charges 12% commission on the sales. How much does he earn if the total sales amounts to ~ 36,000? How muuch does the seller get from this sale?
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.09] Commission, Brokerage and Discount
[2]4.A.iii
Find the Age-Specific Death Rate (SDR) for the following data :
Age groups (in years) | Population | Number of deaths |
0 - 10 | 11,000 | 220 |
10 - 20 | 12,000 | 240 |
20 - 60 | 9,000 | 180 |
60 and above | 2,000 | 90 |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.09] Commission, Brokerage and Discount
[2]4.A.iv
If the Crude Death Rate (CDR) for the following data is 13.4 per thousand, find x:
Age groups (in years) | Population | Number of deaths |
0 - 20 | 40,000 | 350 |
20 - 65 | 65,000 | 650 |
65 and above | 15,000 | x |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.09] Commission, Brokerage and Discount
[2]4.A.v
If a fair die is rolled four times,. what is the probability that two of the rolls will show '1'.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[2]4.A.vi
Solve the inequation -8 ≤ 3x - 5 < 7 and represent it on the real number line.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
Advertisements
[2]4.A.vii
Sketch the graph of | y | ≤ 3 in a coordinate plane.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.11] Demography
[2]4.A.viii
Find the sequence that minimizes the total elapsed time (in hours) required to
complete the following jobs on the machine M1 , M2 and M3 in the order M1M2M3 :
Machine Jobs | A | B | C | D |
M1 | 5 | 6 | 9 | 5 |
M2 | 2 | 4 | 5 | 3 |
M3 | 3 | 5 | 6 | 7 |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.02] Matrices
[14]5
[6]5.A|Attempt any two
[3]5.A.i
Find accumulated value after 1 year of annuity immediate in which Rs 20,000 is invested every quarter, at .16% p.a. compounded quarterly.
[Given : (1.04)4 = 1.1699]
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.09] Commission, Brokerage and Discount
[3]5.A.ii
If a random variable X follows Poisson distribution sucli that P(X = 1) = P(X = 2), find:
(a) the mean and
(b) P(X = 0). [Given: e-2 = 0.1353)
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[3]5.A.iii
The probability of defective bolts in a workshop is 40%. Find the mean and variance of defective bolts out of 10 bolts.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[8]5.B|Attempt any two
[4]5.B.i
Given the following table which relates to the number of animals of a certain species at age x . Complete the life table with dx, qx, Lx and Tx.
x | 0 | 1 | 2 | 3 | 4 | 5 |
lx | 1000 | 850 | 760 | 360 | 25 | 0 |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[4]5.B.ii
Co-efficient of correlation between the variables X and Y is 0.3 and their covariance is 12. The variance of X is 9, find the standard deviation of Y.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[4]5.B.iii
Compute correlation coefficient for the following data :
X | 9 | 7 | 6 | 8 | 5 |
Y | 19 | 17 | 16 | 18 | 15 |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.14] Random Variable and Probability Distribution
[14]6
[6]6.A
[3]6.A.i
Surabhi, Simona and Shruti started a business in a partnership by investing ₹ 60,000, ₹ 40,000 and ₹ 75,000 respectively. At the end of the year they found that they have incurred a loss of ₹ 24,500. Find that how much loss each one had to bear?
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.08] Ratio, Proportion and Partnership
[3]6.A.ii
Three cars were sold through an agent for Rs 1,60,000, Rs1,48,000 and Rs 1,50,000 respectively. The rates of commission were 17 .5% on the first, and 12.5% on the second. If on the whole, the agent received 14% commission on the total sales, find the rate of commission paid on the third car.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.09] Commission, Brokerage and Discount
[3]6.A.iii
The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.
Find:
(a) Correlation coefficient
(b)`sigma_x/sigma_y`
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.023] Linear Regression [0.13] Regression Analysis Introduction
[8]6.B|Attempt any two
[4]6.B.i
If Σx1 = 56 Σy1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σx1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.023] Linear Regression [0.13] Regression Analysis Introduction
[4]6.B.ii
Solve the following minimal assignment problem :
Machines | A | B | C | D | E |
M1 | 27 | 18 | ∞ | 20 | 21 |
M2 | 31 | 24 | 21 | 12 | 17 |
M3 | 20 | 17 | 20 | ∞ | 16 |
M4 | 21 | 28 | 20 | 16 | 27 |
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.027000000000000003] Assignment Problem and Sequencing [0.15] Management Mathematics
[4]6.B.iii
Solve the following L.P.P.:
Maximize Z = 4x + 5y
subject to 2x + y ≥ 4
x + y ≤ 5,
0 ≤ x ≤ 3,
0 ≤ y ≤ 3
VIEW SOLUTION
Concept: undefined - undefined
Chapter: [0.15] Management Mathematics