12th Business Maths Model Exam -1

St. Britto Hr. Sec. School - Madurai

12th Business Maths Model Exam -1-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

For a demand function p, if ഽ\(\frac{dp}{p}\) = k ഽ\(\frac{dx}{x}\) then k is equal to
\(\eta \)d

-\(\eta \)d

\(\frac{-1}{\eta d}\)

\(\frac{1}{\eta d}\)
If F(x) is the probability distribution function, then F(- \(\infty \)) is ___________.
1

2

\(\infty \)

0

The starting annual salaries of newly qualified chartered accountants (CA's) in South Africa follow a normal distribution with a mean of Rs.1,80,000 and a standard deviation of Rs.10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs.1,65,000 and Rs.1,75,000 per annum?

0.819
0.242
0.286
0.533

Given E(X) = 5 and E(Y) = -2, then E(X – Y) is

Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is

log2 sq.units
log5 sq.units
log3 sq.units
log 4 sq.units

ഽ2^xdx is

2^x log 2 + c
2^x+ c
\(\frac { 2^{ x } }{ log2 } +c\)
\(\frac { log2 }{ { 2 }^{ x } } +c\)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

there is only one solution
there exists infinitely many solutions
there is no solution
None of these

A finite subset of statistical individuals in a population is called __________

a sample
a population
universe
census

The quantities that can be numerically measured can be plotted on a

p - chart
c – chart
x bar chart
np – chart

E[X-E(X)] is equal to

E(X)
V(X)
0
E(X) - X

A ________ is a statement or an assertion about the population parameter.

hypothesis
statistic
sample
census

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,
y = v x

v = y x

x = v y

x = v
Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of Rs.1,295.00 and a standard deviation of Rs.750.00. What proportion of credit card holders spend more than Rs.1,500.00 on their credit cards per month?
0.487

0.392

0.500

0.791

If c is a constant, then E(c) is

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is
\(\frac{30}{3}\) sq.units

\(\frac{31}{3}\)sq.units

\(\frac{32}{3}\) sq.units

\(\frac{15}{2}\) sq.units
A formula or equation used to represent the probability distribution of a continuous random variable is called
probability distribution

distribution function

probability density function

mathematical expectation

The probability that a standard normal variate z will be

A B

1) Greater than 1.09 a) 0.8163

2) less than - 1.65 b) .1379

3) lying between - 1.00 and 1.96 c) 0.0495

4) lying between 1.25 and 2.75 d) 0.1026

The correct match is

1 - a, 2 - b, 3 - c, 4 - d
1 - d, 2 - c, 3 - a, 4 - b
1 - d, 2 - a, 3 - c, 4 - b
1 - b, 2 - c, 3 - a, 4 - d

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { x }{ y } \right) \) can be solved by making substitution,

x = v y
y = v x
y = v
x = v

If f (x) is a continuous function and a < c < b ,then \(\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx\) is

\(\int _{ a }^{ b }{ f(x) } dx+\int _{ a }^{ c }{ f(x) } dx\)
\(\int _{ a }^{ c }{ f(x) } dx+\int _{ a }^{ b }{ f(x) } dx\)
\(\int _{ a }^{ b }{ f(x) } dx\)
0

North-West Corner refers to ________

top left corner
top right corner
bottom right corner
bottom left corner

Part - B

Generic 2 - Answer All Question

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

A sample of 100 students are drawn from a school. The mean weight and variance of the sample are 67.45 kg and 9 kg. respectively. Find
(a) 95% and
(b) 99% confidence intervals for estimating the mean weight of the students.

Explain Factor Reversal Test.

Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be atleast two fatal accidents in a year. (given e^-0.25 = 0.7788).

The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x , the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.
The distribution of a continuous random variable X in range (–3, 3) is given by p.d.f.
f(x)={\(\frac { 1 }{ 16 } (3+{ x) }^{ 2 },\quad -3\le x\le -1\\ \frac { 1 }{ 16 } { (6-2x) }^{ 2 },-1\le x\le 1\\ \frac { 1 }{ 16 } { (3-x) }^{ 2 },1\le x\le 3\)
Verify that the area under the curve is unity.

Integrate the following with respect to x.
sin³ x

What is the difference between Assignment Problem and Transportation Problem?

In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability
that it will take less than 16.35 seconds to develop prints.

A discrete random variable. X has the following probability distribution

X 0 1 2 3 4 5 6 7 8

P (X) a 3a 5a 7a 9a 11a 13a 15a 17a

Find the value of a and P(X < 3)

The population of a city in a censes taken once in 10 years is given below. Estimate
the population in the year 1955.

Year 1951 1961 1971 1981

Population in lakhs 35 42 58 84

The birth weight of babies is normally distributed with mean 3,500 g and standard deViation 500 g. What is the probability that a baby is born that weighs less than 3,100 g?

Integrate the following with respect to x.
xⁿlog x

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x.
x⁸(1+x⁹)⁵

Part - C

Generic 3 - Answer All Question

Suppose, the life in hours of a radio tube has the following p.d.f
f(x)=\(\frac { 100 }{ { x }^{ 2 } } ,when\quad \ge 100\\ 0,\quad when\quad x<100\)
Find the distribution function.

The following data gives readings of 10 samples of size 6 each in the production of a certain product. Draw control chart for mean and range with its control limits.

Sample 1 2 3 4 5 6 7 8 9 10

Mean 383 508 505 582 557 337 514 614 707 753

Range 95 128 100 91 68 65 148 28 37 80

A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.

A continuous random variable X has the following p.d.f
f(x)=ax, 0\(\le\)x\(\le\)1
Determine the constant a and also find P\(\\ \left[ X\le \frac { 1 }{ 2 } \right] \)

The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart.

Sample 1 2 3 4 5 6

Mean 300 342 351 319 326 333

Range 25 37 20 28 30 22

Given for n = 6, A₂ = 0.483,

In tossing of a five fair coin, find the chance of getting exactly 3 heads.

Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

Consider the following pay-off (profit) matrix Action States

Action States

(s₁) (s₂) (s₃) (s₄)

A₁ 5 10 18 25

A₂ 8 7 8 23

A₃ 21 18 12 21

A₄ 30 22 19 15

Determine best action using maximin principle.

If a random variable X follows Poisson distribution such that P(X = 2) = 9. P(X = 4) + 90 P(X = 6) then find the mean and variance.

Find the initial basic feasible solution for the following transportation problem by VAM

Part - D

Generic 5 - Answer All Question

Determine the mean and variance of a discrete random variable, given its distribution as follows.

X=x 1 2 3 4 5 6

F_x(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Price Quandity

2000 2010 2000 2010

Rice 38 35 6 7

Wheat 12 18 7 10

Rent 10 15 10 15

Fuel 25 30 12 16

Miscellaneous 30 33 8 10

The probability distribution of the discrete random variables X and Y are given below.

X 0 1 2 3

P(X) \(\frac { 1 }{ 5 } \) \(\frac { 2 }{ 5 } \) \(\frac { 1 }{ 5 } \) \(\frac { 1 }{ 5 } \)

Y 0 1 2 3

P(Y) \(\frac { 1 }{ 5 } \) \(\frac{3}{10}\) \(\frac { 2 }{ 5 } \) \(\frac{1}{10}\)

Prove that E(Y²) = 2 E(X).

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

Calculate the cost of living index number by consumer price index number for the year 2016 with respect to base year 2011 of the following data.

Commodities Price Quantity

Base year Current year

Rice 32 48 25

Sugar 25 42 10

Oil 54 85 6

Coffe 250 460 1

Tea 175 275 2

Comment

Add Comment

A	B
1) Greater than 1.09	a) 0.8163
2) less than - 1.65	b) .1379
3) lying between - 1.00 and 1.96	c) 0.0495
4) lying between 1.25 and 2.75	d) 0.1026

Sample	1	2	3	4	5	6	7	8	9	10
Mean	383	508	505	582	557	337	514	614	707	753
Range	95	128	100	91	68	65	148	28	37	80

Action	States
Action	(s₁)	(s₂)	(s₃)	(s₄)
A₁	5	10	18	25
A₂	8	7	8	23
A₃	21	18	12	21
A₄	30	22	19	15

X=x	1	2	3	4	5	6
F_x(x)	\(\frac{1}{6}\)	\(\frac{2}{6}\)	\(\frac{3}{6}\)	\(\frac{4}{6}\)	\(\frac{5}{6}\)	1

Commodities	Price		Quandity
Commodities	2000	2010	2000	2010
Rice	38	35	6	7
Wheat	12	18	7	10
Rent	10	15	10	15
Fuel	25	30	12	16
Miscellaneous	30	33	8	10

X	0	1	2	3
P(X)	\(\frac { 1 }{ 5 } \)	\(\frac { 2 }{ 5 } \)	\(\frac { 1 }{ 5 } \)	\(\frac { 1 }{ 5 } \)

Y	0	1	2	3
P(Y)	\(\frac { 1 }{ 5 } \)	\(\frac{3}{10}\)	\(\frac { 2 }{ 5 } \)	\(\frac{1}{10}\)

Commodities	Price		Quantity
Commodities	Base year	Current year	Quantity
Rice	32	48	25
Sugar	25	42	10
Oil	54	85	6
Coffe	250	460	1
Tea	175	275	2

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12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

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12th Business Maths Model Exam -1

St. Britto Hr. Sec. School - Madurai

12th Business Maths Model Exam -1-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

For a demand function p, if ഽ\(\frac{dp}{p}\) = k ഽ\(\frac{dx}{x}\) then k is equal to

If F(x) is the probability distribution function, then F(- \(\infty \)) is ___________.

Given E(X) = 5 and E(Y) = -2, then E(X – Y) is

Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is

ഽ2xdx is

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

A finite subset of statistical individuals in a population is called __________

The quantities that can be numerically measured can be plotted on a

E[X-E(X)] is equal to

A ________ is a statement or an assertion about the population parameter.

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { y }{ x } \right) \) can be solved by making substitution,

Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of Rs.1,295.00 and a standard deviation of Rs.750.00. What proportion of credit card holders spend more than Rs.1,500.00 on their credit cards per month?

If c is a constant, then E(c) is

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

A formula or equation used to represent the probability distribution of a continuous random variable is called

The probability that a standard normal variate z will be A B 1) Greater than 1.09 a) 0.8163 2) less than - 1.65 b) .1379 3) lying between - 1.00 and 1.96 c) 0.0495 4) lying between 1.25 and 2.75 d) 0.1026 The correct match is

A homogeneous differential equation of the form \(\frac { dy }{ dx } \) = f\(\left( \frac { x }{ y } \right) \) can be solved by making substitution,

If f (x) is a continuous function and a < c < b ,then \(\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx\) is

North-West Corner refers to ________

Part - B

Generic 2 - Answer All Question

From the following table obtain a polynomial of degree y in x x 1 2 3 4 5 y 1 -1 1 -1 1

A sample of 100 students are drawn from a school. The mean weight and variance of the sample are 67.45 kg and 9 kg. respectively. Find (a) 95% and (b) 99% confidence intervals for estimating the mean weight of the students.

Explain Factor Reversal Test.

Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be atleast two fatal accidents in a year. (given e-0.25 = 0.7788).

The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x , the marginal revenue is given by R'(x) = 18 and the fixed cost is Rs. 120. Find the profit function.

The distribution of a continuous random variable X in range (–3, 3) is given by p.d.f. f(x)={\(\frac { 1 }{ 16 } (3+{ x) }^{ 2 },\quad -3\le x\le -1\\ \frac { 1 }{ 16 } { (6-2x) }^{ 2 },-1\le x\le 1\\ \frac { 1 }{ 16 } { (3-x) }^{ 2 },1\le x\le 3\) Verify that the area under the curve is unity.

Integrate the following with respect to x. sin3 x

What is the difference between Assignment Problem and Transportation Problem?

In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints.

A discrete random variable. X has the following probability distribution X 0 1 2 3 4 5 6 7 8 P (X) a 3a 5a 7a 9a 11a 13a 15a 17a Find the value of a and P(X < 3)

The population of a city in a censes taken once in 10 years is given below. Estimate the population in the year 1955. Year 1951 1961 1971 1981 Population in lakhs 35 42 58 84

The birth weight of babies is normally distributed with mean 3,500 g and standard deViation 500 g. What is the probability that a baby is born that weighs less than 3,100 g?

Integrate the following with respect to x. xn log x

Using second fundamental theorem, evaluate the following: \(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x. x8(1+x9)5

Part - C

Generic 3 - Answer All Question

Suppose, the life in hours of a radio tube has the following p.d.f f(x)=\(\frac { 100 }{ { x }^{ 2 } } ,when\quad \ge 100\\ 0,\quad when\quad x<100\) Find the distribution function.

The following data gives readings of 10 samples of size 6 each in the production of a certain product. Draw control chart for mean and range with its control limits. Sample 1 2 3 4 5 6 7 8 9 10 Mean 383 508 505 582 557 337 514 614 707 753 Range 95 128 100 91 68 65 148 28 37 80

A die is thrown 120 times and getting 1 or 5 is considered a success. Find the mean and variance of the number of successes.

A continuous random variable X has the following p.d.f f(x)=ax, 0\(\le\)x\(\le\)1 Determine the constant a and also find P\(\\ \left[ X\le \frac { 1 }{ 2 } \right] \)

The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart. Sample 1 2 3 4 5 6 Mean 300 342 351 319 326 333 Range 25 37 20 28 30 22 Given for n = 6, A2 = 0.483,

In tossing of a five fair coin, find the chance of getting exactly 3 heads.

Find the sample size for the given standard deviation 10 and the standard error with respect of sample mean is 3.

Consider the following pay-off (profit) matrix Action States Action States (s1) (s2) (s3) (s4) A1 5 10 18 25 A2 8 7 8 23 A3 21 18 12 21 A4 30 22 19 15 Determine best action using maximin principle.

If a random variable X follows Poisson distribution such that P(X = 2) = 9. P(X = 4) + 90 P(X = 6) then find the mean and variance.

Find the initial basic feasible solution for the following transportation problem by VAM

Part - D

Generic 5 - Answer All Question

Determine the mean and variance of a discrete random variable, given its distribution as follows. X=x 1 2 3 4 5 6 Fx(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data. Commodities Price Quandity 2000 2010 2000 2010 Rice 38 35 6 7 Wheat 12 18 7 10 Rent 10 15 10 15 Fuel 25 30 12 16 Miscellaneous 30 33 8 10

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

Calculate the cost of living index number by consumer price index number for the year 2016 with respect to base year 2011 of the following data. Commodities Price Quantity Base year Current year Rice 32 48 25 Sugar 25 42 10 Oil 54 85 6 Coffe 250 460 1 Tea 175 275 2

Comment

Other Study material

12th Business Maths Weekly Test - 3 ( Operations R

12th Business Maths Weekly Test - 4 ( Operations R

12th Business Maths Monthly Test - 1 ( Operations

ഽ2^xdx is

The probability that a standard normal variate z will be

A B

1) Greater than 1.09 a) 0.8163

2) less than - 1.65 b) .1379

3) lying between - 1.00 and 1.96 c) 0.0495

4) lying between 1.25 and 2.75 d) 0.1026

The correct match is

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

A sample of 100 students are drawn from a school. The mean weight and variance of the sample are 67.45 kg and 9 kg. respectively. Find
(a) 95% and
(b) 99% confidence intervals for estimating the mean weight of the students.

Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be atleast two fatal accidents in a year. (given e^-0.25 = 0.7788).

The distribution of a continuous random variable X in range (–3, 3) is given by p.d.f.
f(x)={\(\frac { 1 }{ 16 } (3+{ x) }^{ 2 },\quad -3\le x\le -1\\ \frac { 1 }{ 16 } { (6-2x) }^{ 2 },-1\le x\le 1\\ \frac { 1 }{ 16 } { (3-x) }^{ 2 },1\le x\le 3\)
Verify that the area under the curve is unity.

Integrate the following with respect to x.
sin³ x

In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability
that it will take less than 16.35 seconds to develop prints.

A discrete random variable. X has the following probability distribution

X 0 1 2 3 4 5 6 7 8

P (X) a 3a 5a 7a 9a 11a 13a 15a 17a

Find the value of a and P(X < 3)

The population of a city in a censes taken once in 10 years is given below. Estimate
the population in the year 1955.

Year 1951 1961 1971 1981

Population in lakhs 35 42 58 84

Integrate the following with respect to x.
xⁿlog x

Using second fundamental theorem, evaluate the following:
\(\int _{ 0 }^{ 3 }{ \frac { { e }^{ x }dx }{ 1+{ e }^{ x } } } \)

Integrate the following with respect to x.
x⁸(1+x⁹)⁵

Suppose, the life in hours of a radio tube has the following p.d.f
f(x)=\(\frac { 100 }{ { x }^{ 2 } } ,when\quad \ge 100\\ 0,\quad when\quad x<100\)
Find the distribution function.

The following data gives readings of 10 samples of size 6 each in the production of a certain product. Draw control chart for mean and range with its control limits.

Sample 1 2 3 4 5 6 7 8 9 10

Mean 383 508 505 582 557 337 514 614 707 753

Range 95 128 100 91 68 65 148 28 37 80

A continuous random variable X has the following p.d.f
f(x)=ax, 0\(\le\)x\(\le\)1
Determine the constant a and also find P\(\\ \left[ X\le \frac { 1 }{ 2 } \right] \)

The following data gives the readings for 8 samples of size 6 each in the production of a certain product. Find the control limits using mean chart.

Sample 1 2 3 4 5 6

Mean 300 342 351 319 326 333

Range 25 37 20 28 30 22

Given for n = 6, A₂ = 0.483,

Consider the following pay-off (profit) matrix Action States

Action States

(s₁) (s₂) (s₃) (s₄)

A₁ 5 10 18 25

A₂ 8 7 8 23

A₃ 21 18 12 21

A₄ 30 22 19 15

Determine best action using maximin principle.

Determine the mean and variance of a discrete random variable, given its distribution as follows.

X=x 1 2 3 4 5 6

F_x(x) \(\frac{1}{6}\) \(\frac{2}{6}\) \(\frac{3}{6}\) \(\frac{4}{6}\) \(\frac{5}{6}\) 1

the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

Commodities Price Quandity

2000 2010 2000 2010

Rice 38 35 6 7

Wheat 12 18 7 10

Rent 10 15 10 15

Fuel 25 30 12 16

Miscellaneous 30 33 8 10

Calculate the cost of living index number by consumer price index number for the year 2016 with respect to base year 2011 of the following data.

Commodities Price Quantity

Base year Current year

Rice 32 48 25

Sugar 25 42 10

Oil 54 85 6

Coffe 250 460 1

Tea 175 275 2