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12th Business Maths Important 2 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

12th Business Maths Important 2 Mark Question Paper-Aug 2020

Time : 1.00 Hours

Part - A

Generic 2 - Answer All Question

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

Assign the programmers to the programme in such a way that the total computer time is least.

A company requires f(x) number of hours to produce 500 units. It is represented by f (x) = 1800x^−0.4 . Find out the number of hours required to produce additional 400 units. [(900)^0.6=59.22, (500)^0.6=41.63]

Integrate the following with respect to x.
\(\int \frac { { x }^{ 3 } }{ x+2 } dx\)

Let X be a discrete random vafiable with the following p.m.f

\(p(x)=\begin{cases} 0.3\quad for\quad x=3 \\ 0.2\quad for\quad x=5 \\ 0.3\quad for\quad x=8 \\ 0.2\quad for\quad x=10 \\ 0\quad otherwise \end{cases}\)

Find and plot the c.d.f. of X.

Derive the mean and variance of poisson distribution.

The marginal revenue (in thousands of Rupees) functions for a particular commodity is 5 + 3 ^{−0 03} e . x where x denotes the number of units sold. Determine the total revenue the sale of 100 units. (Given e⁻³= 0.05 approximately)

The random variable X has the normal distribution f(x) = C e^{\(-\left( \frac { x-100 }{ 50 } \right) ^{ 2 }\)}, then find the value of C.

State any two merits for systematic random sampling.

If the marginal revenue function for a commodity is MR = 9 − 4x² . Find the demand function.

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ log\left( \frac { 1 }{ x } -1 \right) dx } \)

In a business venture a man can make a profit of Rs. 2,000 with a probability of 0.4 or have a loss of Rs.1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?

(D²−2D−15)y = 0 given that \(\frac{dy}{dx}\)= 0 and \(\frac{d^2 y}{dx^2}\) = 2 when x = 0

Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525

Evaluate the following:
\(\int _{ -1 }^{ 1 }{ f(x) } dx\) where f(x) = \(\begin{cases} x, \\ -x, \end{cases}\begin{matrix} x & \ge & 0 \\ x & < & 0 \end{matrix}\)

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

Solve the following equations by using Cramer’s rule
2x + 3y = 7; 3x + 5y = 9

The probability function of a random variable X is given by

p(x) = \(\begin{cases} \frac { 1 }{ 4 } ,\quad for\quad x=-2 \\ \frac { 1 }{ 4 } ,\quad for\quad x=0 \\ \frac { 1 }{ 2 } ,\quad for\quad x=10 \\ 0,\quad elsewhere \end{cases}\)

Evaluate the following probabilities.
(i) P(X\(\le\)0), (ii) P(X < 0),
(iii) P(\(|\)X\(|\)\(\le\)2) and (iv) P(0\(\le\)X\(\le\)10)

If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank
of BA.

Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?

The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded .Also calculate consumer’s surplus.

Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?

Commodity Price in Rupees per unit Number of units

Base year Current year Base year Current year

A 6 10 50 56

B 2 2 100 120

C 4 6 60 60

D 10 12 50 24

E 8 12 40 36

Let X be a discrete random variable with the following p.m.f
p(x)={\(0.3\quad \quad for\quad x=3\\ 0.2\quad \quad for\quad x=5\\ 0.3\quad \quad for\quad x=8\)
{\(0.2\quad \quad for\quad x=10\\ 0\quad \quad \quad otherwise\\ \\ \)
Find and plot the c.d.f. of X.

Integrate the following with respect to x
\(\frac { 1 }{ \sqrt { { 9x }^{ 2 }-7 } } \)

Explain the distribution function of a random variable.

What is sampling distribution of a statistic?

Vehicles pass through a junction on a busy road at an average rate of 300 per hour.
1. Find the probability that none passes in a given minute.
2. What is the expected number passing in two minutes?

The demand function for a commodity is p = \(\frac { 36 }{ x+4 } \). Find the consumer’s surplus when the prevailing market price is Rs. 6.

Integrate the following with respect to x.
\(\frac { { x }^{ e-1 }+{ e }^{ x-1 } }{ { x }^{ e }+{ e }^{ x } } \)

Evaluate the following integrals:
ഽ\(\frac { dx }{ { { 2-3x-2x }^{ 2 } } } \)

Given the marginal revenue function \(\frac { 4 }{ ({ 2x+3 })^{ 2 } } \)-1, show that the average revenue function is P = \(\frac { 4 }{ 6x+9 } \)-1

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