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Business Mathematics - I

bbasemester 1
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Faculty of Management

2025

Bachelor in Business Administration

Business Mathematics - I

MTH - 201

Full Marks: 100

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

"Section A"

Brief Answer Questions .

[10*2=20 ]

1.

Find the equation of straight line which passes through the points (3, 6) and (-5, 2).

[2]
2.

A manufacturing company has an investment of Rs 90,000 to purchase two raw materials X and Y whose prices are Rs 1,500 and Rs 1,800 each respectively. Write down the slope of budget constraint.

[2]
3.

Find the \( 10^{\text{th}} \)term of the geometric series:\( 2 + 6 + 18 + \dots.. \)

[2]
4.

Determine whether the following system of linear equations have a unique solution or many solution or no solution: x + 4y = 9 and 2x + y = 8.

[2]
5.

Find the roots of following quadratic equation: \( x^2 - 3x - 10 = 0 \).

[2]
6.

Form the quadratic equation whose roots are \( (1 + \sqrt{3}) and (1 - \sqrt{3}) \).

[2]
7.

Solve: \( 2^{9-x} \cdot 4^x = 2^{2x-1} \)

[2]
8.

Find the sum of the first twenty terms of the arithmetic series: \( 3 + 5 + 7 + \dots... \)

[2]
9.

Find the point of stationary of \( y = 5x^3 - 3x^2 + 25 \)

[2]
10.

Find the compound interest on a sum of Rs 1,000 for 2 years at\( 5\% \) per annum.

[2]

"Section B"

Short Answer Questions : (Attempt any SIX Questions )

[6*5=30 ]

1.

Sketch the graph of parabola \( y = x^2 - 2x - 8 \). Find the minimum value of y.

[5]
2.

Solve the following system of linear equations: x + 2y + z = 9, x + y - 2z = -9 and 2x - y + z = -2.

[5]
3.

Given the national income model Y = E, E = C + I where C = 600 + 0.24Y and I = 280. Determine the equilibrium level of national income and the equilibrium level of consumption.

[5]
4.

A consumption function is modeled by the equation \( C = 800 \left(1 - e^{-0.5y}\right) \), where y represents income level. Estimate the values of C when y\( = 5, 10, 15, 20 \text{ and } 25 \).

[5]
5.

Find the amount of immediate annuity where periodical payment is Rs 50,000 for 15 years at 5% compounded per annum.

[5]
6.

In how many years a computer costing Rs 50,000 be reduced to its half at the rate of 5% depreciation each year?

[5]
7.

Find \( \frac{dy}{dx} \) from the following:

 (i) \( x^2 + y^2 = 25 \)

 (ii)\( x = 3t^2 and y = t^3 \)

[5]

"Section C"

Long Answer Questions : ( Attempt Any Three Questions ) .

[3*10=30 ]

1.

The following table shows the yearly profit of a company [in million Rs].

Year 2008 2009 2010 2011 2012 2013 2014
Profit 150 180 170 190 160 170 210

Obtain the equation of trend line by least squares method. Also, estimate the profit of the company for the years 2015.

[10]
2.

The supply and demand equations of goods are\( P_s = 6Q_s + 40 \)and \( P_d = -2Q_d + 120 \) respectively. The government decides to impose a tax of Rs t per unit of goods. Find the value of t that maximizes the government's total tax revenue on the assumption that equilibrium conditions prevail in the market. Also, find the equilibrium price, the equilibrium quantity and the total tax raised.

[10]
3.

Project A and B involved the following net cash flows:

Projects Initial cost Year 1 Year 2 Year 3
Project A 24,000 6,000 12,000 16,000
Project B 24,000 4,000 10,000 20,000

Decide which project is the most profitable by determining the NPV at discount rate of 15%.

[10]
4.

The demand and supply functions for goods are given by:

\( P_d = 42 - 0.2Q_d and P_s = 2 + 0.2Q_s \)

a. Calculate the equilibrium price and quantity.

b. Find the consumer's surplus, producer's surplus and total surplus.

[10]