Assignment-1
Section- A
1.Define the term bank discount on a bill of exchange.
2.Explain the meaning of true discount and how it differs from bank discount.
3.State the formula for bank discount to find the discount on a bill of ₹10,000 due in 6 months at 8%
per annum.
4.Define differentiation.
5.State the formula for the derivative of a constant times a function.
6.State the meaning of the term “rate of change” in the context of derivatives.
7.Define : Linear Programming Problem
8.State the objective of Operations Research.
9.Write the steps involved in the formulation of LPP ?
Section- B
1. Calculate the net selling price, A merchant marks a product 20% above cost price but allows a
series discount of 10% followed by 5% on the marked price. Determine the profit or loss percentage.
b) Explain the concepts of nominal due date and legal due date.
2.a) Compute the nominal due date, present value, banker’s discount, and the sum received by the
holder,A bill of exchange for ₹50,000 is drawn to be paid in 90 days. It is discounted 30 days
before maturity at a banker’s discount rate of 12% per annum.
b) Find the true discount and the present worth of a bill for Rs.1,660 due in 9 months at 5% per
annum.
3.a) Find the rate of interest on the bill of ₹.3,887.50 due after 11 months whose true present worth is
₹.3750.
b) Find the term of a bill of ₹ 18,450 whose true discount at 5% per annum is ₹.450.
4.a) A seller sells a washing machine at a cost price of ₹18000 with a profit of 10%. Calculate the price
at which the customer will purchase it. And also, find profit earned by the shopkeeper.
b) The cost of a flower vase is ₹. 150. If the shopkeeper sells it at a loss of 10%, find the price at
which is sold.
1.a) Differentiate y = x2+5x+2 with respect to x
b) Differentiate f(x)=6x3-9x+4 with respect to x
2.a) Find the derivative of y=12x3 -10x2-3x+2
b) Find f(x)’,if f(x)=4x4 3x 3+2x2 5x+7
3. a) Evaluate dy/dx, y =10x4-2x+4
b) Find d(f(x))/dx, f(x)=4x4 3x 3
+2x2 5x+7
4.a) Differentiate dy/dx, y = x4-4
b) Differentiate f(x)= x5-3x+4 with respect to x
1.a) Explain the steps of the graphical method.
b) ABC animal feed company must produce at least 200 kg of a mixture consisting of ingredients A
and B daily. A costs Rs.3 per kg B costs Rs.5 per kg .Not more than 80 kg. Of A can be used and
at least 60 kg. of B must be used. Find the minimum cost mixture by graphical Method
2.a) Explain the uses of LPP.
b) A company makes three products X, Y& Z which pass through three departments : Drill,Lathe and
Assembly. The hours available in each department, hours required by each product in each
department and profit contribution of
each product are given below: Product Time required in Profit per
hours unit(Rs)
X 3 3 8 9
Y 6 5 10 15
Z 7 4 12 20
Hours 210 240 260
Available
3.a) Explain the steps of the graphical method.
b)Solve this simple LPP using the graphical method:
Max Z = 3x + 2y
Subject to the Constraint:
4.a)Explain the general form of a Linear Programming Problem.
b) Describe the main limitations of Operations Research?
Section- C
1.(i) Find the face value of a bill due after 8 months whose true discount is Rs.550 at 5 ½ %
per annum.
(ii)The difference between true and banker’s discounts on a certain bill due in 4 months hence is 50
paise.If the rate of interest is 6 per cent, find the amount of the bill
2. (i)Find the cash value of a bill of Rs. 4,200 due to 5 months hence at 7.5% p.a.
(ii)The cost of a flower vase is Rs. 150. If the shopkeeper sells it at a loss of 10%, find the price
at which it is sold.
3.(i) A shopkeeper buys an article for ₹500 and sells it for ₹600. Find the profit percentage.
(ii) A man sells two articles at ₹1000 each. On one he gains 25% and on the other, he loses 25%. Find
the overall profit or loss percentage.
4.Differentiate the following function with respect to x:
(i) y=3x3+2x2 5x+7 (ii) y=6x 3
+4x2 7x+1
9 100 2
5. If (i)y =4x +2x ,(ii) y=x +5x , find dy/dx
6.Find dy/dx, if (i)y=x 5-3x 2 +4x+3 (ii) y=x5+ 3 x -4
7.A Person requires at least 10,12 and 12 units of the chemicals A,B and C respectively for his garden.
A liquid product contains 1,2 and 4 units of A,B and C respectively per jar. A dry product contains 5,2
and 1 units of A,B and C per carton . The liquid product sells for Rs. 3 per jar and dry product sells
for Rs. 2 per carton Formulate this as an L.P.P for minimizing the cost and ensuring the requirement.
8.A company produces two products, P and Q. The profit per unit of P is ₹3 and of Q is ₹5. Each product is
processed in two machines, M1 and M2. One unit of P requires 1 hour on M1 and 2 hours on M2. One unit of Q
requires 2 hours on M1 and 1 hour on M2. Machine M1 is available for 100 hours and M2 for 80 hours.
9..Solve graphically:
Minimize Z=3x+5y
Subject to the Constraint:
x+y6
3x+2y12
x0, y0
