A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.

Months	Sales in Units			Commission
	A	B	C
January	9	10	2	800
February	15	5	4	900
March	6	10	3	850

Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters
a) cannot be repeated
b) can be repeated
c) cannot be repeated but must begin with E
d) cannot be repeated but end with CAB.

Determine whether the points P(0,1), Q(5,9), R(–2, 3) and S(2, 2) lie outside the circle, on the circle or inside the circle x²+y²-4x+4y-8 = 0.

If cosA =\(\frac{4}{5}\)and cosB =\(\frac{12}{13}\),\(\frac{3 \pi}{2}<(A, B)<2 \pi\), find the value of sin(A - B)

Show that the function f(x) = |x| is not differentiable at x = 0.

For the demand function p =100 - 6x², find the marginal revenue and also show that  MR = \(p\left[ 1-\frac { 1 }{ { n }_{ d } } \right] \)

Gopal invested Rs. 8,000 in 7% of Rs. 100 shares at Rs. 80. After a year he sold these shares at Rs. 75 each and invested the proceeds (including his dividend) in 18% for Rs. 25 shares at Rs. 41. Find
(i) his dividend for the first year
(ii) his annual income in the second year
(iii) The percentage increase in his return on his original investment

In a screw factory machines A, B, C manufacture respectively 30%, 40% and 30% of the total output of these 2%, 4% and 6% percent are defective screws. A screws is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by Machine C?

The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficient.

Solve the following linear programming problem graphically.
Maximize Z = 3x₁ + 5x₂ subject to the constraints x₁ + x₂ ≤ 6, x₁ ≤ 4; x₂ ≤ 5, and x₁, x₂ ≥ 0