Que 12:
(a) A box contains 4 red and 5 black marbles. Find the probability distribution of the red marbles in a random draw of three marbles. Also find the mean and standard deviation of the distribution. [5] (b) Bag A contains 2 white, 1 black and 3 red balls, Bag B contains 3 white, 2 black and 4 red balls and Bag C contains 4 white, 3 black and 2 red balls. One Bag is chosen at random and 2 balls are drawn at random from that Bag. If the randomly drawn balls happen to be red and black, what is the probability that both balls come from Bag B? [5] Solution 12:
(a) The box contains 4 red and 5 black marbles
3 marbles are drawn.
Probability of one red marble drawn is

(b) Let E1, E2 and E3 the following events
E1 = Bag A chosen; E2 = Bag B chosen; E3 = Bag C chosen.
$P\left(E_{1}\right)=P\left(E_{2}\right)=P\left(E_{3}\right)=\frac{1}{3}$
Now, the probability of drawing a red and a black ball from bag A is,

Section – C (20 Marks)

### ISC Maths 2011 Class-12 Previous Year Question Papers Solved

Que 13:
(a) The price of a tape recorder is ₹ 1,661. A person purchases it by making a cash payment of ₹ 400 and agrees to pay the balance with due interest in 3 half-yearly equal instalments. If the dealer charged interest at the rate of 10% per annum compounded half-yearly, find the value of the instalment. [5] (b) A manufacturer manufactures two types of tea-cups, A and B. Three machines are needed for manufacturing the tea-cups. The time in minutes required for manufacturing each cup on the machines is given below:

Each machine is available for a maximum of six hours per day. If the profit on each cup of type A is ₹ 1.50 and that on each cup of type B is ₹ 1.00, find the number of cups of each type that should be manufactured in a day to get maximum profit. [5] Solution 13:
(a) The price of a tape recorder is ₹ 1661.
The man purchases it by ₹ 400 cash down payment.
Due amount = 1661 – 400 = ₹ 1261

Que 14:
(a) If the difference between Banker’s discount and True discount of a bill for 73 days at 5% per annum is ₹ 10, find
(i) the amount of the bill
(ii) Banker’s discount. [5] (b) Given that the total cost function for x units of a commodity is: [5]
$C(x)=\frac{x^{3}}{3}+3 x^{2}-7 x+16$
(i) Find the Marginal Cost (MC)
(ii) Find the Average Cost (AC)
(iii) Prove that: Marginal Average Cost (MAC) = $\frac{x(MC)-C(x)}{x^{2}}$
Solution 14:

Que 15:
(a) The price quotations of four different commodities for 2001 and 2009 are as given below. Calculate the index number for 2009 with 2001 as the base year by using a weighted average of price relative method.

(b) The profit Of a soft drink firm (in thousands of ₹) during each month of the year is as given below:

Calculate four monthly moving averages and plot these and the original data on a graph sheet.
Solution 15:

-: End of ISC Maths 2011 Class-12 Solved Previous Year Question Paper :-

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