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.  (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?  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.  (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.  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.  (b) Given that the total cost function for x units of a commodity is: $C(x)=\frac{x^{3}}{3}+3 x^{2}-7 x+16$
(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 :-

Thanks