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ISC Class 12 Mathematics Solved Question Paper 2016

Short Answer Type

31.
A man borrows 20,000 per annum 2 % compounded semi-annually and agrees to pay it in 10 equal semi-annual installments. Find the value of each installment, if the first payment is due at the end of two years.

Given, P= 20,000, R = 12 %, n = 10, m = 3

Amount of installment = A

We have,

P = $\frac{A}{0.06} \{\frac{1}{{(1 + i)}^{m}} - \frac{1}{{(1 + i)}^{n + m}}\}$

$20000 = \frac{A}{0.06} \{\frac{1}{{(1 . 06)}^{3}} - \frac{1}{{(1.06)}^{13}}\}$

$∴$ A = 3235.90

The value of each installment is 3235.90

32.

A company manufactures two types of products A and B. Each unit of A requires 3grams of nickel and 1 gram of chromium, while each unit of B requires 1 gram of nickel and 2 gram of chromium. The firm can produce 9 grams of nickel and 8 grams of chromium. The profit is Rs. 40 on each unit of product of type A and Rs. 50 on each unit of product of type B. How may units of each type should the company manufacture so as to earn maximum profit? Use linear programming to find the solution?

33.

A bill of Rs. 1,800 drawn on 10^thSeptember, 2010 at 6 months was discounted for Rs. 1,782 at a bank. If the rate of interest was 5 % per annum, on what date was the bill discounted?

34.

The index number by the method of aggregates for the year 2010, taking 2000 as abse year, was found to be 116. If sum of the prices in the year 2000 is 300, find the values of x and y in the data given below:

Commodity	a	B	C	D	E	F
Price in the year 2000()	50	x	30	70	116	20
Price in the year 2010()	60	24	y	80	120	28

35.

From the details given below, calculate the five yearly moving averages of the number of candidates who have studied in a school. Also, plot these and original data on the same graph paper.

Year	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002
Number of Students	332	317	357	392	402	405	410	427	405	438

Long Answer Type

36.

Find the image of the point (2, - 1, 5) in the line $\frac{x - 11}{10} = \frac{y + 2}{- 4} = \frac{z + 8}{- 11}$ . Also, find the length of the perpendicular from the point (2, - 1, 5) to the line.

37.

Find the cartesian equation of the plane, passing through line of intersection of the planes: $\vec{r} . (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) + 5 and \vec{r} . (\hat{i} - 5 \hat{j} + 7 \hat{k}) + 2 = 0$ and intersecting y-axis at (0, 3)