**MATHEMATICS**

**(Three hours)**

**Section A**

**Question 1**

(i) Deepak rolls two dice and gets a sum more than 9. What is the probability that the number on the first die is even?

(ii) You are given the following two lines of regression. Find the regression of Y on X and X on Y and justify your answer:

3x + 4y = 8; 4x + 2y = 10

(iii) If w is the cube root of unity, then find the value of (1-3w+w2) (1+w-3w2)

(iv) Solve: (y + xy)dx + y (1-y^{2})dy = 0

**Question 2**

Using matrix method, solve the following system of linear equations:

x – 2y – 2z – 5 = 0;

–x + 3y + 4 = 0 and

–2x + z – 4 = 0

**Question 3**

Find the equation of the parabola whose vertex is at the point (4, 1) and focus is (6, -3).

**Question 4**

(a) Prove that: Tan-1[Sin-1(1/√17) + Cos-1(9/√85] = ½.

(b) A, B and C represent three switches in ‘on’ position and A’, B’ and C’ represent the three switches in ‘off’ position. Construct a switching circuit representing the polynomial:

(A + B)( B’+ C)(A’+C’).

Using the laws of Boolean Algebra, show that the above polynomial is equivalent to AB’ + AC + B and construct an equivalent switching circuit.

**Question 5**

Sketch the graphs of y = x(4 - x) and find the area bounded by the curve, x – axis and the lines x = 0 and x = 5.

**Please refer to attached file for ISC Question Papers 2013 Mathematics**