IIT JEE Advanced 2008 Paper 1

We have the system of equations:
ax + by = 0
cx + dy = 0
Since the system of homogeneous equation always have solution,
Statement-2 is true.
Now, Δ = |

a	b
c	d

| and a , b , c , d ∊ {0 , 1}
= ad - bc
The number of possible ways of selecting a, b, c, d from the set {0, 1} is 2 × 2 × 2 × 2 = 16
If the system has unique solution, Δ ≠ 0, we get the following:
• Either ad = 1, bc = 0 or ad = 0, bc = 1
• Favourable cases = 6
Hence, the probability that system of equation has unique solution is

6

16

=

3

8