Question

Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$x+y+z=1$ $2 x + Ny +2 z=2$ $3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

• A. 18
• B. 19
• C. 20
• D. 21

Answer 1

Answer: (C)

20

Answer 2

The correct answer is (C) : 20
x+y+z=1
2x+Ny+2z=2
3x+3y+Nz=3
Δ=∣∣​123​1N3​12N​∣∣​
=(N−2)(N−3)
For unique solution Δ=0
So N=2,3
⇒P( system has unique solution )=64​
So k=4
Therefore sum =4+1+4+5+6=20