Singleton Set

Q. If S is the set of distinct values of b for which the folowing system of linear equations
$x+y+z=1$,
$x+ay+z=1$
and $ax+by+z=0$ has no solution, then S is

1. an infinite set
2. a finite set containing two or more elements
3. singleton set
4. a empty set

Q. The solution set of the system of equations $x+y-z=6;3x-2y+z=-5;x+3y-2z=14$ is $(x,y,z)$ then $x+y+z$ is equal to

Q.

What is the vertex of the quadratic function y = $x^2-6x+12$?

1. (1, 1)
2. (2, 2)
3. (2, 3)
4. (3, 3)

Q. Which of the following is/are singleton sets?

1. $A=\{x:x\text{is H.C.F. of}12\text{and}18\}$
2. $B=\{x:x\text{is a common prime factor of}16\text{and}27\}$
3. $C=\{x:x\text{is a prime factor of}35\}$
4. $D=\{x:x\text{is L.C.M. of}6\text{and}11\}$