Class XII

The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, ααx + 2 y + 3z = 1 has a unique solution for
  1. all rational α
  2. ααnot equal to 0
  3. all integral α
  4. all real α
If A and B are two matrices such that A + B and AB are both defined, then
  1. A and B can be any matrices
  2. number of columns of A = number of ros of B.
  3. A, B are square matrices of same order
  4. A, B are square matrices not necessarily of same order
The system of equations, 3 x + y – z = 0, 5 x + 2y – 3z = 2, 15 x + 6 y – 9 z = 5 has
  1. two distinct solutions
  2. no solution
  3. infinitely many solutions.
  4. a unique solution
The system of equations,x + y = 2 and 2x + 2y = 3 has
  1. infinitely many solutions
  2. no solution
  3. a unique solution
  4. finitely many solutions
The equations2x + 3y = 7, 14 x + 21 y = 49 has
  1. infinitely many solutions
  2. finitely many solutions.
  3. a unique solution
  4. no solution
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