Class XII

Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then
  1. ad - bc need not be equal to ±1
  2. ad – bc = - 1
  3. ad – bc = ±1
  4. ad – bc = 1
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 x + 2y = 11,-2 x – 4y = 22 has
  1. no solution
  2. only one solution
  3. infinitely many solutions.
  4. finitely many solution
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
The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have
  1. only one solution
  2. infinitely many solutions.
  3. no solution
  4. only two solutions
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