If [x+6]+[x+3] ≤ 7 and let call its solution as set A and set B is the solution of inequality 35x-8 < 3-3x.
Let α,β, and γ be real numbers. Consider the following system of linear equations:
x + 2y + z = 7
x + αz = 11
2x - 3y + βz = γ
Match each entry in List I to the correct entries in List II
List I | List II | ||
(P) | If β=\(\frac{1}{2}\)(7α - 3) and \(\gamma\)=28, then the system has | (1) | a unique solution |
(Q) | If β=\(\frac{1}{2}\)(7α - 3) and \(\gamma\)\(\neq\)28, then the system has | (2) | no solution |
(R) | If β\(\neq\)\(\frac{1}{2}\)(7α - 3) where \(\alpha\)=1 and \(\gamma\)\(\neq\)28, then the system has | (3) | infinitely many solutions |
(S) | If β\(\neq\)\(\frac{1}{2}\)(7α - 3) where \(\alpha\)=1 and \(\gamma\)=28, then the system has | (4) | x = 11, y = - 2 and z = 0 as a solution |
(5) | x = -15 , y = 4 and z = 0 as a solution |
The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, is