List of top Mathematics Questions on linear inequalities asked in JEE Main

For the system of linear equations 
\(x+y+z=6\) 
\(\alpha x+\beta y+7 z=3\) 
\(x+2 y+3 z=14\). 
which of the following is NOT true ?

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 the system of linear equations \[ x + 2y + z = 2, \quad \alpha x + 3y - z = \alpha, \quad -\alpha x + y + 2z = -\alpha \] be inconsistent. Then $\alpha$ is equal to:
If \(\displaystyle\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0 \) then \(8(\alpha+\beta)\) is equal to :

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

Fill in the blanks. (i) If $x > y$ and $z < 0$, then $-xz$ $-yz$. (ii) If $p > 0$ and $q < 0$, then $p - q$ $p$. (iii) If $-2x + 1 \ge 9$, then $x$ $-4$.