List of top Mathematics Questions on linear inequalities

Point \((a,2a)\), \(a>0\), lies in region between lines \(3x-y-3=0\) and \(6x-y-6=0\). Then \(a\in\)

A milkman has \(250\) litres of milk containing \(5\%\) fat. How many litres of milk containing \(15\%\) fat should he add to his stock so that the fat content in the mixture would be more than \(7\%\) but less than \(10\%\)?

A student needs to buy notebooks (\(n\)) for a semester. Double the number of notebooks plus \(5\) must strictly exceed \(15\), but the number of notebooks plus \(10\) must be no more than \(22\). What is the range of notebooks they can buy?

The value of the greatest integer \(k\) satisfying the inequation \(2^{n+4} + 12 \ge k(n + 4)\) for all \(n \in N\) is

The solution of $3x - 5<2x - 4$ is

If $|2x-3|<5, x\in\mathbb{R}$, then $x$ lies in the interval

If $\frac{21x-6}{4}-9\le0$ and $\frac{x-1}{3}+1\ge0, x\in\mathbb{R}$ then $x$ lies in the interval

Let $x$ be a real number such that $\dfrac{x-3}{x-2} \geq 1$. Then the solution set of the inequality is:

The shaded region \(ABC\) shown in the diagram is given by the inequalities

The solution set of inequality \( |x+2|<3 \) is

If \(\frac{x+1}{x-1}<2\), then \(x\) lies in the interval

The inequality representing the following graph is

The solution set of the system of inequalities \( 5-4x \leq -7 \) or \( 5-4x \geq 7,\ x \in R \) is

If \(x \neq 11\) satisfies the inequality \(\frac{2x - 21}{x - 11} \geq 3\), then \(x\) lies in the interval

If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is:

If \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} \] and \[ A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}, \] then the values of \( a \) and \( c \) are respectively:

The number of pairs of consecutive positive even integers such that the sum of their squares is \(290\) is:

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 :