The set of all real values of $x$ satisfying the inequalities $x^2-4x+3 > 0$ and $x^2-2x-8 \leq 0$ is

The least integral value $\alpha$ of $x$ such that $\frac{x - 5}{x^2 + 5x - 14} > 0$ satisfies:

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180 \ cm$,then:

There are $30$ questions in a multiple-choice test. $A$ student gets $1$ mark for each unattempted question,$0$ mark for each wrong answer,and $4$ marks for each correct answer. If a student answered $x$ questions correctly and scored $60$,then the number of possible values of $x$ is:

The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \geq 1$ is

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to