Number of integral values of $m$ for which ${x}^2 + 5m{x} - 3m + 1 < 0$ $\forall x \in R$ is (where ${.}$ denotes the fractional part function).

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is

Number of rational roots of the equation $x^{2016} - x^{2015} + x^{1008} + x^{1003} + 1 = 0$ is equal to

The surface area of a pipe,open at both ends,is equal to $628 \, m^2$. The difference between its length and its radius is $15 \, m$. If the pipe were closed at one end,what amount of water could it hold (in $, m^3$)?

Let $p, q \in \{1, 2, 3, 4\}$. The number of equations of the form $px^2 + qx + 1 = 0$ having real roots is

Solve the given two equations and select the correct answer from the given options.
$I.$ $4x^2 - 43x + 105 = 0$
$II.$ $7y^2 - 29y + 30 = 0$