Suppose the height of a pyramid with a square base is decreased by $p \%$ and the lengths of the sides of its square base are increased by $p \%$ (where $p > 0$). If the volume remains the same,then:

Consider the cubic equation $x^3+ax^2+bx+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?

If roots of the equation $ax^2 + bx + c = 0$ are $(\alpha - \beta)$ and $(\gamma - \delta)$,and roots of the equation $Ax^2 + Bx + C = 0$ are $(\alpha + \delta)$ and $(\beta + \gamma)$,then $\left| \frac{a}{A} \right|$ is equal to (where $D_1$ and $D_2$ are discriminants of the given equations respectively).

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then .........

Let $[x]$ be the greatest integer less than or equal to $x$ for a real number $x$. Then the equation $[x^2] = x + 1$ has:

Let $f(x) = Ax^2 + Bx$ and $g(x) = Lx^2 + Mx + N$. Given that $f(2) - g(2) = 1$, $f(3) - g(3) = 4$, and $f(4) - g(4) = 9$. Then a root of $f(x) - g(x) = 0$ is