If one root of the equation $x^2 + px + 12 = 0$ is $4$,and the equation $x^2 + px + q = 0$ has equal roots,then what is the value of $q$?

If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

If the bi-quadratic equation $f(x)=x^4+2x^3-16x^2-22x+7=0$ has $2+\sqrt{3}$ as one of its roots,then which of the following is not a root of $f(x)$?

The number of real values of $a$ satisfying the equation $a^2 - 2a\sin x + 1 = 0$ is

Let $a_n, a_{n-1}, \ldots, a_1, a_0 \in \mathbb{C}$ and $f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0$ be a polynomial. If the polynomial $f(x)$ is monic,then:

Let $N$ be the number of quadratic equations of the form $ax^2 + bx + c = 0$ with coefficients $a, b, c \in \{0, 1, 2, \dots, 9\}$ such that $0$ is a solution of each equation. Then the value of $N$ is