Each of the roots of the equation $x^3-6x^2+6x-5=0$ are increased by $h$. If the new transformed equation does not contain the $x^2$ term,then $h$ is equal to:

The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

Let the roots of the equation $E_1 \equiv x^3+x^2+lx+n=0$ be $x_i, (i=1, 2, 3)$ and the roots of $E_2 \equiv x^3+ax^2+bx+c=0$ be $\frac{x_i-1}{2}$. If the equation $E_2=0$ is a reciprocal equation of class one,then the roots of these two equations excluding the common roots are

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

Let $S = \{x^{3} + ax^{2} + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\}$ be a set of polynomials. Then the number of polynomials in $S$,which are divisible by $x^{2} + 2$,is

The sum of the non-real roots of $(p^2+p-3)(p^2+p-2)-12=0$ is