If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then

Let $\lambda \in R$ and let the equation $E$ be $| x |^2-2| x |+|\lambda-3|=0$. Then the largest element in the set $S =$ $\{ x +\lambda: x$ is an integer solution of $E \}$ is $..........$

If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then

All the points $(x, y)$ in the plane satisfying the equation $x^2+2 x \sin (x y)+1=0$ lie on

If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are

The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is