If the curve $a y+x^2=7$ and $x^3=y$, cut orthogonally at $(1,1)$, then the value of $a$ is

If $y=x^4-10$ and $x$ changes from 2 to 1.99, then what is the change in $y$ ?

The equation of tangent to the curve $y\left(1+x^2\right)=2-x$, where it crosses $X$-axis, is

The points at which the tangents to the curve $y=x^3-12 x+18$ are parallel to $X$-axis are

The tangent to the curve $y=e^{2 x}$ at the point $(0,1)$ meets $X$-axis at