Bamboo and grasses elongate by the activity of ......

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169} + \frac{y^2}{25} = 1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is:

The force acting on a body moving along the $x-$axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,then $\operatorname{det}(\operatorname{adj} A)$ is equal to

Which one is an incorrect statement?

The speed of an electron having a wavelength of $10^{-10} \ m$ is ........... $\times 10^6 \ m/s$.