If $x + \sqrt{x^2 + 1} = a$,then $x =$

Which of the following statements is not correct?

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the time period will be

The differential of ${e^{{x^3}}}$ with respect to $\log x$ is

$A$ particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the Earth and the speed of the particle at that instant are respectively:

The points on the curve $9y^{2} = x^{3}$ where the normal to the curve makes equal intercepts with the axes are