The de-Broglie wavelength of a particle moving with a velocity $2.25 \times 10^8 \, m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the energy of the photon is (velocity of light is $3 \times 10^8 \, m/s$):- (in $/8$)

The eccentricity of the conic $36x^2 + 144y^2 - 36x - 96y - 119 = 0$ is

Which of the following is known as the pacemaker of the heart?

The length of the subtangent at any point of the curve $x^m y^n = a^{m+n}$ is proportional to -

Which of the following pairs is incorrectly matched?

Consider two statements $S_1$ and $S_2$. $S_1$: If $f(x)$ is a differentiable function with $f^{\prime}(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f^{\prime}(x)}$ is also increasing in $(a, b)$. $S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $\left(0, \frac{\pi}{2}\right)$. Which of the following is true?