The radius of the larger circle lying in the first quadrant and touching the line $4x + 3y - 12 = 0$ and the coordinate axes is:

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then, the rate at which the area increases, is

Which of the following compounds does not exhibit mutarotation?

The differential equation of the family $y=a e^x+b x e^x+c x^2 e^x$ of curves, where $a, b, c$ are arbitrary constants, is

An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. If the initial pressure is $P_1$ and the final pressure is $P_3$,and the total work done is $W$,then:

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 $/8$)