The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is '$$V_e$$', then the escape velocity from the planet is

A biconvex lens $$\left(R_1=R_2=30 \mathrm{~cm}\right)$$ has focal length equal to the focal length of concave mirror. The radius of curvature of concave mirror is [Refractive index of material of lens $$=1.6$$ ]

In an a.c. circuit, a resistance R = 40 $$\Omega$$ and an inductance 'L' are connected in series. If the phase angle between voltage and current is 45$$^\circ$$, then the value of the inductive reactance is (tan 45$$^\circ$$ = 1)

A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)