JEE Advanced Mi...

A body is thrown with a velocity of 10 m s⁻¹ at an angle of 45° to the horizontal. The radius of curvature of its trajectory in t = 1/√2 s after the body began to move is,

The figure below shows a conducting rod of negligible resistance that can slide on smooth U-shaped rail made of wire of resistance 2 Ω/m. The position of the conducting rod at t = 0 is shown. A time-dependent magnetic field B = 4t T is switched on at t = 0.

The current in the loop at t = 0 due to induced emf is

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half-submerged in a liquid of density ρ at equilibrium position. When the cylinder is given a small downward push and released, it starts oscillating vertically with a small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is

Consider the cell:

Cd(s) | Cd²⁺ (1.0 M) || Cu²⁺ (1.0, M) | Cu(s)

If we want to make a cell with a more positive voltage using the same substances, we should

Given below are two cleavage reactions:

(i) (CH₃)₃COCH₃ → CH₃I + (CH₃)₃COH

(ii) (CH₃)₃COCH₃ → CH₃OH + (CH₃)₃CI

In which of the following molecules / ions resonance structures are equivalent:

A continuous, even periodic function f with period 8 is such that f(0) = 0, f(1) = −2, f(2) = 1, f(3) = 2, f(4) = 3, then the value of tan⁻¹tan{f(−5) + f(20) + cos⁻¹(f(−10)) + f(17)} is equal to

Let the eccentricity of the hyperbola  be the reciprocal of that of the ellipse x² + 4y² = 4. Also, the hyperbola passes through a focus of the ellipse. Then, the equation of the hyperbola is