JEE Advanced Mix Test 40

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

Which of the following statements is correct?

Out of the following pairs one which does not have identical dimensions is

A system of two identical uniform truncated discs is shown in the figure. Different relevant coordinates are given in the figure. Coordinates of the centre of mass of the system are

Two aliphatic aldehydes P and Q react in the presence of aqueous K₂CO₃ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below.

The hydrogen-like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light, the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

The orbital S₂ and the energy of the state S₁ in units of the hydrogen atom ground state energy respectively are;

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.

If chord PQ subtends an angle θ at the vertex of y² = 4ax, then tanθ equals

Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies f(x) - 12f'(x) + f(x) ≥ e^x, x ∈ [0,1].

If the function e^-x f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true?