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JEE Advanced Mix Test 52

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JEE Advanced Mix Test 52
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  • Question 1
    4 / -1

    Directions For Questions

    A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current  A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant .

    ...view full instructions

    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

    Solution

    Induced electric field due the change in magnetic flux is

    Hence magnitude of the induced electric field is

    E = BR/2

     

  • Question 2
    4 / -1

    A moving ball collides a pendulum bob as shown, the coefficient of restitution so that bob performs vertical circular motion about 0 is (g = 10 m/s2)

    Solution

     

  • Question 3
    4 / -1

    Directions For Questions

    The mass of nucleus . z X A is less than the sum of the masses of ( A − Z )  number of neutrons and Z  number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M  can break into two light nuclei of mass m1 and m2 only if ( m1 + m2 ) < M . Also two light nuclei of massws m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if ( m3 + m4 ) > M

    The masses of some neutral atoms are given in the table below:

    ...view full instructions

    Which of the following statements is correct?

    Solution

     

  • Question 4
    4 / -1

    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.

    Solution

     

  • Question 5
    4 / -1

    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;

    Solution

    The spherically symmetric state S1 of Li2+ has one radial node 2s. Upon absorbing light, the ion gets excited to state S2, which also has one radial node.

    The energy of electron in S2 is same as that of H-atom in its ground state.

     

  • Question 6
    4 / -1

    The correct set of the products obtained in the following reactions

    Solution

     

  • Question 7
    4 / -1

    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

    Solution

     

  • Question 8
    4 / -1

    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) ≥ ex, 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?

    Solution

     

  • Question 9
    4 / -1

    Solution

     

  • Question 10
    4 / -1

    For x ∈(0, π), the equation sinx + 2sin2x − sin3x = 3 has

    Solution

     

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