Exams › JEE Advanced › General

Let f : (0, ∞ ) → R be a differentiable function such that f ′ (x) = 2 – x ) x ( f for all x ∈ (0, ∞ ) and f(1) ≠ 1. Then

1. + → 0 x lim f ′ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ x 1 = 1
2. + → 0 x lim xf ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ x 1 = 2
3. + → 0 x lim x 2 f ′ (x) = 0
4. |f(x)| ≤ 2 for all x ∈ (0, 2)

Correct answer: + → 0 x lim f ′ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ x 1 = 1

Related JEE Advanced General questions

• A particle of mass m is projected form the ground with an initial speed μ 0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u 0 . The angle that the composite system makes with the horizontal immediately after the collision is
• The image of an object, formed by a plano-convex lens at a distance of 8m behind the lens, is real and is one third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is -
• The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is
• The work done on a particle of mass m by a force , K ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + j ˆ ) y x ( y i ˆ ) y x ( x 2 / 3 2 2 2 / 3 2 2 (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is
• One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
• A ray of light travelling in the direction ( ) j ˆ 3 i ˆ 2 1 + is incident on a plane mirror. After reflection, it travels along the direction ( ) j ˆ 3 i ˆ 2 1 − . The angle of incidence is

⚔️ Practice JEE Advanced General free + battle 1v1 →