NTA JEE Main 4th September 2020 Shift 1

Dimensional formula for thermal conductivity is (here K denotes the temperature):

A tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h/2. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and on not to scale)

Starting from the origin at time t = 0, with initial velocity $$5\hat{j}$$ ms$$^{-1}$$, a particle moves in the $$x$$-$$y$$ plane with a constant acceleration of $$\left(10\hat{i} + 4\hat{j}\right)$$ ms$$^{-2}$$. At time t, its coordinates are (20 m, $$y_0$$ m). The values of t and $$y_0$$ are, respectively:

Blocks of masses m, 2m, 4m and 8m are arranged in a line of a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of 'p' is close to:

On the $$x$$-axis and at a distance $$x$$ from the origin, the gravitational field due to a mass distribution is given by $$\frac{Ax}{(x^2 + a^2)^{3/2}}$$ in the $$x$$-direction. The magnitude of the gravitational potential on the $$x$$-axis at a distance $$x$$, taking its value to be zero at infinity is:

An air bubble of radius 1 cm in water has an upward acceleration of 9.8 cms$$^{-2}$$. The density of water is 1 gm cm$$^{-3}$$ and water offers negligible drag force on the bubble. The mass of the bubble is $$(g = 980$$ cm/s$$^2)$$.

The specific heat of water = 4200 J kg$$^{-1}$$ K$$^{-1}$$ and the latent heat of ice = $$3.4 \times 10^5$$ J kg$$^{-1}$$. 100 grams of ice at 0°C is placed in 200 g of water at 25°C. The amount of ice that will melt as the temperature of water reaches 0°C is close to (in grams)

Match the $$\frac{C_p}{C_v}$$ ratio for ideal gases with different type of molecules:
Molecule Type                                    $$C_p/C_v$$
(A) Monoatomic                                 (I) 7/5
(B) Diatomic rigid molecules             (II) 9/7
(C) Diatomic non-rigid molecules      (III) 4/3
(D) Triatomic rigid molecules            (IV) 5/3

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are:

Two charged thin infinite plane sheets of uniform charge density $$\sigma_+$$ and $$\sigma_-$$, where $$|\sigma_+| > |\sigma_-|$$, intersect at the right angle. Which of the following best represents the electric field lines for the system: