NTA JEE Main 12th April 2019 Shift 1

Which of the following combinations has the dimension of electrical resistance ($$\varepsilon_0$$ is the permittivity of vacuum and $$\mu_0$$ is the permeability of vacuum)?

The trajectory of a projectile near the surface of the earth is given as $$y = 2x - 9x^2$$. If it were launched at an angle $$\theta_0$$ with speed $$v_0$$ then g = 10 m s$$^{-2}$$:

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t$$_1$$ and t$$_2$$ are the values of the time taken by it to hit the target in two possible ways, the product t$$_1$$t$$_2$$ is:

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s$$^{-1}$$ with respect to the man. The speed of the man with respect to the surface is:

A person of mass M is sitting on a swing of length L and swinging with an angular amplitude $$\theta_0$$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $$l$$ ($$l << L$$), is close to:

A uniform rod of length $$l$$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\frac{\sigma_0}{r}$$, then the radius of gyration of the disc about its axis passing through the center is

At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m. The value of M is close to:
(Coefficient of linear expansion of brass are $$10^{-5}$$/°C and Young's modulus of brass is $$10^{11}$$ N/m$$^2$$, respectively; g = 10 m s$$^{-2}$$)

When M$$_1$$ gram of ice at -10°C (specific heat = 0.5 cal g$$^{-1}$$ °C$$^{-1}$$) is added to M$$_2$$ gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g$$^{-1}$$ is:

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is: