NTA JEE Main 4th September 2020 Shift 1

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid-points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is $$I_0$$. If part ADE is removed, the moment of inertia of the remaining part about the same axis is $$\frac{NI_0}{16}$$ where N is an integer. Value of N is:

A circular disc of mass M and radius R is rotating about its axis with angular speed $$\omega_1$$. If another stationary disc having radius $$\frac{R}{2}$$ and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $$\omega_2$$. The energy lost in the process is p% of the initial energy. Value of p is

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to __________

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eye-piece lens (in cm) is __________

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is 305 $$\mathring{A}$$. The corresponding difference for the Paschan series in $$\mathring{A}$$ is __________

The region in the electromagnetic spectrum where the Balmer series lines appear is:

The elements with atomic numbers 101 and 104 belong to, respectively:

The ionic radii of $$O^{2-}$$, $$F^-$$, $$Na^+$$ and $$Mg^{2+}$$ are in the order:

The intermolecular potential energy for the molecules A, B, C and D given below suggests that:

For one mole of an ideal gas, which of these statements must be true?
(a) Internal energy (U) and enthalpy (H) each depends on temperature.
(b) Compressibility factor Z is not equal to 1
(c) $$C_{P,m} - C_{V,m} = R$$
(d) $$dU = C_v dT$$ for any process