51.

A luminous object is separated from a screen by distance d. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

• 4d

• 2d

• $\frac{\mathrm{d}}{2}$

• $\frac{\mathrm{d}}{4}$

In the bandgap between valence band and conduction band in a material is 5.0 eV, then the material is

• semiconductor

• good conductor

• superconductor

• insulator

Two coherent monochromatic beams of intensities I and 41 respectively are superposed. The maximum and minimum intensities in the resulting pattern are

• 5I and 3I

• 9I and 3I

• 4I and I

• 9I and I

In a transistor output characteristics commonly used in common emitter configuration, the base current I_B, the collector current l_C and the collector emitter voltage V_CE have values of the following orders of magnitude in the active region

• I_B and I_C both are in µA and V_CE in volt

• I_B is in µA and I_C is in mA and V_CE in volt

• I_B is in mA and I_C is in µA and V_CE in volt

• I_B is in mA and I_C is in mA and V_CE in mV

For the radioactive nuclei that undergo either α or β decay, which one of the following cannot occur ?

• Isobar of original nucleus is produced

• Isotope of the original nucleus is produced

• Nuclei with higher atomic number than that of the original nucleus is produced

• Nuclei with lower atomic number than that of the original nucleus is produced

The intermediate image formed by the objective of a compound microscope is

• real, inverted and magnified

• real, erect and magnified

• virtual, erect and magnified

• virtual, inverted and magnified

The de-Broglie wavelength of an electron is the same as that of a 50 keV X-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass is 0.5 MeV)

• 1 : 50

• 1 : 20

• 20 : 1

• 50 : 1

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is µ − m Δµ. Here, µ and Δµ denote the RI of 0th layer and the difference in RI between any two consecutive layers, respectively. The integer m =0, 1, 2, 3, ... denotes the numbers of the successive layers. A ray of light from the 0th layer enters the 1st layer at an angle of incidence of 30°. After undergoing the mth refraction, the ray emerges parallel to the interface. If µ = 1.5 and Δµ = 0.015, the value of m is

• 20

• 30

• 40

• 50

An object is placed 30 cm away from a convex lens of focal length 10 cm and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by 45 cm to get a sharp image again. The magnitude of focal length of the concave lens is (in cm)

• 72

• 60

• 36

• 20

Find the correct statement(s) about photoelectric effect.

• There is no significant time delay between the absorption of a suitable radiation and the emission of electrons.

• Einstein analysis gives a threshold frequency above which no electron can be emitted

• The maximum kinetic energy of the emitted photoelectrons is proportional to the frequency of incident radiation.

• The maximum kinetic energy of electrons does not depend on the intensity of radiation.