31.

The I- V characteristics of a metal wire at two different temperatures (T₁ and T₂) are given in the adjoining figure. Here, we can conclude that

          

• T₁ > T₂

• T₁ < T₂

• T₁ = T₂

• T₁ = 2T₂

A Wheatstone bridge has the resistances 10 Ω, 10 Ω, 10 Ω and 30 Ω in its four arms. What resistance joined in parallel to the 30 Ω resistance will bring it to the balanced condition ? 

• 2 Ω

• 5 Ω

• 10 Ω

• 15 Ω

A magnetic needle is placed in a uniform magnetic field and is aligned with the field. The needle is now rotated by an angle of 60° and the work done is W. The torque on the magnetic needle at this position is

• $2\sqrt{3} \mathrm{W}$

• $\sqrt{3} \mathrm{W}$

• $\frac{\sqrt{3}}{2} \mathrm{W}$

• $\frac{\sqrt{3}}{4} \mathrm{W}$

In the adjoining figure, the potential difference between X and Y is 60 V. The potential difference between the points M and N will be

• 10 V

• 15 V

• 20 V

• 30 V

If the velocity of light in vacuum is 3 x 10⁸ ms^-1, the time taken (in nanosecond) to travel through a glass plate of thickness 10 cm and refractive index 1.5 is

• 0.5

• 1.0

• 2.0

• 3.0

The de-Broglie wavelength of an electron moving with a velocity c/2 (c = velocity of light in vacuum) is equal to the wavelength of a photon. The ratio of the kinetic energies of electron and photon is

• 1 : 4

• 1 : 2

• 1 : 1

• 2 : 1

The decimal number equivalent to a binary number 1011001 is

• 13

• 17

• 89

• 178

When a certain metal surface is illuminated with light of frequency v, the stopping potential for photoelectric current is V₀. When the same surface is illuminated by light of frequency $\frac{\mathrm{v}}{2}$,the stopping potential is $\frac{{\mathrm{V}}_0}{4}$. The threshold frequency for photoelectric, emission is

• $\frac{\mathrm{v}}{6}$

• $\frac{\mathrm{v}}{3}$

• $\frac{2\mathrm{v}}{3}$

• $\frac{4\mathrm{v}}{3}$

An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image. If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror is

• 15 cm

• 20 cm

• 25 cm

• 30 cm

Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0, they have the same number of nuclei. The ratio of number of nuclei of A to that of B will be (1/e)² after a time interval of

• $\frac{1}{\mathrm{\lambda }}$

• $\frac{1}{2\mathrm{\lambda }}$

• $\frac{1}{3\mathrm{\lambda }}$

• $\frac{1}{4\mathrm{\lambda }}$