51.

Two slits are separated by a distance of 0.5 mm and illuminated with light of wavelength λ = 6000 A^o. If the screen is placed at 2.5 m from the slits. The distance of the third bright fringe from the centre will be

• 1.5 mm

• 3 mm

• 6 mm

• 9 mm

Light of two different frequencies whose photons
have energies 1 eV and 2.5 eV respectively, successively illuminate a metallic surface whose work function is 0.5 eV. Ratio of maximum speeds of emitted electrons will be

• 1 : 4

• 1 : 1

• 1 : 5

• 1 : 2

In the circuit shown in figure, when the input voltage of the base resistance is 10 V, Vb, is zero and V_ce is also zero. Value of β is

• 133

• 154

• 196

• 105

Two radioactive materials X₁ and X₂ have decay constants 6 and 3A respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be $\frac{1}{\mathrm{e}}$  after a time

• $\frac{1}{6 \mathrm{\lambda }}$

• $\frac{1}{3 \mathrm{\lambda }}$

• $\frac{3}{6 \mathrm{\lambda }}$

• $\frac{6}{9 \mathrm{\lambda }}$

A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is

• $\frac{11}{12}$

• $\frac{2}{11}$

• $\frac{48}{121}$

• $\frac{48}{169}$

Assertion: Thermonuclear fusion reactions may become the source of unlimited power for the mankind.

Reason: A single fusion event involving isotopes of hydrogen produces more energy from nuclear fission of  ${}_{93}{}^{235}\mathrm{U}$

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  A ray of light is incident from outside on a glass sphere surrounded by air. This ray may suffer total internal reflection at second interface.

Reason:  If a ray of light goes from denser to rarer medium, it bends away from the normal.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  As work function of a material increases by some mechanism, it requires greater energy to excite the electrons from its surface.

Reason:  A plot of stopping potential (V_s) versus frequency (v) for different metals, has greater slope for metals with greater work functions.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion: An n-type semiconductor has a large number of electrons but still it is electrically neutral.

Reason: An n-type semiconductor is obtained by doping an intrinsic semiconductor with a pentavalent impurity.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  Two point coherent sources of light S₁ and S₂ are placed on a line as shown. P and Q are two points on that line. If at point P maximum intensity is observed then maximum intensity should also be observed at Q.

Reason:  In the figure of assertion the distance $\left|{\mathrm{S}}_1\mathrm{P} - {\mathrm{S}}_2\mathrm{P} \right|$ is equal to distance $\left| {\mathrm{S}}_2\mathrm{Q} - {\mathrm{S}}_1\mathrm{Q} \right|$.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.