Which one of the following is the natural nanomaterial ?
a.
Grain of sand
b.
Peacock feather
Correct Answer
c.
Skin of the whale
d.
Peacock beak
Step-by-Step AI Explanation
Verified Method
Peacock feather is a classic example of a natural nanomaterial. Its vibrant colors are not due to pigments but due to periodic nanostructures that cause interference of light. A grain of sand is typically macroscopic. Whale skin and beak are biological tissues not characterized primarily as nanomaterials.
Q2mcq
In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the voltage is changed to 224 kV, then the de-Broglie wavelength associated with the electrons would :
a.
decrease by 4 times
Correct Answer
b.
increase by 2 times
c.
increase by 4 times
d.
decrease by 2 times
Step-by-Step AI Explanation
Verified Method
The de-Broglie wavelength is given by $\lambda = \frac{h}{\sqrt{2meV}}$. Thus, $\lambda \propto \frac{1}{\sqrt{V}}$. If the voltage $V_1 = 14 \text{ kV}$ is changed to $V_2 = 224 \text{ kV}$, the ratio $\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{V_1}{V_2}} = \sqrt{\frac{14}{224}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$. Therefore, the wavelength decreases by 4 times.
Q3mcq
The variation of frequency of carrier wave with respect to the instantaneous amplitude of the modulating signal is called :
a.
Phase modulation
b.
Amplitude modulation
c.
Pulse width modulation
d.
Frequency modulation
Correct Answer
Step-by-Step AI Explanation
Verified Method
Frequency modulation (FM) is defined as the process where the frequency of the carrier wave is varied in accordance with the instantaneous amplitude of the modulating signal. Amplitude modulation varies amplitude, and phase modulation varies the phase.
Q4mcq
Q factor is equal to __________.
a.
$\frac{1}{R}\sqrt{\frac{L}{C}}$
b.
$\frac{1}{R}\sqrt{\frac{L}{C}}$
c.
$\frac{X_L}{R}$
d.
All the above
Correct Answer
Step-by-Step AI Explanation
Verified Method
The Q factor for a series RLC circuit is defined as $Q = \frac{1}{R}\sqrt{\frac{L}{C}}$. At resonance, $X_L = X_C$, and $Q$ can also be expressed as $\frac{X_L}{R}$ or $\frac{X_C}{R}$. Since the options represent equivalent mathematical forms for this circuit, 'All the above' is correct.
Q5mcq
Two metallic spheres of radii 1 cm and 3 cm are given charges of $-1 \times 10^{-2}$ C and $5 \times 10^{-2}$ C respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is :
a.
$1 \times 10^{-2}$ C
b.
$3 \times 10^{-2}$ C
Correct Answer
c.
$2 \times 10^{-2}$ C
d.
$4 \times 10^{-2}$ C
Step-by-Step AI Explanation
Verified Method
When two spheres are connected, charge flows until both are at the same potential $V = \frac{kQ_1}{r_1} = \frac{kQ_2}{r_2}$. Thus, $\frac{Q_1'}{r_1} = \frac{Q_2'}{r_2}$. Given $r_1 = 1, r_2 = 3$, $Q_2' = 3Q_1'$. Total charge $Q_{total} = -1 + 5 = 4 \times 10^{-2} \text{ C}$. Substituting $Q_2' = 3Q_1'$, we get $Q_1' + 3Q_1' = 4 \times 10^{-2}$, so $Q_1' = 1 \times 10^{-2}$ and $Q_2' = 3 \times 10^{-2} \text{ C}$.
Q6mcq
Which of the following is an electromagnetic wave ?
a.
$\beta$-rays
b.
$\gamma$-rays
Correct Answer
c.
$\alpha$-rays
d.
All of the above
Step-by-Step AI Explanation
Verified Method
\gamma-rays are electromagnetic waves. $\alpha$-rays are helium nuclei and $\beta$-rays are high-speed electrons (particles), therefore they are not electromagnetic waves.
Q7mcq
An air bubble in glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is :
a.
12 cm
Correct Answer
b.
8 cm
c.
16 cm
d.
10 cm
Step-by-Step AI Explanation
Verified Method
Real depth $d = \mu \times \text{apparent depth}$. Let the actual depths be $d_1$ and $d_2$. $d_1 = 1.5 \times 5 = 7.5 \text{ cm}$. $d_2 = 1.5 \times 3 = 4.5 \text{ cm}$. Total thickness $t = d_1 + d_2 = 7.5 + 4.5 = 12 \text{ cm}$.
Q8mcq
In India electricity is supplied for domestic use at 220 V. It is supplied at 110 V in USA. If the resistance of a 60 W bulb for use in India is R, the resistance of a 60 W bulb for use in USA will be :
a.
R/4
Correct Answer
b.
R
c.
R/2
d.
2R
Step-by-Step AI Explanation
Verified Method
Power $P = \frac{V^2}{R}$, so $R = \frac{V^2}{P}$. For a given power rating, $R \propto V^2$. If the voltage is halved ($220 \to 110$), the resistance must decrease by a factor of $2^2 = 4$. Thus, the new resistance is $R/4$.
Q9mcq
A wire of length $l$ carrying a current $I$ along the Y direction is kept in a magnetic field given by $\vec{B} = \beta(i + j + k)$. The magnitude of Lorentz force acting on the wire is :
a.
$\sqrt{2} Il\beta$
Correct Answer
b.
$\frac{I}{3}l\beta$
c.
$\frac{1}{2}Il\beta$
d.
$\frac{1}{3}Il\beta$
Step-by-Step AI Explanation
Verified Method
The Lorentz force is given by $\vec{F} = I(\vec{l} \times \vec{B})$. Here, $\vec{l} = l\hat{j}$ and $\vec{B} = \beta(\hat{i} + \hat{j} + \hat{k})$. The cross product is $\vec{l} \times \vec{B} = l\hat{j} \times \beta(\hat{i} + \hat{j} + \hat{k}) = l\beta(-\hat{k} + \hat{i})$. The magnitude $|\vec{F}| = I |l\beta(-\hat{k} + \hat{i})| = I l \beta \sqrt{(-1)^2 + 1^2} = \sqrt{2}Il\beta$.
Q10mcq
Emission of electrons by the absorption of heat energy is called __________ emission.
a.
Thermionic
Correct Answer
b.
Photo electric
c.
Secondary
d.
Field
Step-by-Step AI Explanation
Verified Method
Thermionic emission is the process where electrons are emitted from the surface of a metal when it is heated to a high temperature, providing sufficient thermal energy for the electrons to overcome the work function. Photoelectric involves light, secondary involves impact of other particles, and field involves high electric fields.
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The electric potential of an electron is given by $V = V_0 \ln(\frac{r}{r_0})$, where $r_0$ is a constant. If Bohr atom model is valid, then variation of radius of $n^{th}$ orbit $r_n$ with the principal quantum number $n$ is :
a.
$r_n \propto \frac{1}{n^2}$
b.
$r_n \propto \frac{1}{n}$
c.
$r_n \propto n^2$
d.
$r_n \propto n$
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Find the:
(i) Angular momentum
(ii) Velocity of the electron revolving in the 5th orbit of hydrogen atom.
($h=6.6 \times 10^{-34}$ Js ; $m=9.1 \times 10^{-31}$ kg)
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Find the impedance of a series RLC circuit, if the inductive reactance, capacitive reactance and resistance are 184 $\Omega$, 144 $\Omega$ and 30 $\Omega$ respectively. Also calculate the phase angle between voltage and current.
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(a) Derive an expression for electrostatic potential due to an electric dipole. OR (b) Obtain the equation for bandwidth in Young’s Double Slit Experiment.
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(a) Using Biot-Savart Law deduce the relation for the magnetic field at a point due to an infinitely long straight conductor carrying current. OR (b) Discuss the spectral series of hydrogen atom.
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(a)(i) How do we obtain characteristic X-ray spectra ? (ii) Calculate the cut-off wavelength and cut-off frequency of X-rays from an X-ray tube of accelerating potential 20,000 V. OR (b) What is spectrum ? Explain the types of emission spectrum.
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