List of practice Questions

For the following circuit, the collector voltage with respect to ground will be .............. V. (Emitter diode voltage is 0.7 V and $\beta_{DC}$ of the transistor is large.) (Specify your answer in volts up to one digit after the decimal point.) 

For the given circuit, the value of base current $I_b$ of the npn transistor is ........... mA. ($\beta$ is the current gain and assume the Op-Amp as ideal.) (Specify your answer in mA up to two digits after decimal.) 

A monoatomic ideal gas undergoes a closed cycle shown in the P–V diagram. The ratio $\frac{P_2}{P_1}$ is ........... (Specify your answer up to two digits after the decimal point.)

Using the sublimation relation $\log_{10}(P)=\frac{C_1}{T}+C_2$ for zinc, with $C_1=6790$ K, $C_2=9$, compute the latent heat of sublimation using the Clausius–Clapeyron equation. (Specify answer in kJ/mol up to one digit after decimal.)
 

A system of 8 non-interacting electrons is confined by a 3-dimensional potential $V(r)=\frac{1}{2}m\omega^2 r^2$. The ground state energy of the system in units of $\hbar\omega$ is ............ (Specify your answer as an integer.)

A body of mass 1 kg moves in an elliptical orbit with semi-major axis 1000 m and semi-minor axis 100 m. The orbital angular momentum is 100 kg m$^2$ s$^{-1}$. The time period of motion is ............. hours. (Specify answer up to two digits after the decimal point.)
 

A syringe is used to exert 1.5 atmospheric pressure to release water horizontally. The speed of water immediately after ejection is ............ m s$^{-1}$. (Take 1 atmospheric pressure = $10^5$ Pa, density of water = $10^3$ kg m$^{-3}$.) (Specify your answer in m s$^{-1}$ as an integer.) 
 

A syringe is used to exert 1.5 atmospheric pressure to release water horizontally. The speed of water immediately after ejection is .............. m s$^{-1}$. (Take 1 atmospheric pressure = $10^5$ Pa, density of water = $10^3$ kg m$^{-3}$.) (Specify your answer in m s$^{-1}$ as an integer.)
 

A particle of mass $m$ moves in a circular orbit with $x = R\cos(\omega t)$ and $y = R\sin(\omega t)$ observed in inertial frame $S_1$. Another frame $S_2$ moves with velocity $\vec{v} = \omega R \hat{i}$ with respect to $S_1$, and origins coincide at $t=0$. The angular momentum at $t = \frac{2\pi}{\omega}$ as observed in $S_2$ about its origin is $(mR^2\omega)x$. Then $x$ is ............. (Specify answer up to two digits after decimal.)

Rod $R_1$ has rest length 1 m and rod $R_2$ has rest length 2 m. $R_1$ and $R_2$ move with velocities $+v\hat{i}$ and $-v\hat{i}$ respectively relative to the lab. If $R_2$ has a length of 1 m in the rest frame of $R_1$, $\frac{v}{c}$ is ................... (Specify answer up to two digits after decimal.)

In the following circuit, $RC$ is much larger than the input period. Assume diode is ideal and $R$ is large. The dc output voltage across $R$ will be .............. V. (Specify answer up to one digit after the decimal point.) 

For a metal, electron density is $6.4\times10^{28}\ \mathrm{m}^{-3}$. The Fermi energy is ................. eV. (Specify answer up to one digit after the decimal point.)
 

The moon moves around the earth in a circular orbit with a period of 27 days. If $R = 6.4 \times 10^6$ m is Earth's radius and $g = 9.8$ m/s$^2$, and if $D$ is the moon's orbital radius, find $D/R$. (Specify answer up to one digit after decimal point.)
Two events occur in frame $S$ at $(t_1 = 0,\ r_1 = 0)$ and $(t_2 = 0,\ x_2 = 10^8\mathrm{m}, y_2 = 0, z_2 = 0)$. Another frame $S'$ moves with $v = 0.8c$ relative to $S$. The time difference $(t_2' - t_1')$ in $S'$ is ................... s. (Specify answer up to two digits after decimal.)
The lattice constant of NaCl crystal is $0.563$ nm. X-rays of wavelength $0.141$ nm are diffracted by this crystal. The angle at which the first order maximum occurs is .......... degrees. (Specify answer up to two digits after decimal.)
In a pn junction, dopant concentration on p-side is higher than n-side. Which statements are correct when the junction is unbiased?
Which of the combinations of crystal structure and coordination number is correct?
The coefficient of $x^3$ in the Taylor expansion of $\sin(\sin x)$ around $x = 0$ is .............. (Specify your answer up to two digits after the decimal point.)
Let $f(x)=3x^6 - 2x^2 - 8$. Which of the following statements is (are) true?
Two beams of visible light (400–700 nm) interfere at a point. The optical path difference is 5000 nm. Which wavelength interferes constructively?
Which of the following relations is (are) true for thermodynamic variables?
The Boolean expression $(AB)(\bar{A}+B)(A+\bar{B})$ can be simplified to
Consider the transformation to a new set of coordinates $(\xi,\eta)$ from rectangular coordinates $(x,y)$, where $\xi=2x+3y$ and $\eta=3x-2y$. In the $(\xi,\eta)$ coordinate system, the area element $dx\,dy$ is
A raindrop falls under gravity and captures water molecules from the atmosphere. Its mass changes at the rate $\lambda m(t)$, where $\lambda$ is a positive constant and $m(t)$ is the instantaneous mass. Assume gravity is constant and captured water is at rest before capture. Which of the following statements is correct?
Consider two waves $y_1=a\cos(\omega t-kz)$ and $y_2=a\cos[(\omega+\Delta \omega)t-(k+\Delta k)z]$. The group velocity of the superposed wave will be ($\Delta \omega \ll \omega$ and $\Delta k \ll k$)