List of practice Questions

The magnitude of the current gain $\frac{I_{\text{load}}}{I_{\text{in}}}$ in the circuit below is ______ (rounded off to two decimal places).

The linear temperature coefficient of the material of a wire is $x \times 10^{-4} \, \text{°C}^{-1}$. The resistance of this wire increased from 50 $\Omega$ at 25 °C to 60 $\Omega$ at 75 °C. The value of $x$ is ________ (rounded off to two decimal places).

A series RLC circuit is connected to 220 V, 50 Hz supply. For a fixed value of R and C, the inductor $L$ is varied to deliver the maximum current. This value is 0.4 A and the corresponding potential drop across the capacitor is 330 V. The value of the inductor $L$ is ______ H (rounded off to two decimal places).

In the circuit diagram shown below, the MOSFET is biased in the saturation region. The MOSFET has a threshold voltage $V_{th} = 0.5 \, V$, width $W = 100 \, \mu m$, length $L = 0.1 \, \mu m$, and $\mu_n C_{ox} = 100 \, \mu A.V^{-2}$. Assuming $v_i = 1 \, mV$ as a small-signal input to MOSFET, the magnitude of the output voltage $V_o$ is ______ mV (accurate to two decimal places). Ignore channel-length modulation for the MOSFET.}

The deltoid muscle connects the humerus to the shoulder blade and facilitates outstretching of the arm as shown in the figure. Assume the equivalent weight (W) of the arm to be 30 N and acts vertically down at a horizontal distance of 30 cm. Assume that the deltoid muscle is connected to the humerus at a distance of 15 cm and makes an average angle of $20^\circ$ with the horizontal. The magnitude of tension in the deltoid muscle is _________ N.

For blood flow through arteries, which one of the following relations approximates the pulse wave propagation speed $ C $ as a function of the inner diameter $ D $ of the artery, wall thickness $ t $, modulus of elasticity $ E $, and fluid density $ \rho $?

A person has a total blood volume of 5 L. Out of this total, assume that 4 L is contained in the systemic circulation and 1 L in pulmonary circulation. The cardiac output of the person is 5 L.min$^{-1}$. Time taken for a drop of blood to go from right ventricle to left ventricle is _________ s.

Based on the stress-strain curves of three different materials (X, Y, and Z) shown in the figure, which one of the following choices is CORRECT?

Consider two radionuclides P and Q. Suppose the half-life of P ($ t_{1/2}^P $) is four times that of Q ($ t_{1/2}^Q $). At time $ t = 0 $, there are $ N_0 $ atoms of both radionuclides. When will the radioactivity of the two radionuclides be equal?

In a biological study, the experimental values measured from 6 subjects are given in the table below. Using this data, the linear regression coefficient for estimating the weight of the heart based on the systolic pressure is ________ (rounded off to two decimal places).

A filter is designed using opamps, resistors, and capacitors as shown below. Opamps are ideal with infinite gain and infinite bandwidth. If $ \frac{V_o(s)}{V_i(s)} $ is an all-pass transfer function, the value of resistor R2 is _________ kΩ.

If $g(t)=\dfrac{df(t)}{dt}$, and $F(s)=\dfrac{1+s}{s^{2}+12s+32}$ where $F(s)$ is the Laplace transform of $f(t)$, then the value of $g(t)$ at $t=0$ is _________.

Consider the Einthoven’s triangle of frontal ECG for the electrodes RA, LA, and LL. At the peak of the R-wave, the cardiac vector $M$ points vertically downward with $|M| = 5 \text{ mV}$. The voltages on leads I and II are _________ mV and _________ mV, respectively.

Which one of the following statements is TRUE?

The concentration $ S(x, t) $ of pollutants in a one-dimensional reservoir at position \$( x \text{ and time } t \text{ satisfies the diffusion equation}$

\[\frac{\partial s(x, t)}{\partial t} = D \frac{\partial^2 s(x, t)}{\partial x^2}\]

on the domain $ 0 \le x \le L $, where $ D $ is the diffusion coefficient of the pollutants. The initial condition $ S(x, 0) $ is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by $ \frac{\partial s(x, t)}{\partial x} = 0 $ at the boundary points $x = 0 \text{ and }$ $x = L \text{ at all times}$. Consider $D = 0.1 \ \text{m}^2/ \text{s}, S_0 = 5 \ \mu \text{mol/m}$, $\text{and} L = 10 \ \text{m}.$ The steady-state concentration} $\hat{s} \left( \frac{L}{2} \right) = s \left( \frac{L}{2}, \infty \right)$ at the center $x = \frac{L}{2} $$ \text{ of the reservoir is}$ _________ (in $\mu \text{mol/m}) $(in integer).

If the given matrices \[ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}, \quad I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] satisfy $ A^{2} = kA - 2I$, $\text{ the value of coefficient }$ k $\text{ is}$ _________.