List of top Questions asked in GATE BM

Choose one of the following options that correctly fills the blanks labelled as I and II in the paragraph below.

Lower critical solution temperature (LCST) polymers exhibit a decrease in their water solubility with an increase in temperature. This happens because, at low temperatures, the hydrogen bonding between the I segments of polymer chain and the water molecules dominates. At high temperatures, the interactions between the II segments dominate.
The output \(y[n]\) of a digital moving average filter for an input \(x[n]\) is given by
\[ y[n] = \frac{1}{4}\big(x[n] + 2x[n-1] + x[n-2]\big) \]
Which one of the following options is a correct statement about the transfer function of this filter?
A uniform shear force of magnitude 0.01 Newton (N) is applied to the top surface of a cubical tissue sample with side of length 1 cm (marked with dashed lines in the figure below). In the deformed configuration (marked with solid lines), the angle \(\theta = 5\) degrees.
The shear modulus of the tissue is kilopascals (kPa).
Assume the tissue to be a linear, isotropic and homogenous elastic solid.
The Newton-Raphson method is used to find the roots of the equation \(x = e^{-2x}\). If the initial guess \(x_0 = 0\), the estimate of the root after the first iteration, \(x_1 =\)
The vital capacity, tidal volume, and inspiratory reserve volume of the lungs of a healthy individual are 4600 milliliters (mL), 500 mL, and 2500 mL, respectively. The expiratory reserve volume of the lungs of this individual is mL. (Round off to the nearest integer).
A drug is loaded in a polymeric device through a process. Which one of the following ratios defines the drug encapsulation efficiency of this process?
Which one of the following complement system pathways is most likely to be activated on biomaterials implanted in a healthy human?
An MRI signal acquired from a tissue has a transverse relaxation time (\(T_2\)) of 100 milliseconds (ms). If the signal intensity at time \(t = 0\) ms is 500 a.u., the signal intensity at \(t = 50\) ms is a.u. (Round off to one decimal place).
Which one of the following epithelial cell types is primarily located in the tracheal mucosa of a healthy adult human?
The \(I-V\) characteristics of a diode with a knee voltage \(V_{knee} = 0.8\) volts is shown in Figure 1.

This diode is used in the circuit shown in Figure 2, in which an input signal of \(V_{in} = 100\sin(1000t)\) volts is applied. What is the voltage \(V_{out}\) (in volts) across the capacitor at steady state?

Assume that the capacitor is initially discharged and the reverse breakdown voltage of the diode is much greater than 100 volts.
Which one of the following options is the Thevenin voltage (in volts) across the resistor \(R_{Load}\) in the circuit given below?
In humans, the pyloric sphincter is located between .
The shell of a hollow spherical nanoparticle has a uniform thickness of 3 nanometers (nm). The outer radius of the nanoparticle is 5 nm. The ratio of the volume of the shell to the volume of the hollow core is (Round off to one decimal place).
A standard n-type MOSFET, biased in the saturation region, has the following parasitic capacitances:
1. \(C_{GS}\): gate to source capacitance
2. \(C_{GD}\): gate to drain capacitance
3. \(C_{DS}\): drain to source capacitance
Which one of the following options is correct?
\(x[n]\) is a real and odd signal. Which one of the following statements is true about its Discrete Time Fourier Transform (DTFT) \(X(e^{j\omega})\)?
A control system shown in the figure below has a forward gain \(G = 100\). An input \(V_{in} = 5\) volts is supplied to the system. What is the absolute error between the output \(V_{out}\) and input \(V_{in}\) in volts?
The three curves shown in the figure represent the trends in Stress-Strain relationship in Bone, Glass and Steel. Which one of the following options correctly matches the curve labels (\(P\), \(Q\), and \(R\)) with these three materials?
The circuit given below is initially in steady-state with the switch S open. Immediately after the switch S is closed, the voltage \(V_A\) is ________ volts.
Which one of the following options represents the correct order of the speed of ultrasound wave propagation in bone, air, and soft tissue?
An invertible \(n \times n\) matrix \(P\) satisfies \(P^3 = I\), where \(I\) is the identity matrix of size \(n\). Which one of the following options is true?
Which one of the following cell types is the most abundant in healthy adult human blood?
Consider an incompressible cylindrical tissue with a diameter of 2 cm and a height of 3 cm. If this tissue is stretched by 10% in the axial direction, its diameter in the stretched configuration is cm.
Assume homogeneous deformation of the tissue.
A biased coin has a probability of heads equal to \(1/3\) and a probability of tails equal to \(2/3\). A binary random variable \(X\) assumes a value \(1\) for heads and \(-1\) for tails. The variance of \(X\) is
The eigenvalues of the matrix \( P = \begin{pmatrix} 1 & -2 \\ 3 & -4 \end{pmatrix} \) are
Let \(f\) be a function of real variables \(x\) and \(y\), defined as:
\[ f(x,y) = x^2y + 3y^2x \]
The value of \( \frac{\partial^2 f}{\partial x^2} \) at \(x=1, y=1\) is