List of top Questions asked in GATE BM- 2022

The _________ is too high for it to be considered _________.

A function \( y(x) \) is defined in the interval [0, 1] on the x-axis as
\[ y(x) = \begin{cases} 2 & \text{if } 0 \leq x<\frac{1}{3} \\ 3 & \text{if } \frac{1}{3} \leq x<\frac{3}{4} \\ 1 & \text{if } \frac{3}{4} \leq x \leq 1 \end{cases} \] Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

Let $r$ be a root of the equation $x^2 + 2x + 6 = 0$. Then the value of the expression $(r+2)(r+3)(r+4)(r+5)$ is

Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
\[ \boxed{A} \qquad \boxed{D} \] From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome? The player should use all the five plates exactly once. The plates can be rotated in their plane.

Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work culture. Which one of the following is the CORRECT logical inference based on the information in the above passage?

In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information provided in the above passage?

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball. First ball is drawn. What is the probability of getting an orange ball in the next draw?

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T, and U, but not necessarily in the same order. Consider the following statements:


The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.
What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

The inverse square law has a very practical use in radiography. While taking an acceptable chest radiograph of a subject at a distance of 0.75 m from the X-ray generator, X-ray source settings were kept at 50 kVp, 50 mAs. If the subject is moved to a distance of 1 m, and the kVp is kept the same, the new value of mAs to obtain the same exposure will be ________ mAs (rounded off to two decimal places).

An ideal opamp with an infinite gain and infinite bandwidth is connected in feedback as shown below. The output voltage \(V_o\) for the given input voltages in the circuit is ________ V (accurate to one decimal place).

Independent voltage measurements \((\mu \pm \sigma)\) of three sensors where \(\mu\) and \(\sigma\) are the mean and standard deviation of the measurements, respectively are as follows: \(v_1 = 4.52 \pm 0.02 \, \text{V}, \, v_2 = 4.21 \pm 0.20 \, \text{V}, \, v_3 = 3.96 \pm 0.15 \, \text{V}\). The measurement uncertainty in \(v_1 + v_2 + v_3\) is ________ V (rounded off to two decimal places).

A moving coil voltmeter has an internal resistance of 50 \(\Omega\). The scale of the meter is divided into 100 equal divisions. When a potential of 1 V is applied to terminals of the voltmeter, a deflection of 100 divisions is obtained. However, it is desired that when a potential of 500 V is applied to the terminals, a deflection of 100 divisions should be obtained. The value of resistance that needs to be connected in series to achieve this is ________ \(\Omega\).

A Hall effect flow meter is used to measure the volumetric flow through a blood vessel. The system calculated the flow rate to be 100 cm\(^3\cdot\text{s}^{-1}\). Later, calibration revealed that (i) the voltmeter was reading 40% higher than actual, and (ii) the caliper was measuring the vessel diameter 10% smaller than actual. Assuming a uniform flow profile and ignoring viscosity, the actual blood flow is _________ cm\(^3\cdot\text{s}^{-1}\) (rounded off to two decimal places).

A catheter based arterial blood pressure measurement device uses a flexible diaphragm mounted with four identical strain gauges in a Wheatstone bridge configuration as shown in the figure. Assume that the strain gauges have a nominal resistance value of \(R_G = 10\ \text{k}\Omega\), Gauge Factor \(G = 40\) and Young’s Modulus \(E = 10\ \text{MPa}\). Blood pressure variations result in small finite change in strain \(\varepsilon (\varepsilon>0)\). If \(V_o\) is the output voltage of the Wheatstone bridge and \(\sigma\) is the stress in MPa, the sensitivity \[ \frac{V_o}{\sigma} \] is ________ V.MPa\(^{-1}\).

A patient has a breathing rate of 18 breaths per minute, with a tidal volume of 500 mL, having an anatomical dead space of 150 mL. If the person has a heart rate of 120 beats per minute and a stroke volume of 50 mL, the alveolar ventilation to perfusion ratio is ________ (accurate to two decimal places).

Assume that the ratio of total blood volume in liters to total body weight in kg is 0.07 and the blood consists of plasma and RBCs only. The plasma volume of a 70-kg man with 52% hematocrit is _____ L (rounded off to two decimal places).

The 1stgeneration (1G) CT scanner uses a point X-ray source and a detector. The source-detector assembly can move linearly at a speed of 0.5 m.s\(^{-1}\) and it takes 0.5 s for source-detector assembly to rotate one angular increment, regardless of the angle. This scanner is expected to collect 360 projections over 180° of span. The field of view used for data collection has a diameter of 0.5 m. The scan time required is _____ s.

In the circuit diagram shown below, BJTs are biased with \(V_{EB} = 0.7\ V\). Neglect the base current for operating point calculations. Assume infinite input and output impedance for the BJTs. The output voltage \(V_o\) with small input voltage \(v_i = 10\ mV\) is ______ mV (rounded off to one decimal place). The thermal voltage \(V_T = 25\ mV\) at room temperature.

Using divergence theorem, evaluate the integral \(\iint_{S} \vec{F} \cdot \vec{n}\, dA\), where \(S\) is the surface of the cone \(x^{2}+y^{2} \le z^{2},\ 0 \le z \le 3\). If \(\vec{F} = 4x\hat{i} + 3z\hat{j} + 5y\hat{k}\) is a vector function with outer unit normal vector \(\vec{n}\), the value of the integral is ______ (rounded off to the nearest integer).

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.}