List of top Questions asked in GATE BM

Which one of the following statements is TRUE?

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 $\text{ is}$ _________.

The time delay between the peaks of the voltage signals $ v_1(t) = 2\cos(6t + 60^\circ) $ and $ v_2(t) = -3\sin(6t) $ is ____ s.

Solution of the differential equation \[ \frac{dy}{dx} - y = \cos x \] is

An input $x(t)$ is applied to a system with a frequency transfer function given by $H(j\omega)$ as shown. The magnitude and phase response are shown. If $y(t_d)=0$ for $x(t)=u(t)$, the time $t_d (>0)$ is _________ µs.

The block diagram of a two-tap high-pass FIR filter is shown below. The filter transfer function is given by $ H(z) = \frac{Y(z)}{X(z)} $.
If ratio of the maximum to minimum value of $ H(z) $ is 2 and $ |H(z)|_{\max} = 1 $, the coefficients $ \beta_0 $ and $ \beta_1 $ are _________ and _________, respectively.

The block diagrams of an ideal system and a real system with their impulse responses are shown below. An auxiliary path is added to the delayed impulse response in the real system. For a unit impulse input ($x(t)=\delta(t)$) to both systems, gain $\beta$ is chosen such that $y(4T)$ is the same for both systems. The value of $\beta$ is _________.

Which of the following statements related to biomedical measurements are TRUE?

Which of the following mechanical prosthetic valves were invented as a replacement for diseased heart valves?

Due to the current COVID pandemic conditions, assume that positive or negative status of any individual are equally likely. There are 3 members in a family. If one of the members has tested COVID positive, the conditional probability that at least 2 members are COVID positive is ______ (rounded off to three decimal places).

A series RLC circuit with $R=10\,\Omega$, $L=50\text{ mH}$, $C=100\ \mu\text{F}$ connected to $200\ \text{V}$, $50\ \text{Hz}$ supply consumes power $P$. The value of $L$ is changed such that the circuit consumes the same power but operates with lagging power factor. The new value of $L$ is _____ mH (rounded off to two decimal places).

The thickness of piezoelectric crystal (PZT5A) used in ultrasound applications will determine the resonant frequency of the transducer. To work at a resonance frequency of 5 MHz, the thickness of a PZT5A transducer must be ________ mm (rounded off to three decimal places).

Power consumed by the $3\,\Omega$ resistor is $12\ \text{W}$ in the given circuit. The value of the resistor $R$ in the circuit is _______ $\Omega$.

In the complex z-domain, the value of the integral \[ \oint_{C} \frac{z^{3} - 9}{3z - i} \, dz \] is

Skeletal muscles are recruited to lift loads. If the force generated in the muscle due to contraction is not sufficient to lift the load, it is known as _________ contraction.

Backscattered electron detector of a scanning electron microscope is used to

In MRI, the terms T1 and T2 time constants are crucial for obtaining suitable weighted images. Choose the correct explanation.

Given $x$ is real, identify all the even-functions among the following:

An ideal coronary stent should

Which of the following statements related to the safety of biomedical instruments are TRUE?

Which of the following statements related to the operating principle of pulse oximetry are CORRECT?

In the circuit diagram shown below, the logic gates operate with a supply voltage of 1 V. NAND and XNOR have 200 ps and 400 ps input-to-output delay, respectively.
At time $ t = T $, $ A(t) = 0 $, $ B(t) = 1 $ and $ Z(t) = 0 $. When the inputs are changed to $ A(t) = 1 $, $ B(t) = 0 $ at $ t = 2T $, a 1 V pulse is observed at $ Z $. The pulse width of the 1 V pulse is _________ ps.

Input bits X and Y are added by using the combinational logic as shown below. S represents the sum of the two bits. For a correct implementation of the sum, the signals $D_0, D_1, D_2, D_3$ are _________, respectively.

For the balanced Owen-bridge circuit shown in the figure, the values of $L_x$ and $R_x$ are:

Myopia occurs when the focal point falls _________ the retina. This can be corrected using a _________ lens.