List of top Questions asked in GATE BM

In a measurement process, groups A and B recorded 10 and 15 values, respectively. The arithmetic means and standard deviations of group A are \(\mu_A = 35\), \(\sigma_A = 0.4\) and group B are \(\mu_B = 38\), \(\sigma_B = 0.6\). The standard deviation for the combined set of group A and group B measurements is \(\underline{\hspace{2cm}}\). (rounded off to two decimal places)

A pacemaker was implanted in a cardiac patient. It has a battery of 2.4 A·h (Ampere·hour). It is designed to deliver a rectangular pulse of amplitude 1.5 V for 1 ms ON time for every one second. The electrode-heart resistance is 150 Ω. Assuming the current drained from the battery is negligible, the lifetime of the pacemaker is \(\underline{\hspace{1cm}}\) years (rounded off to the nearest integer).

An inexperienced clinician was measuring the cardiac output of a healthy human by thermodilution technique. A 2.0 mL of cold saline solution of volume \( V_i \) at \( 7^\circ C \) was injected at the entrance of the right atrium. The change in blood temperature \( \int_0^{t_1} \Delta T_b \, dt \) at the pulmonary artery was measured to be \(-20\) Kelvin-second. The cardiac output \( F \) was calculated using the following formula \[ F = \frac{Q}{\rho_b c_b \int_0^{t_1} \Delta T_b \, dt}, \] where \( Q \) is the heat content of injectate in Joules, given by \( V_i \Delta T_i \rho_i c_i \) and \( \Delta T_i \) is the temperature difference between the injectate and blood. It was assumed that the density of blood (\( \rho_b \) in kg/m\(^3\)) and the specific heat capacity of blood (\( c_b \) in J/(kg.K)) were respectively equal to that of the injectate \( \rho_i \) and \( c_i \).
The clinician realized that there was an error in the measurement of \( F \). Which of the following is TRUE?

Which of the following statements about smooth muscles are TRUE?

Consider a unity feedback system with closed-loop transfer function \[ C(s) = \frac{s + 90}{s^2 + 10s + 90} \] The steady-state error with respect to a unit ramp input is \(\underline{\hspace{2cm}}\). (rounded off to one decimal place)

The diameter of a renal artery lumen in humans is 5 mm. If the mean velocity of the blood flowing in the renal artery is 40 cm/s, the density of blood (ρ) is 1060 kg/m³, and the viscosity of blood (μ) is 3 cP, the Reynolds number for the blood flowing in the renal artery is \(\underline{\hspace{2cm}}\). (rounded off to the nearest integer)

A longitudinal pressure wave travelling inside a muscle tissue is incident at an angle of 60° at the interface between the muscle and kidney. Let the wave impedance be \( Z_{\text{muscle}} = 1.70 \times 10^5 \, \text{g cm}^{-2} \, \text{s}^{-1} \), \( Z_{\text{kidney}} = 1.62 \times 10^5 \, \text{g cm}^{-2} \, \text{s}^{-1} \) and wave velocities in muscle and kidney tissues be 1590 and 1560 m/s respectively. The transducer centre frequency is 1.5 MHz. The pressure wave propagation angle in the kidney tissue and intensity transmission coefficient at the tissue interface are \(\underline{\hspace{2cm}}\) degrees (rounded off to the nearest integer) and \(\underline{\hspace{2cm}}\) (rounded off to two decimal places), respectively.

In comparison to ECG amplifiers, the surface-EMG amplifiers have

An RF pulse is applied to acquire an axial MR image at the isocenter of a 1.5T MRI scanner with slice thickness of 2.5 mm. Assuming a gradient field strength of 2 Gauss/cm is applied and Gyromagnetic ratio of protons is 42.58 MHz/T, the RF pulse bandwidth required for slice selection is \(\underline{\hspace{2cm}}\) kHz.

The closed-loop characteristic equation of a system is given by \[ s^4 + 2s^3 + 8s^2 + 8s + 16 = 0 \] The frequency of oscillations of this closed-loop system at steady state is \(\underline{\hspace{2cm}}\) rad/s.

An analog signal is sampled at 100 MHz to generate 1024 samples. Only these samples are used to evaluate 1024-point FFT. The separation between adjacent frequency points (\( \Delta F \)) in FFT is \(\underline{\hspace{2cm}}\) kHz.

The Trace and Determinant of a 2 × 2 nonsingular matrix A are 12 and 32, respectively. The eigen values of \(A^{-1}\) are \(\underline{\hspace{2cm}}\) and \(\underline{\hspace{2cm}}\)

Consider the following first-order partial differential equation, also known as the transport equation \[ \frac{\partial y(x,t)}{\partial t} + 5 \frac{\partial y(x,t)}{\partial x} = 0 \] with initial conditions given by \( y(x, 0) = \sin x, -\infty < x < \infty \). The value of \( y(x,t) \) at \( x = \pi \) and \( t = \frac{\pi}{6} \) is

The minimum value, \(f_{\text{min}}\), of the function given below is: \[ f(x_1, x_2, x_3) = \frac{1}{2} (x_1^2 + x_2^2 + x_3^2) - 2(x_1 + x_2 + x_3) \] (round off to the nearest integer).

If we consider blood as a suspension of RBCs in a Newtonian fluid, the shear forces experienced by the RBCs during blood flow would

As shown in the figure, the water contact angles of surfaces A and B are $\theta_A$ and $\theta_B$, respectively. Based on the figure, which of the following statements given below is TRUE?
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Which of the following is a bone resorbing cell?

Which of the following is a cranial bone in the human body?

Which of the following glands produces the thyroid stimulating hormone (TSH)?