List of top Questions asked in GATE BM

The frequency of the oscillator circuit shown in the figure below is _______(in kHz, rounded off to two decimal places). 

Given: \( R = 1 \, k\Omega; R_1 = 2 \, k\Omega; R_2 = 6 \, k\Omega; C = 0.1 \, \mu F \)

Resistance \( R \) of a thermistor varies as a function of temperature \( T \) such that \[ R(T) = R_0 \exp \left[ \beta \left( \frac{1}{T} - \frac{1}{T_0} \right) \right] \] where \( \beta = 3100 \, {K} \), \( R_0 \) and \( T_0 \) are positive constants. If the relative error in measuring \( R \) is 10%, what is the relative error (in percentage) in measuring 310 K temperature? (rounded off to the nearest integer)

What is the output voltage \( V_{{out}} \) for the circuit shown below? 


 

At a given frequency, the storage modulus \( G' \) and loss modulus \( G'' \) of four biomaterials are shown in the table below. Which of the following option(s) is/are CORRECT?


 

A Newtonian fluid of viscosity \( \mu \) is undergoing laminar flow in a tube of radius \( R \). For a constant pressure drop per unit length along the tube, which of the following statement(s) is/are CORRECT?
Note: \( r \) represents the radial position; assume no slip condition at the boundaries.
Which of the following statement(s) is/are CORRECT about isotonic and isometric tests?
A discrete linear time invariant system has an impulse response function given by \[ h[n] = \delta[n] + \frac{1}{2}\delta[n - 1] + \frac{1}{3}\delta[n - 2]. \] For input signal \( x[n] = \delta[n] + \delta[n - 1] \), which of the following option(s) is/are CORRECT for the output signal \( y[n] \)?
Which of the following statement(s) is/are CORRECT about neuronal membrane and neuronal action potential?
Which of the following statement(s) about pulse oximetry is/are TRUE?
Two systems \( U \) and \( V \) are defined as shown below. Which of the following statement(s) is/are CORRECT? \[ x(t) \quad {System} \, U \quad y(t) = x(t)^2 + 1 \] \[ x(t) \quad {System} \, V \quad y(t) = x(t) + 1 \]
Which of the following statement(s) about ultrasound waves is/are true?
Which of the following is/are CORRECT about the value of \( y = \log_e(-e^x) \), where \( x \) is a real number.
Gelatin solutions P and Q of concentrations 3.5% and 0.5%, respectively, need to be mixed to obtain a 3% solution R. How much volume (in ml) of P needs to be mixed with 100 ml of Q to obtain R? (Choose the correct option)

In the circuit shown below, \( V_{{in}} = 10 \cos(1000t) \) volts. The magnitude of the input impedance of the circuit is _______k\(\Omega\). (rounded off to one decimal place)


 

Given a function \( y(x) \) satisfying the differential equation \[ y'' - 0.25y = 0, \] with initial conditions \( y(0) = 1 \); \( y'(0) = 1 \), what is the value of \( y(\log_e 100) \)? 
here, y' and y'' are the first and second derivatives of y, respectively.
 

The elements of the dataset \( \{-5, 1, a, 5, b\} \) are in ascending order. If both the mean and median of the dataset are equal to 3, what is the value of \( b \)?

If \( f(x) = x - \frac{1}{x} \), the value of 

Which one of the following does NOT use piezoelectric transducers?
Which one of the following hormones is NOT secreted by the adrenal gland in humans?
In the electrocardiogram (ECG) of humans, the electrical signature of atrial repolarization is masked by the ________
In the context of temperature sensitive polymers, LCST stands for _______.
Cerebrospinal fluid in humans is present in the _______space.
\( ^9_6{C} \) and \( ^{10}_6{C} \) are ________, whereas \( ^9_6{C} \) and \( ^8_5{B} \) are _______
The shape of an elastic rod of length \( l \) is represented by the position vector \( \vec{r}(s) \) corresponding to the arc length \( s \). If the bending energy of the rod is \[ E = K \int_0^l \left( \frac{\partial^2 \vec{r}}{\partial s^2} \right)^2 \, ds, \] what is the dimension of \( K \) in terms of mass \( M \), length \( L \), and time \( T \)?

Let \( R_1, R_2 \) and \( R_3 \) be the Reynolds numbers corresponding to the following three cases, respectively: 
Case 1: A 1 \(\mu\)m long bacterium swimming in water
Case 2: A 10 cm long fish swimming in water
Case 3: A 10 m long whale swimming in water
If each of them covers a distance equal to their respective body length in one second, which one of the following is CORRECT?