List of practice Questions

Assuming ideal op-amps, the circuit represents a 

Which one of the following statements is true about the small signal voltage gain of a MOSFET based single stage amplifier?
Let \( P = \begin{bmatrix} 2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} \) and let \( I \) be the identity matrix. Then \( P^2 \) is equal to
Let \( \mathbf{A} = \begin{bmatrix} 1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1 \end{bmatrix} \), and \( \mathbf{b} = \begin{bmatrix} \frac{1}{3} \\ -\frac{1}{3} \\ 0 \end{bmatrix} \). Then, the system of linear equations \( \mathbf{A} \mathbf{x} = \mathbf{b} \) has
Consider the set \( S \) of points \( (x, y) \in \mathbb{R}^2 \) which minimize the real-valued function \( f(x, y) = (x + y - 1)^2 + (x + y)^2 \). Which of the following statements is true about the set \( S \)?
What is the pH of a solution with a hydrogen ion concentration of \(1 \times 10^{-4}\) mol/L?

In triangle \( PQR \), the lengths of \( PT \) and \( TR \) are in the ratio \( 3:2 \). ST is parallel to QR. Two semicircles are drawn with \( PS \) and \( PQ \) as diameters, as shown in the figure. Which one of the following statements is true about the shaded area \( PQS \)? (Note: The figure shown is representative.) 

Spheres of unit diameter are centered at \( (l, m, n) \), where \( l, m, \) and \( n \) take every possible integer value. The distance between two spheres is computed from the center of one sphere to the center of another sphere. For a given sphere, \( x \) is the distance to its nearest sphere and \( y \) is the distance to its next nearest sphere. The value of \( \frac{y}{x} \) is:

Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT? 

In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii)?

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: 
P. It is because deer, like most of the animals that tigers normally prey on, run much faster! It simply means, another day of empty stomach for the big cats. 
Q. Tigers spend most of their life searching for food. 
R. If they trace the scent of deer, tigers follow the trail, chase the deer for a mile or two in the dark, and yet may not catch them. 
S. For several nights, they relentlessly prowl through the forest, hunting for a trail that may lead to their prey.

What is the value of \( \left( \frac{3^{81}}{27^4} \right)^{\frac{1}{3}} \)?

Each row of Column-I has three items and each item is represented by a circle in Column-II. The arrangement of circles in Column-II represents the relationship among the items in Column-I. Identify the option that has the most appropriate match between Column-I and Column-II. Note: The figures shown are representative. 

The relationship between two variables \( x \) and \( y \) is given by \( x + py + q = 0 \) and is shown in the figure. Find the values of \( p \) and \( q \). Note: The figure shown is representative. 

Good : Evil :: Genuine : _________ Select the most appropriate option to complete the analogy.
Kavya _________ go to work yesterday as she _________ feeling well. Select the most appropriate option to complete the above sentence.
Consider two coupled circuits, having self-inductances \( L_1 \) and \( L_2 \), that carry non-zero currents \( I_1 \) and \( I_2 \), respectively. The mutual inductance between the circuits is \( M \) with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of \( \frac{I_1}{I_2} \)?
A 3-phase, 400 V, 4 pole, 50 Hz star connected induction motor has the following parameters referred to the stator:
\( R_r' = 1 \, \Omega \), \( X_s = X_r' = 2 \, \Omega \)
Stator resistance, magnetizing reactance and core loss of the motor are neglected.
The motor is run with constant \( V/f \) control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to:
The bus impedance matrix of a 3-bus system (in pu) is: \[ Z_{{bus}} = \begin{bmatrix} j0.059 & j0.061 & j0.038
j0.061 & j0.093 & j0.066
j0.038 & j0.066 & j0.110 \end{bmatrix} \] A symmetrical fault (through a fault impedance of \( j0.007 \) pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1 during the fault is: \[ {(round off to three decimal places).} \]
The input voltage \( v(t) \) and current \( i(t) \) of a converter are given by, \[ v(t) = 300 \sin(\omega t) \, {V} \] \[ i(t) = 10 \sin\left(\omega t - \frac{\pi}{6}\right) + 2 \sin\left(3\omega t + \frac{\pi}{6}\right) + \sin\left(5\omega t + \frac{\pi}{2}\right) \, {A} \] where \( \omega = 2\pi \times 50 \) rad/s. The input power factor of the converter is closest to:
Let \( \mathbf{v}_1 \) and \( \mathbf{v}_2 \) be the two eigenvectors corresponding to distinct eigenvalues of a \( 3 \times 3 \) real symmetric matrix. Which one of the following statements is true?
Three-point charges \( Q \), \( q \), and \( -q \) are kept at the vertices of an equilateral triangle of side \( L \). What is the total electrostatic potential energy of the system?
If the function
\[ f(x) = \begin{cases} \sin(2x), & \text{for } x > 0, \\ a + bx, & \text{for } x \leq 0, \end{cases} \]
where \( a \) and \( b \) are constants, is differentiable at \( x = 0 \), then \( a + b \) is equal to:
A 24 cm line AB is vertically standing on a horizontal plane. The station point is located 18 cm above ground and 15 cm in front of the line AB. The picture plane is located in between the line AB and station point perpendicular to the sight line. The distance between the picture plane and the station point is 9 cm. The height of the perspective view of the line AB is ________cm. (rounded off to one decimal place)
Which of the following shows recessive traits?