General Aptitude (GA) Questions

Which of the following conjunction pairs correctly completes the sentence: 'Mr. X speaks _____ Japanese _____ Chinese.'?

A sum of money is distributed among P, Q, R, and S in the proportion 5:2:4:3 respectively. If R receives $1000 more than S, how much does Q receive?

A trapezium PQRS has vertices P, Q, R, and S in anticlockwise order. PQ is parallel to SR, PQ = 11 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm. What is the shortest distance between PQ and SR?

A 4x4 grid of unit squares contains an unshaded unit square, representing a hole. What is the maximum number of squares, not containing the hole, that can be formed using the unit squares as building blocks?

An art gallery uses a security guard to monitor the space. Given the gallery's layout where boundary walls are opaque, and the need for the guard to have a 360 view covering all inner space, from which location(s) P, Q, R, and S can the guard effectively watch over the entire gallery?

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences. Based on this information, which is the most accurate logical inference?

Consider the inequalities: (i) $2x - 1 > 7$ (ii) $2x - 9 < 1$. Which of the following expressions satisfies both inequalities?

The points P(0, 1), Q(0, -3), R(-2, -1), and S(2, -1) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

In a class of five students P, Q, R, S, and T, only one student cheated on the exam. The disciplinary committee recorded these statements: P: R cheated. Q: S cheated. R: P did not cheat. S: Only one of us is telling the truth. T: R is telling the truth. Given S never lies, who cheated?

Consider a square with corners P, Q, R, S, and center T. Let X be a rotation by 180 degrees about SQ, Y a 180 degree rotation about PR, and Z a 90 degree clockwise rotation about T. Which statement is correct about the following sequences: (1) XYZZ (2) XY (3) ZZZZ

Consider the two-dimensional vector field $\vec{F}(x, y) = x \hat{i} + y \hat{j}$, where $\hat{i}$ and $\hat{j}$ denote the unit vectors along the x-axis and the y-axis, respectively. A contour C in the x-y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral $\oint_c \vec{F}(x, y) \cdot (dx \hat{i} + dy \hat{j})$ is:

Consider a system of linear equations $Ax = b$, where $A = \begin{bmatrix} 1 & -\sqrt{2} & 3\ -1 & \sqrt{2} & -3 \end{bmatrix}$ and $b = \begin{bmatrix} 1 \ 3 \end{bmatrix}$. This system of equations admits:

What is the current $I$ in the circuit shown?

Consider the circuit shown in the figure. What is the current $I$ flowing through the 10 $\Omega$ resistor?

The Fourier transform $X(j\omega)$ of the signal $x(t)=\frac{t}{(1+t^2)^2}$ is:

Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is $10^{17}$ cm$^{-3}$ and the intrinsic carrier concentration is $10^{10}$ cm$^{-3}$. Electron and hole diffusion lengths are 2$\mu$m and 1$\mu$m, respectively. The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is $10^{14}$ cm$^{-3}$ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation of the steady state electron density at x = 2$\mu$m, is:

In a non-degenerate bulk semiconductor with electron density $n = 10^{16}$ cm$^{-3}$, the value of $E_c - E_{F_n} = 200$ meV, where $E_c$ and $E_{F_n}$ denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is $10^{10}$ cm$^{-3}$. For $n = 0.5 \times 10^{16}$ cm$^{-3}$, the closest approximation of the value of $(E_c - E_{F_n})$, among the given options, is:

Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width ($W$) to gate length ($L$) ratios ($\frac{W}{L}$) of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the pMOSFET, the threshold voltage is $-1$ V and the mobility of holes is $40 \frac{cm^2}{V.s}$. For the nMOSFET, the threshold voltage is $1$ V and the mobility of electrons is $300 \frac{cm^2}{V.s}$. What is the steady state output voltage $V_o$

Consider the 2-bit multiplexer (MUX) shown in the figure. For $OUTPUT$ to be the XOR of $C$ and $D$, what are the values for $A_0, A_1, A_2,$ and $A_3$?

The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and -1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, what are the steady state voltages $V_1$ and $V_2$

Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path, where the gain $K = 2$. The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Assuming $G(s)$ has no poles on the closed right-half of the complex plane, what is the number of poles of the closed-loop transfer function in the closed right-half of the complex plane?

The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Select the transfer function G (s) that results in the root-locus plot of the closed-loop system as shown in the figure.

The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure. Which one of the following combinations is true?

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is $2sin(t + \pi/2)$. The displacement current (in Amperes) through the capacitor is:

Consider the following partial differential equation (PDE) \newline a$\frac{\partial^2 f (x, y)}{\partial x^2}$ + b$\frac{\partial^2 f (x, y)}{\partial y^2}$ = f(x, y), where a and b are distinct positive real numbers. What is $\xi$ and $\eta$ if $f(x, y) = e^{\left(\xi{}x + \eta{}y\right)}$ is a solution.