Choose the most appropriate word from the options given below to complete the following sentence.

Communication and interpersonal skills are ________ important in their own ways.

Which of the options given below best completes the following sentence?

She will feel much better if she _________

Find the odd one in the following group.

Q, W, Z, B B, H, K, M W, C, G, J M, S, V, X

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg?

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence:

1 ^{$\rightarrow$} 0.167 2 ^{$\rightarrow$} 0.167 3 ^{$\rightarrow$} 0.152 4 ^{$\rightarrow$} 0.166 5 ^{$\rightarrow$} 0.168 6 ^{$\rightarrow$} 0.180

We call this die

The value of ^{_{$\lim\limits_{x \rightarrow \infty}$}$\bigg(1 + \frac{1}{x}\bigg)^2$}

Norton's theorem states that a complex network connected to a load can be replaced with an equivalent impedance

Choose the most appropriate pair of words from the options given below to complete the following sentence.

She could not _________ the thought of _________ the election to her bitter rival.

For 0 ^$\leq$ t < _^$\infty$, the maximum value of the function f(t) = e^–t – 2e^–2t occurs at

In CMOS technology, shallow P-well or N-well regions can be formed using

The feedback topology in the amplifier circuit (the base bias circuit is not shown for simplicity) in the figure is

An increase in the base recombination of a BJT will increase

In the differential amplifier shown in the figure, the magnitudes of the common mode and differential-mode gains are A_CM and A_d, respectively. If the resistance R_E is increased, then

For an n-variable Boolean function, the maximum number of prime implicants is

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X – Y) are given by

Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z)?

An FIR system is described by the system function

H(z) = 1 + ^{$\frac{7}{2}$} z^–1 + ^{$\frac{3}{2}$} z^–2

The system is

A silicon bar is doped with donor impurities N_D 2.25 ^_x 10¹⁵ atoms/cm³. Given the intrinsic carrier concentration of silicon at T = 300 K is n_i = 1.5 ^_x 10¹⁰ cm³. Assuming complete impurity ionization, the equilibrium election and hole concentrations are

For the following system,

when X₁(s) = 0, the transfer function ^{$\frac{Y(s)}{X_2(s)}$} s

Which one of the following field patterns represents a TEM wave travelling in the positive x direction?

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by C = Wlog₂ ^{$\bigg( 1 + \frac{P}{\sigma^2 W} \bigg)$} bits per second (bps), where W is the channel bandwidth, P is the average power received and ^_$\sigma$2 is the one sided power spectral density of the AWGN. For a fixed ^{$\frac{P}{\sigma^2}$} = 1000 the channel capacity (in kbps) with infinite bandwidth (W ^{_{$\rightarrow$}} 3) is approximately

The outputs of the two flip-flops Q1, Q2 in the figure shown are initialized to 0, 0. The sequence generated at Q1 upon application of clock signal is

For the n-channel MOS transistor shown in the figure, the threshold voltage V_TH is 0.8 V. Neglect channel length modulation effects. When the drain voltage V_D = 1.6 V, the drain current I_D was found to be 0.5 mA. If V_D is adjusted to be 2 V by changing the values of R and V_DD, the new value of I_D (in mA) is

In the circuit shown, choose the correct timing diagram of the output (y) from the given waveforms W1, W2, W3 and W4.

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI₀- DI₇) from an external device is shown in the figure. The instruction for correct data transfer is

The diode in the circuit shown has V_on = 0.7 Volts but is ideal otherwise. If V_i = 5 sin (wt) Volts, the minimum and maximum values of V_o (in Volts) are, respectively,

In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I (t) (in mA) for t > 0?

The system of linear equations

$\begin{bmatrix} \ 2 & 1 & 3 \ \ 3 & 0 & 1 \ \ 1 & 2 & 5 \ \end{bmatrix}$$\begin{bmatrix} \ a \ \ b \ \ c \ \end{bmatrix}$$\begin{bmatrix} \ 5 \ \ -4 \ \ 14 \ \end{bmatrix}$

The real part of an analytic function f (z) where z = x + jy is given by e^–y cos (x). The imaginary part of f (z) is

An unforced linear time invariant (LTI) system is represented by

$\begin{bmatrix} \ . \ \ X_1 \ \ . \ X_2 \ \end{bmatrix}$= $\begin{bmatrix} \ -1 & 0 \ \ 0 & -2 \ \end{bmatrix}$$\begin{bmatrix} \ X_1 \ \ X_2 \ \end{bmatrix}$

If the initial condition are x₁ (0) = 1 and x₂ (0) = – 1, the solution of the state equation is

Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is

If the electric field of a plane wave is ^{$\overrightarrow{E}$} (z, t) = x³ cos (wt - kz + 30^o) – y⁴ sin (wt - kz + 45^o) (mV/m), the polarization state of the plane wave is

The input-output relationship of a causal stable LTI system is given as Y[n] = ^_$\alpha$y[n – 1] + ^_$\beta$x[n]

If the impulse response h6n@ of this system satisfies the condition ^{_{$\sum_{n=0}^\infty h$}}[n] = 2, the relationship between a and b is

When a silicon diode having a doping concentration of N_A = 9 ^_x 10 cm¹⁶ on p-side and N_D = 1 ^_x 10¹⁶ cm^-3 on n-side is reverse biased, the total depletion width is found to be 3 ^_$\mu$m. Given that the permittivity of silicon is 1.04 ^_x 10^-12 F/cm, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s₁ (t) = acos 2^_$\pi$f₁ t and s₂ (t) = ^_$\alpha$cos 2^_$\pi$f₂ t, where ^_$\alpha$ = 4 mV. Assume an AWGN channel with two sided noise power spectral density ^{$\frac{N_0}{2}$} = 0.5 ^_x 10 W/Hz. Using an optimal receiver and the relation Q (v) = ^{$\frac{1}{\sqrt{2 \pi}} \int\limits_v^\infty$$e^{-u^2/2}$} du, the bit error probability for a data rate of 500 kbps is

If the characteristic equation of the differential equation ^{$\frac{d^2 y}{dx^2} + 2 \alpha \frac{dy}{dx} + y = 0$} has two equal roots, then the values of a are