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Which of the following is an adverb?

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Choose the word that is most similar in meaning to the given word:

Awkward

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If a² + b² + c² = 1, then ab + bc + ac lies in the interval

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Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is ^{$\frac{1}{6}$} and that of Ramesh's selection is ^{$\frac{1}{8}$}. What is the probability that only one of them will be selected?

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In the following sentence, certain parts are underlined and marked P, Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose (4) as your answer if there is no error.

The student corrected ^{$\frac{\text{all the errors}}{P}$} that ^{$\frac{\text{the instructor marked}}{Q}$} on the ^{$\frac{\text{answer book}}{R}$}.

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Lamenting the gradual sidelining of arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funds coming in the future.

Which of the following statements are logically valid and can be inferred from the above statements?

I. The artists expected funding for arts to increase this year. II. The Chief Minister was receptive to the idea of increasing funding for arts. III. The Chief Minister is a prominent artist. IV. Schools are giving less importance to arts education nowadays.

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Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which conclusion(s) logically follow(s).

Statements: All film stars are playback singers. All film directors are film stars. Conclusions: I. All film directors are playback singers. II. Some film stars are film directors.

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Choose the appropriate word/phrase out of the four options given below to complete the following sentence.

Dhoni, as well as the other team members of the Indian team, _________ present on the occasion.

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The electric field of a uniform plane electromagnetic wave is

$\overrightarrow{E} = (\overrightarrow{a_z} + j4 \overrightarrow{a_y})exp[j(2 \pi \times 10^7 t - 0.2z)]$

The polarization of the wave is

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By performing cascading and/or summing/differencing operations using transfer function blocks G₁(s) and G₂(s), one cannot realise a transfer function of the form

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An electric bus has on-board instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P, in that order. The cumulative distance travelled and the corresponding electricity consumption are shown in the table below. Stretch| Cumulative distance (km)| Electricity used (kWh) | | M| 20|12| | N| 45| 25| | O| 75| 45| | P| 100| 57|

Which of the following is the stretch where the electricity consumption per km is the minimum?

In the figure shown, the output Y is required to be Y = AB + ^{$\overline{CD}$}.

The gates G1 and G2 must respectively be

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Let the signal f(t) = 0 be outside the intervals T₁ and T₂, where T₁ and T₂ are finite. Furthermore, |f(t)| < ^_$\infty$. The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is

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The bilateral Laplace transform of a function , is

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The value of x for which all the eigen values of the matrix given below are real is

$\begin{bmatrix} \ 10 & 5+j & 4 \ \ x & 20 & 2 \ \ 4 & 2 & -10 \ \end{bmatrix}$

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The general solution of the differential equation ^{$\frac{dy}{dx} = \frac{1 + cos 2y}{1 - cos 2x}$} is

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The 2-port admittance matrix of the circuit shown is given by

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The magnitude and phase of the complex Fourier series coefficients a_k of a periodic signal x(t) are shown in the figure. Choose the correct answer from the given options.

Notation: C is the set of complex numbers, R is the set of purely real numbers and P is the set of purely imaginary numbers.

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In an 8085 microprocessor, which of the following instructions change(s) the content of the accumulator?

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If the circuit shown has to function as a clamping circuit, which one of the following conditions should be satisfied for sinusoidal signal of period T?

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For the signal flow graph shown in the figure, the value of ^{$\frac{C(s)}{R(s)}$} is

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Let X ^_$\epsilon$ P{0, 1} and Y _^$\epsilon$ {0, 1} be two independent binary random variables. If P(X = 0) = p and P(Y = 0) = q, then P(X + Y ^$\geq$ 1) is equal to

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An LC tank circuit consists of an ideal capacitor C that is connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

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The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a

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The state variable representation of a system is given as

The response y(t) is

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is an independent and identically distributed (i, i, d) random process with X_n equally likely to be +1 or –1. is another random process obtained as Y_n = X_n + 0.5 X_{n – 1}. The autocorrelation function of is another random process obtained as Y_n = X_n + 0.5 X_{n – 1}. The autocorrelation function of denoted by Ry[k] is

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Consider the differential equation ^{$\frac{ds}{dt}$} = 10 – 0.2x with initial condition x(0) = 1. The response x(t) for t > 0 is

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Input x(t) and output y(t) of an LTI system are related by the differentiation equation y’’(t) – y’(t) – 6y(t) = x(t). If the system is neither casual nor stable, the impulse response h(t) of the system is

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A zero mean white Gaussian noise having power spectral density of ^{$\frac{N_o}{2}$} is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is

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A function of Boolean variables X, Y and Z is expressed in terms of the minterms as

$F(X, Y, Z) = \sum(1, 2, 5, 6, 7)$

Which of the following products of sums given below is equal to the function F(X, Y, Z)?

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Consider a binary, digital communication system which uses pulses g(t) and –g(t) for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which of the following pulses will give the minimum probability of bit error?

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A 1-to-8 demultiplexer with data input D_in, address inputs S₀, S₁ and S₂ (with S₀ as the LSB) and ^{$\overline{y}_o$} to ^{$\overline{y}_7$} as the eight demultiplexed output, is to be designed using two 2 - to - 4 decoders (with enable input ^$\bar{E}$ and address input A₀ and A₁). As shown in the figure, D_in, S₀, S₁ and S₂ are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R and S terminals should be

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The output of a standard second-order system for a unit step input is given as y(t) = 1 – ^{$\frac{2}{\sqrt{3}}$}e^–t cos^{$\Big( \sqrt{3t} - \frac{\pi}{6} \Big)$}. The transfer function of the system is

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The electric field of a plane wave that is propagating in a lossless non-magnetic medium is given by

E(z, t) = a_x 5 cos(2^_$\pi$ x 10⁹ t + ^_$\beta$z) + a_y3 cos x (2^_$\pi$ x 10⁹t + ^_$\beta$z - ^{$\frac{\pi}{2}$})

The polarization is

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The energy band diagram and electron density profile n(x) in a semiconductor are shown in the figure. Assume that n(x) = 10⁵ e^{$\Big( \frac{q \alpha x}{kT} \Big)$}cm^–3, with _^$\alpha$ = 0.1 V/cm and x expressed in cm. Given^{$\frac{kT}{q}$}= 0.026 V, D_n = 36 cm² s^–1, and^{$\frac{D}{\mu}$}=^{$\frac{kT}{q}$}. The electron current density (in A/cm²) at x = 0 is

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The signal cos(10^_$\pi$t + ^{$\frac{\pi}{4}$}) is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response ^{$\bigg( \frac{sin (\pi t)}{\pi t} \bigg)$}cos^{$\bigg( 40 \pi t - \frac{\pi}{2} \bigg)$}. The filter output is