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

The aircraft ________ take off as soon as its flight plan was filed.

Read the statements: All women are entrepreneurs. Some women are doctors.

Which of the following conclusions can be logically inferred from the above statements?

For submitting tax returns, all resident males with annual income below Rs. 10 lakh should fill up Form P and all resident females with income below Rs. 8 lakh should fill up Form Q. All people with incomes above Rs. 10 lakh should fill up Form R, except non residents with income above Rs. 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is

Find the odd one from the following group:

W, E, K, O I, Q, W, A F, N, T, X N, V, B, D

For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z₁ of the first section to the input impedance Z₂ of the second section is

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

Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped __________ such notions.

In the ac equivalent circuit shown in the figure, if i_in is the input current and R_F is very larger, the type of feedback is

In the figure, assume that the forward voltage drops of the PN diode D₁ and Schottky diode D₂ are 0.7 V and 0.3 V, respectively. If ON denotes conducting state of the diode and OFF denotes non-conducting state of the diode, then in the circuit,

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

Consider the configuration shown in the figure which is a portion of a larger electrical network For R = 1^$\Omega$ and currents i1 = 2 A, i4 = - 1A, i5 = - 4 A, which one of the following is TRUE?

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5^th of the exports?

If fixed positive charges are present in the gate oxide of an n-channel enhancement type MOSFET, it will lead to

A good current buffer has

The Boolean expression ^{$(X + Y)(X + \bar{Y}) + \overline{(X \bar{Y}) + \bar{X}}$} simplifies to

C is a closed path in the z-plane by |z| = 3. The value of the integral ^{$\oint_c \bigg(\frac{z^2 - z + 4j}{z + 2j}\bigg)dz$} is

The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity e is

A two-port network has scattering parameters given by [S] = ^{$\begin{bmatrix} \ s_{11} & s_{12} \ \ s_{21} & s_{22} \ \end{bmatrix}$.} If the port-2 of the two port is short circuited, the s11 parameter for the resultant one port network is

In the following circuit employing pass transistor logic, all NMOS transistors are identical with a threshold voltage of 1V. Ignoring the body-effect, the output voltages at P, Q and R are,

A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is

For a function g(t), it is given that ^{$\int\limits_{-\infty}^{+ \infty}$}g(t) e^-jwt dt = we^-2w2 for any real value w. if y(t) = ^{$\int\limits_{-\infty}^{t}$}g(T), then ^{$\int\limits_{-\infty}^{+\infty}$}y(t) dt is

A discrete time signal x[n] = sin (^{$\pi^2$} n), n being an integer, is

In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The output voltage V_out is

The doping concentrations on the p-side and n-side of a silicon diode are 1 ^_x 10¹⁶ cm^-3 and 1 ^_x 10¹⁷ cm^-3, respectively. A forward bias of 0.3 V is applied to the diode. At T = 300 K, the intrinsic carrier concentration of silicon n_i = 1.5 ^_x 10¹⁰ cm^-3 and ^{$\frac{kT}{q}$} = 26 m V. The electron concentration at the edge of the depletion region on the p-side is

The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to input A of the XOR gate.

Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram?

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. ^{$\begin{matrix} \ . \ \ y \ \end{matrix}$} (t) + 5y(t) = u(t) when y(0) = 1 and u(t) is a unit step function, y(t) is

Consider the Boolean function, F(w, x, y, z) = wy + xy + ^$\bar{w}$xyz + ^{$\bar{w}$$\bar{x}$}y + xz + ^{$\overline{XYZ}$}. Which one of the following is the complete set of essential prime implicants?

Let x [n] = ^{$\bigg(- \frac{1}{9} \bigg)^n$} u (n) – ^{$\bigg(- \frac{1}{3} \bigg)^n$} u (– n – 1). The Region of Convergence (ROC) of the z-transform of x [n]

For the following feedback system G(s) = ^{$\bigg( \frac{1}{(s + 1)(s+2)} \bigg)$}. The 2% settling time of the step response is required to be less than 2 seconds.

Which one of the following compensators C(s) achieves this?

Let X be a real-valued random variable with E[X] and E[X²] denoting the mean values of X and X², respectively. The relation which always holds true is

Consider the state space model of a system, as given below:

^{$\begin{bmatrix} \ . \ \ x_1 \ \ . \ \ x_2 \ \ . \ \ x_3 \ \end{bmatrix}$} = ^{$\begin{bmatrix} \ -1 & 1 & 0 \ \ 0 & -1 & 0 \ \ 0 & 0 &-2 \ \end{bmatrix}$$\begin{bmatrix} \ x_1 \ \ x_2 \ \ x_3 \ \end{bmatrix}$} + ^{$\begin{bmatrix} \ 0 \ \ 4 \ \ 0 \ \end{bmatrix}$} u; y = ^{_{$\begin{bmatrix} \ 1 & 1 & 1\ \end{bmatrix}$}$\begin{bmatrix} \ x_1 \ \ x_2 \ \ x_3 \ \end{bmatrix}$}

The system is

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in

The Taylor series expansion of 3 sinx + 2 cos x is

The output F in the digital logic circuit shown in the figure is

Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following conclusions is correct?

Consider a random process X(t) = ^$\sqrt{2}$ sin(2_^$\pi$t + _^$\varphi$), where the random phase _^$\varphi$ is uniformly distributed in the interval [0, 2_^$\pi$]. The auto-correlation E[X(t₁) X(t₂)] is