GATE 2022 Electronics & Communication

Mr. X speaks ____________ Japanese ___________ Chinese.

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively. If R gets Rs. 1000 more than S, what is the share of Q (in Rs.) ?

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and...

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes...

Consider the following inequalities. (i) 2x $$-$$ 1 > 7 (ii) 2x $$-$$ 9 Which one of the following expressions below satisfies the above two inequalities?

Four 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 is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the state...

Consider a system of linear equations Ax = b, where $$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill \cr { - 1} \hfill & {\sqrt 2 } \hfill & { - 3} \hfill \cr } }...

Consider the following partial differential equation (PDE) $$a{{{\partial ^2}f(x,y)} \over {\partial {x^2}}} + b{{{\partial ^2}f(x,y)} \over {\partial {y^2}}} = f(x,y)$$, where a a...

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

Select the correct statement(s) regarding CMOS implementation of NOT gates.

The function f(x) = 8log e x $$-$$ x 2 + 3 attains its minimum over the interval [1, e] at x = __________. (Here log e x is the natural logarithm of x.)

Let $$\alpha$$, $$\beta$$ two non-zero real numbers and v 1 , v 2 be two non-zero real vectors of size 3 $$\times$$ 1. Suppose that v 1 and v 2 satisfy $$v_1^T{v_2} = 0$$, $$v_1^T{...

Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 $$\mu$$m and width 100 $$\mu$$m. The product of electron mobility ($$\mu$$ n ) and oxide capacitance p...

Consider an even polynomial p(s) given by $$p(s) = {s^4} + 5{s^2} + 4 + K$$ where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the im...

Consider the following series : $$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$ For which of the following combinations of c, d values does this series converge?

Consider a Boolean gate (D) where the output Y is related to the inputs A and b as, Y = A + $$\overline B $$, where + denotes logical OR operation. The Boolean inputs '0' and '1' a...

Two linear time-invariant systems with transfer functions $${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10} + 10}}$$ have unit step resp...

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 displac...

Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?

Consider the following wave equation, $${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \over {\partial {x^2}}}$$ Which of the given options is/are sol...

A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is ___...

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10 $$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\t...

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarro...

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

In a non-degenerate bulk semiconductor with electron density n = 10 16 cm $$-$$3 , the value of E C $$-$$ E Fn = 200 meV, where E C and E Fn denote the bottom of the conduction ban...

Let x 1 (t) = e $$-$$t u(t) and x 2 (t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denotes the convolution of x 1 (t) and x 2 (t), then $$\math...

Select the CORRECT statements regarding semiconductor devices

For a vector $$\overline x $$ = [x[0], x[1], ....., x[7]], the 8-point discrete Fourier transform (DFT) is denoted by $$\overline X $$ = DFT($$\overline x $$) = [X[0], X[1], .....,...

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability (1 $$-$$ $$\in$$), and fl...

Consider a channel over which either symbol x A or symbol x B is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. Th...