GATE 2018 Electronics & Communication

"Even though there is a vast scope for its __________, tourism has remained a/an _________ area." The words that best fill the blanks in the above sentence are

A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to touris...

A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is tur...

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold t...

If the number 715 ■ 423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ■ is _______.

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height...

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F = $$\overline A .\overline B .\overline C + \overline A .B.\over...

Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and vector $$X = \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$. The number of d...

Let X 1 , X 2 , X 3 and X 4 be independent normal random variables with zero mean and unit variance. The probability that X 4 is the smallest among the four is _______.

The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. Whi...

Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f} \over {\partial x}} = {{\partial f} \over {\partial y}}$$ at...

A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{{x^2} + {y^2}} \over {2y}} + {y \over x}$$. The equation tha...

Let M be a real 4 $$ \times $$ 4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular...

"By giving him the last __________ of the cake, you will ensure lasting ________ in our house today." The words that best fill the blanks in the above sentence are

Consider p(s) = s 3 + $${a_2}$$s 2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is

For a unity feedback control system with the forward path transfer function $$G(s) = {K \over {s\left( {s + 2} \right)}}$$ The peak resonant magnitude M r of the closed-loop freque...

What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?

The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matr...

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, i...

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. (i) 85% of cabs in the city are green and the r...

The position of a particle y(t) is described by the differential equation : $${{{d^2}y} \over {d{t^2}}} = - {{dy} \over {dt}} - {{5y} \over 4}$$. The initial conditions are y(0) =...

Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form f(x) = $${a_0} + {a_1}x + {a_2}{x^2}...

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following stat...

Let r = x 2 + y - z and z 3 - xy + yz + y 3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1), the value (correct to two decimal places) of $${{\partial...

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] = $$\sum\limits_{n = 0}^{N - 1} {x\left[ n \right]{e^{ - j2\pi nk/N}}} $$. The value (correct to two decim...

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎 𝑘 , that is $$x\left( t \right) = \sum\limits_{k = - \inft...

A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ $$ and $$\angle 30^\circ $$. Which one of the following statements about the system is TRUE?