Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - GATE MCQ

What is the value of

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. What is the height of the lamp post in meters?

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, if the interest was compounded annually?

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 to copper in alloy C 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. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that the team has finally found a complete captain.

Which of the following statements can be logically inferred from the above paragraph?
(i) Even as a junior cricketer, John was considered a good captain.
(ii) Finding a complete captain is a challenge.
(iii) Fans and the Cricket Board have differing views on what they want in a captain.
(iv) Over the past three seasons John has accumulated big scores.

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 remaining cabs are blue.
(ii) A witness identified the cab involved in the accident as blue.
(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.
Which of the following options is closest to the probability that the accident was caused by a blue cab?

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 tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts.

Which one of the following statements can be logically inferred from the information given in the above paragraph?

Two identical nMOS transistors  M₁ and M₂ are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. V_bias and V_D are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as while the output 
resistance is   where ��_D is the current flowing into the drain of M₂ . Let g_m1 , g_m2 be the transconductances and r_o1 , r_o2 be the output resistances of transistors M₁ and M₂, respectively. 

Which of the following statements about estimates for gm and r_o is correct?

In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. v_IN (t) = u(t) volts. Also, at t = 0, the voltage across each of the capacitors is zero.

The time t, in milliseconds, at which the output voltage v_out crosses −10 V is

A good transimpedance amplifier has

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:

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 statements is FALSE:

Consider  with all real coefficients. It is known that its derivative ��′(s) has no real roots. The number of real roots of ��(s) is

In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

The logic function f ( X , Y ) realized by the given circuit is

A function F(A, B, C ) defined by three Boolean variables A, B and C when expressed as sum of products is given by
where, are the complements of the respective variables. The product of sums (POS) form of the function F is

 The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:

Let M be a real 4x4 matrix. Consider the following statements:
S1:  M has 4 linearly independent eigenvectors.
S2:  M has 4 distinct eigenvalues.
S3:  M is non-singular (invertible).
Which one among the following is TRUE?

Let where a and b are constants. If  at x = 1 and y= 2 , then the relation between a and b is

A discrete-time all-pass system has two of its poles at 0.25∠0 and 2∠30 . Which one of the following statements about the system is TRUE?

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 

The same function  x(t) can also be considered as a periodic function with period T ′ = 40. Let b_k be the Fourier series coefficients when period is taken as  then  is equal to

Consider the following amplitude modulated signal:
The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is __________.

Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is at least 2. The maximum number of codewords such a code can contain is _________.

A binary source generates symbols x ∈ {−1,1} which are transmitted over a noisy channel. The probability of transmitting x = 1 is 0.5. Input to the threshold detector is R = X + ��.
The probability density function f_N (n) of the noise �� is shown below. 

If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1 μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is   _______.

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 turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is   _______.

There are two photolithography systems: one with light source of wavelength λ₁ = 156 nm (System 1) and another with light source of wavelength λ₂ = 325 nm (System 2).  Both photolithography systems are otherwise identical.  If the minimum feature sizes that can be realized using System1 and System2 are L_min1 and L_min2 respectively, the ratio L_min1/L_min2 (correct to two decimal places) is__________.