Electronics And Communication - ECE 2014 GATE Paper (Practice Test) - Electronics and Communication Engineering (ECE) MCQ

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of
throws show the following frequencies of occurrence: 1→0.167; 2→0.167; 3→0.152; 4→
0.166; 5→0.168; 6 →0.180. We call this die

Fill in the missing number in the series.
2   3   6   15   ___   15 7.5    630

Q. No. 6 – 10 Carry One Mark Each

Q.

Find the odd one in the following group
Q,W,Z,B           B,H,K,M           W,C,G,J                  M,S,V,X

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the
ladder there are two lights. If one of the lights is red, the other light on that step will always
be blue. If one of the lights on a step is green, the other light on that step will always be
yellow. Which of the following statements is not necessarily correct?

sum of eight consecutive odd numbers is 656. The average of four consecutive even
numbers is 87. What is the sum of the smallest odd number and second largest even number?

The total exports and revenues from the exports of a country are given in the two charts
shown below. The pie chart for exports shows the quantity of each item exported as a
percentage of the total quantity of exports. The pie chart for the revenues shows the
percentage of the total revenue generated through export of each item. The total quantity of
exports of all the items is 500 thousand tonnes and the total revenues are 250 crore rupees.
Which item among the following has generated the maximum revenue per kg?

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to
simultaneously pump water into the half-full tank while draining it. What is the rate at which
water has to be pumped in so that it gets fully filled in 10 minutes?

Q. No. 11 – 35 Carry One Mark Each

Q.

The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of
matrix AB is ________.

Let X be a random variable which is uniformly chosen from the set of positive odd numbers
less than 100. The expectation E[X]is __________.

For 0 t < ∞, the maximum value of the function f(t) =e^-t -  2e^-2t  occurs at

The value of  

If the characteristic equation of the differential equation

has two equal roots, then the values of α are

Norton’s theorem states that a complex network connected to a load can be replaced with an
equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then
the magnitude of the current (in mA) through the 4k? resistor at t = 0+ is _______.

A silicon bar is doped with donor impurities N_D = 2.25 x 10¹⁵ atoms / cm³. Given the intrinsic
carrier concentration of silicon at T = 300 K is n_i = 1.5 x 1010 cm-3. Assuming complete
impurity ionization, the equilibrium electron and hole concentrations are

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

The feedback topology in the amplifier circuit (the base bias circuit is not shown for
simplicity) in the figure is

In the differential amplifier shown in the figure, the magnitudes of the common-mode and
differential-mode gains are A_cm and A_d, respectively. If the resistance R_E is increased, then

A cascade connection of two voltage amplifiers A1 and A2 is shown in the figure. The openloop
gain A_v0, input resistance R_in, and output resistance RO for A1 and A2 are as follows:

For an n-variable Boolean function, the maximum number of prime implicants is

The number of bytes required to represent the decimal number 1856357 in packed BCD
(Binary Coded Decimal) form is __________ .

In a half-subtractor circuit with X and Y as inputs, the Borrow (M) and Difference (N = X - Y)
are given by

An FIR system is described by the system function

Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j 0.25 is a zero o X(z), which
one of the following must also be a zero of X(z).

Consider the periodic square wave in the figure shown.

The ratio of the power in the 7^th harmonic to the power in the 5^th harmonic for this waveform
is closest in value to _______.

The natural frequency of an undamped second-order system is 40 rad/s. If the system is
damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.