# Electronics and Communication Engg - GATE 2015 Paper Solution

#### SET - 1

Choose the most appropriate word from the options given below to complete the following sentence.
The principal presented the chief guest with a ________, as token of appreciation.

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:
Frogs__________.

Choose the word most similar in meaning to the given word:
Educe

Operators $\square,\Diamond\;\mathrm{and}\;\rightarrow$ are defined by $\mathrm a\square\mathrm b\;=\;\frac{\mathrm a-\mathrm b}{\mathrm a+\mathrm b};\;\mathrm a\Diamond\mathrm b\;=\frac{\mathrm a+\mathrm b}{\mathrm a-\mathrm b};\;\mathrm a\rightarrow\mathrm b=\mathrm{ab}$

Find the value of $(66\square6\;)\rightarrow(66\;\Diamond6)$

If logx=(5/7)=-1/3,then the value of x is

The following question presents a sentence, part of which is underlined. Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.
Tuberculosis, together with its effects, ranks one of the leading causes of death in India.

Read the following paragraph and choose the correct statement.
Climate change has reduced human security and threatened human well being. An ignored reality of human progress is that human security largely depends upon environmental security. But on the contrary, human progress seems contradictory to environment security. To keep up both at the required level is a challenge to be addressed by one and all. One of the ways to curb the climate change may be suitable scientific innovations, while the other may be the Gandhian perspective on small scale progress with focus on sustainability.

Find the missing Value: A cube of side 3 units is formed using a set of smaller cubes of side 1 unit; Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

Humpty Dumpty sits on a every day while having lunch. The wall sometimes breaks. A person sitting on the wall falls if the wall breaks.
Which one of the statements below is logically valid and can be inferred from the above sentences?

Consider a system of linear equations :

x2y +3z = –1
x3y + 4z = 1 and
2x +4y3z = k.

The value of k for which the system has infinitely many solutions is _______.

A function (x) = 1 – x2 + x3 is defined in the closed interval [–1,1]. The value of x, in the open interval (–1,1) for which the mean value theorem is satisfied, is

Suppose $A$ and $B$ are two independent events with probabilities $P(A)\neq0$ and $P(B)\neq0$. Let $\overline{)A}$ and $\overline{)B}$ be their complements Which of the following statement is FALSE?

Let $z=x+iy$ be a complex variable. Consider that contour  integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?

The value of $p$ such that the vector $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ is an eigenvector of the matrix $\begin{bmatrix}4&1&2\\p&2&1\\14&-4&10\end{bmatrix}$ is_______.

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ______ . In the network shown in the figure, all resistors are identical with R = 300 $\mathrm{\Omega }$. The resistance Rab (in $\mathrm{\Omega }$) of the network is __________. In the given circuit, the values of $V_1$ and $V_2$ respectively are A silicon sample is uniformly doped with donor type impurities with a concentration of 1016/cm3. The electron and hole mobilities in the sample are 1200 cm2/V-s and 400 cm2/V-s respectively. Assume complete ionization of impurities. The charge of an electron is 1.6 X 10-19 C. The resistivity of the sample (in $\mathrm{\Omega }$-cm) is _______.