GATE EC question library

Choose the most appropriate word from the options give 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 $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a+b}{a-b};\, a\,\Diamond, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$ Find the value of $(66\,\square\, 6)\rightarrow(66\,\Diamond, 6).$

If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ 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 environmental security. To keep up both at the required …

Fill in 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 wall every day while having lunch. The wall sometimes breaks. A person sitting in the wall falls if the wall breaks. Which one of the statement below is logically valid and can be inferred from the above sentences?

Consider a system of linear equations: $$x-2y+3z=-1, \\ x-3y+4z=1, \text{ and } \\ -2x+4y-6z=k.$$ The value of $k$ for which the system has infinitely many solutions is ___________

A function $f(x)=1-x^2+x^3$ 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 $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements 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 $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ 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 $R = 300 \Omega$. The resistance $R_{ab}$ (in $\Omega$) of the network is __________.

In the given circuit, the values of $V_1$ and $V_2$ respectively are

A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if

A silicon sample is uniformly doped with donor type impurities with a concentration of $10^{16} / cm^3$. The electron and hole mobilities in the sample are $1200 \: cm^2/V-s$ and $400 \: cm^2/V-s$ respectively. Assume complete ionization of impurities. The charge of an electron is $1.6 \times 10^{-19} \:C$. The resistivity of the sample (in …