GATE EC question library

“I cannot support this proposal. My _________ will not permit it.”

Courts : _________: : Parliament : Legislature (By word meaning)

What is the smallest number with distinct digits whose digits add up to $45?$

In a class of $100$ students, there are $30$ students who neither like romantic movies nor comedy movies, the number of students who like romantic movies is twice the number of students who like comedy movies, and the number of students who like both romantic movies and comedy movies is $20$. How many students in the class like romantic movies?

How many rectangles are present in the given figure?

Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws and some that do not. All creatures that have claws are ferocious. Based only on the information provided above, which one of the following options can be logically inferred …

Which one of the following options represents the given graph?

Which one of the following options can be inferred from the given passage alone? When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet. [Excerpt from The Truth about Stories by T. King]

Out of $1000$ individuals in a town, $100$ unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to: Given this strategy, no more than _______ testing kits will be required to identify all the $100$ …

A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions $100 \mathrm{~cm} \times 1 \mathrm{~cm}$. The total number of creases visible when the sheet is unfolded is ___________.

The signal-to-noise ratio $\mathrm{SNR}$ of an $\mathrm{ADC}$ with a full-scale sinusoidal input is given to be $61.96 \mathrm{~dB}$. The resolution of the $\mathrm{ADC}$ is_____________bits (rounded off to the nearest integer).

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of $1 \; \mu \mathrm{s}$. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of $1 \mathrm{~V}$ with $12$-bit accuracy is ___________ $\mu \mathrm{s}$ (rounded off to two decimal places).

Let $v_1=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right]$ and $v_2=\left[\begin{array}{l}2 \\ 1 \\ 3\end{array}\right]$ be two vectors. The value of the coefficient $\alpha$ in the expression $v_1=\alpha v_2+e$, which minimizes the length of the error vector $e$, is

The rate of increase, of a scalar field $f(x, y, z)=x y z$, in the direction $v=(2,1,2)$ at a point $(0,2,1)$ is

Let $w^4=16 j$. Which of the following cannot be a value of $w$ ?

The value of the contour integral, $\oint_C\left(\frac{z+2}{z^2+2 z+2}\right) d z$, where the contour $\mathrm{C}$ is $\left\{z:\left|z+1-\frac{3}{2} j\right|=1\right\}$, taken in the counter clockwise direction, is

Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\left\{\lambda_k \mid 1 \leq k \leq n\right\}$ and $\left\{v_k \mid 1 \leq k \leq n\right\}$, respectively. For any invertible matrix $P$, the sets of eigenvalues and eigenvectors of the matrix $A$, where $B=P^{-1} A P$, respectively, are

In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

For an intrinsic semiconductor at temperature $\text{T}=0 \; \text{K}$, which of the following statement is true?

A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R, L}$ and $\text{C}$ are