List of top Questions asked in GATE IN

A matrix \(P\in\mathbb{R}^{3\times3}\) satisfies \(P^3-4P^2+5P-2I=0\), where \(I\) is a \(3\times3\) identity matrix.
The set of all possible eigenvalues of matrix \(P\) is ____.

Given \(f(x,y) = x^2 -2xy+ y^2\).
The complete contour of the equation \(f(x,y) = 1\) is described by the option(s) ___.

If the definition of SI unit 'X' is required to define SI unit 'Y', the dependency is indicated as \(X \rightarrow Y\). A valid order of dependencies, as per present convention, is __________.

An electric field has a potential of \(V(x,y,z)=\sqrt{x^2+y^2+z^2}\) V.
A charge of \(1\) coulomb placed at \((\hat{i}+\hat{j}+\hat{k})\) experiences a force of
\[\vec{F}=(a\hat{i}+b\hat{j}+c\hat{k})\text{ N}\]
The values of \((a,b,c)\) are ______.

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is \(\_\_\_\_\_\).

A closed Lissajous pattern observed on an oscilloscope in the \(X-Y\) mode has three horizontal tangencies and two vertical tangencies in steady state. If the signal frequency on channel-\(X\) is 600 Hz, then the signal frequency on channel-\(Y\) is __________ Hz.

A single phase transformer has a rating of 10 kVA, 50 Hz, 1100 V/ 220 V. In an open circuit test with the high voltage side open, the following are obtained:
Voltage applied to the low voltage winding = 220 V
Measured power = 363 W
Measured current = 2.75 A
Magnetizing reactance \(X_m\) referred to the high voltage winding is ________ \(\Omega\). (rounded off to the nearest integer)

The RLC filter shown below acts as a ________.

A 16-bit processor has 16-bit wide instructions and a few internal registers. Every 16-bit instruction is encoded in a fixed format with one operation code of 7 bits and up to three operands. The operand can be an internal register and each operand is encoded by 3 bits. All the internal registers can be specified in an instruction using three bits.
The correct statement(s) for this processor is/are ____.

A digital counter increments its count every \(0.1\) \(\mu\text{s}\). The counter is used in an instrument to measure frequency. The counter is operated for one period of the input signal to the instrument to measure its frequency. The input signal is approximately at \(100\) kHz. The maximum error in the measured frequency is kHz (rounded off to the nearest integer).

Consider a matrix
\[ A=\begin{bmatrix}1 & 0 & 2\\ -1 & 1 & 0\\ 0 & 1 & 2\end{bmatrix} \]
Let \(b=\begin{bmatrix}1\\3\\0\end{bmatrix}\) and \(x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\).
The number of solutions to the linear system of equations \(Ax=b\) is _____.

The initial state of \(Q_3Q_2Q_1Q_0\) in the digital circuit shown below is 1011.

The new value of \(Q_3Q_2Q_1Q_0\) after two rising edges of the clock (CLK) will be __________.

The Kelvin double bridge is used to measure ______ valued resistances and has ______ resistors in its construction.

A data set is given to be \([1, 2, 0, -1, -3, 1, 2, 0, 1]\).
The median of the data set is ____. (rounded off to the nearest integer)

In a linear element, the measured current is \(100\) mA \(\pm 2.5\%\) and the measured voltage is \(5\) V \(\pm 5\%\). Which of the following options show(s) the consumed power?

Consider a function \(f(z)=z^2+z+1\), where \(z\in\mathbb{C}\) is a complex variable. A simple closed contour \(\gamma\) in the \(z\)-plane encloses the point \(z=1+0j\).
The value of the integral
\[\oint_{\gamma}\frac{f(z)}{z-1}\,dz\]
is ______.

An amplitude modulated voltage signal \(x(t)\) drives a load of \(1\,\Omega\).
\[ x(t) = K\cos(300\pi t) + L\cos(240\pi t) + L\cos(360\pi t) \]
If the efficiency is \(60\%\) and the carrier power is \(50\) W, the value of \(L\) is ______ V.

Which one among the following statements is true for the function \(f(x)=x|x|\)?

In the following active filter circuit with ideal op-amps, \(R\) is \(1\ \text{k}\Omega\), \(C\) is \(1\ \mu\text{F}\), and \(V_{in}\) has an amplitude of \(1\) V at \(1000\) rad/s.

The amplitude of \(V_{out}\) is __________ V.

Which of the following functions represent(s) the output of the CMOS logic-gate shown in the circuit below?

Given a differential equation \(\dfrac{d^2x}{dt^2} + x= 0\) with \(x(0) \neq 0\).
Which of the following statements is/are true?

A common gate amplifier represents a _____________.

In the circuit below the maximum value of \(v_{out}\) is ________ V. (rounded off to the nearest integer)

A single phase step-down transformer has a high voltage primary winding and a low voltage secondary winding. The secondary winding is connected to a load impedance \(Z_2\). The impedance \(Z_2\) when referred to the primary winding is denoted by \(Z_2'\). Which of the following conditions is true?

The potential difference between nodes \(A\) and \(B\) in a circuit is \(v_A - v_B = 5\) V. The work done in moving a charge of \(1\) coulomb from point \(B\) to \(A\) is ____ J. (answer in integer)