List of top Questions asked in GATE IN

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 _____.

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)

Four people P, Q, R, and S, of different ages, make the following observations.
P: I am younger than S.
Q: I am neither the youngest nor the oldest.
R: P is older than me.
Based on these observations, the youngest person is ______.

The maximum signal to quantization noise ratio (SQNR) for a \(16\)-bit analog-to-digital converter is approximately _________ dB.

Given two signals: \(x(t)=u(t-2)-u(t-3)\), and \(y(t)=e^{-4t}u(t)\).
If \(z(t)=x(t)*y(t)\), then \(Z(s)\) is ______.

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

In the circuit shown, the BJT has a \(\beta\) of \(100\). The base-emitter junction voltage is \(0.65\) V. The quiescent collector current, \(I_C\), is _______ mA.

A coin with heads facing up is shown as a circled letter "H", and a coin with tails facing up is shown as a circled letter "T".
Six coins are placed in the Starting Arrangement, as shown in the figure below. A "step" is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.

An analog speech signal contains signals from \(200\) Hz to \(2400\) Hz. It is sampled at \(6\) kHz and quantized with \(512\) levels for pulse code modulation (PCM). The bit rate will be _____ kbps.

To continue the sequence of tiles shown, the tile indicated by the question mark should be:

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

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

A signal \(x(t)\) is shown below.

The plot of \(y(t)=1-x(4-t)\) is shown in ______.

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?

Suresh said, "I did it yesterday."
Which one of the following options is the correct form of this sentence in indirect speech?

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 linear time invariant (LTI) system has a transfer function \[ G(s)=\frac{10(s+1)}{s(s^2+2s+5)} \] The system is placed in unity negative feedback configuration.
For a unit ramp reference, the steady state error is ________. (rounded off to two decimal places)

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).

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 ____.

In the circuit shown below, \(R\) is \(1\ \text{k}\Omega\) and \(R_f\) is \(10\ \text{k}\Omega\). If \(V_{in}\) is \(100\) mV and the op-amps have supply voltages of \(\pm15\) V, then \(V_{out}\) is ______ V.

A linear time invariant (LTI) system is described by:
\[ \begin{bmatrix}\dot{x}_1\\ \dot{x}_2\end{bmatrix}=\begin{bmatrix}0 & 1\\ -10 & -7\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}+\begin{bmatrix}1\\ 1\end{bmatrix}u \]
\[ y=\begin{bmatrix}1 & 1\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix} \]
The poles of the system are ______.

The system \[ G(s)=\frac{K}{(s+1)^4} \] has a gain margin of 20 dB. The value of \(K\) is ________. (rounded off to two decimal places)

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,
1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.
Then the number of patients who have both diabetes and high BP is _______

Exacerbate : Mitigate :: ___________
Choose the option with the correct pair of words to fill the blank.

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 \(\_\_\_\_\_\).