List of top Questions asked in GATE IN- 2026

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

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

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?

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 _______

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

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

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?

The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

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 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 a series \(RL\) circuit shown in the figure, the current through the resistor lags the AC source voltage by \(45^{\circ}\). Let \(R = 100\pi\) \(\Omega\) and \(L = 2\) H.

The frequency of the source is ____ Hz. (rounded off to the nearest integer)

A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a ________.

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)

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

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

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.

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 ______.

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

Let \[ f(t)= \begin{cases} 1, & t\in[0,2] \\ -t+3, & t\in[2,3] \\ 0, & \text{otherwise} \end{cases} \] Then \[ \int_{-\infty}^{\infty} f(\tau)\,d\tau = \_\_\_\_\_. \] (rounded off to one decimal place)

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.

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)

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 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 ____.

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 __________.

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) ___.

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).