List of top Questions asked in GATE IN

The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are

For a 4-bit Flash type Analog to Digital Converter (ADC) with full scale input voltage range "V", which of the following statement(s) is/are true?

A 16-bit microprocessor has twenty address lines (A0 to A19) and 16 data lines. The higher eight significant lines of the data bus of the processor are tied to the 8-data lines of a 16 Kbyte memory that can store one byte in each of its 16K address locations. The memory chip should map onto contiguous memory locations and occupy only 16 Kbyte of memory space. Which of the following statement(s) is/are correct with respect to the above design?

Let \( u(t) \) denote the unit step function. The bilateral Laplace transform of the function \( f(t) = e^t u(-t) \) is \(\underline{\hspace{2cm}}\) .

Input-output characteristic of a temperature sensor is exponential for a

The signal \( \sin(\sqrt{2\pi t}) \) is

Consider the sequence \[ x_n = 0.5x_{n-1} + 1, n = 1, 2, \ldots \text{ with } x_0 = 0. \text{ Then } \lim_{n \to \infty} x_n \text{ is} \]

An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates \( (r, \phi, z) \), at any point \( \mathbf{P} \) not on the z-axis, the direction of the electric field is

In an ac main, the rms voltage \( V_{ac} \), rms current \( I_{ac} \) and power \( W_{ac} \) are measured as:
\( V_{ac} = 100 \, \text{V} \pm 1% \), \( I_{ac} = 1 \, \text{A} \pm 1% \), \( W_{ac} = 50 \, \text{W} \pm 2% \)
The percentage error in calculating the power factor using these readings is

Consider the row vectors \( v = (1, 0) \) and \( w = (2, 0) \). The rank of the matrix \[ M = 2v^T v + 3w^T w \] where the superscript \( T \) denotes the transpose, is

A function, \( \lambda \), is defined by \[ \lambda ( p,q ) = \begin{cases} (p - q)^2, & \text{if } p \geq q, \\ p + q, & \text{if } p < q. \end{cases} \] The value of the expression \( \dfrac{\lambda ( -(-3 + 2), (-2 + 3) )}{( -(-2 + 1) )} \) is:

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above. The value of \( \theta \), in degrees, is

Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is:

Given two operators \( \oplus \) and \( \odot \) on numbers \( p \text{ and } q \) such that \[ p \oplus q = \frac{p^2 + q^2}{pq} \text{and} p \odot q = \frac{p^2}{q}, \] if \( x \oplus y = 2 \odot 2 \), then \( x = \)