GATE IN 2025 Question Paper (01-Feb-2025) (Shift 2)

An oscilloscope has an input resistance of $1$ M$\Omega$. A $10$ X passive attenuating probe is connected to it to increase the input voltage range as well as the effective input resistance. The effective input resistance, in M$\Omega$, seen into the probe tip is

For the transfer function $G(s)=1+\frac{2s-1}{s^3+5s^2+3s+22}$, the number of zeros lying in the left half of the s-plane is

Consider the control system block diagram given in Figure (a). The loop transfer function $G(s)H(s)$ does not have any pole on the $j\omega$ -axis. The counterclockwise contour with infinite radius, as shown in Figure (b), encircles two poles of $G(s)H(s)$. Choose the correct statement from the following options for closed loop stability of the system.

A Boolean function $X$ is given as $X=\bar{A}\bar{B}+\bar{A}\bar{C}$. The reduced form of $\bar{X}$ is

A $60$ V DC source with an internal resistance $R_{int}=0.5\Omega$ is connected through a switch to a pair of infinitely long rails separated by $l=1$ m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density $B=0.5$ T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is
Note: Assume there is no friction between the bar and the rails. The resistances of the conducting bar and the rails are zero.