List of top Questions asked in GATE Instrumentation Engineering

When the bridge shown is balanced, the current through the resistor $R_a$ is________ mA (rounded off to two decimal places). The bridge has $R_a=R_b=R_c=10~\mathrm{m}\Omega$ and the detector (galvanometer) is ideal/open at balance; the source is $1~\text{V}$.

In the circuit shown, the Thevenin equivalent resistance $R_{\text{th}}$ across the terminals ‘a’ and ‘b’ is ______ $\Omega$ (rounded off to one decimal place).

$X$ is a discrete random variable taking values $0,1,2$ with $P(X=0)=0.25$, $P(X=1)=0.5$, and $P(X=2)=0.25$. With $E[ . ]$ denoting expectation, compute $E[X]-E[X^2]$ (rounded off to one decimal place).

The diode in the circuit is ideal. The current source $i_s(t)=\pi\sin(3000\pi t)$ mA. The magnitude of the average current flowing through the resistor $R$ is _____ mA (rounded off to two decimal places).

The number of zeros of the polynomial $P(s) = s^3 + 2s^2 + 5s + 80$ in the right-half plane is _____.

The number of times the Nyquist plot of \(G(s)H(s)=\dfrac{1}{2}\,\dfrac{(s-1)(s-2)}{(s+1)(s+2)}\) encircles the origin is ____.

The op-amp (ideal except \(I_b=1\,\text{nA}\) input bias current and \(V_{\!os}=10\,\mu\text{V}\) input offset) is the inverting amplifier with \(R_{\text{in}}=1~\text{k}\Omega\) and \(R_f=100~\text{k}\Omega\). Find the worst-case output offset voltage \((\pm~\mu\text{V})\) (rounded to the nearest integer).

The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them, is 10 $\mu$N/m. When the gap is doubled, the force per unit length will be _____ $\mu$N/m (rounded off to one decimal place).

A light emitting diode (LED) emits light when it is ____} biased. A photodiode provides maximum sensitivity to light when it is ____ biased.

$F(z)=\dfrac{1}{1-z}$, when expanded as a power series around $z=2$, would result in $F(z)=\sum_{k=0}^{\infty} a_k (z-2)^k$ with ROC $|z-2|<1$. The coefficients $a_k,\;k\ge 0$, are given by the expression ________.

The solution $x(t)$, $t\ge 0$, to $\ddot{x}=-k\dot{x}$ ($k>0$) with $x(0)=1$ and $\dot{x}(0)=0$ is:

A system has the transfer function $\dfrac{Y(s)}{X(s)}=\dfrac{s-\pi}{s+\pi}$. Let $u(t)$ be the unit–step function. The input $x(t)$ that results in a steady–state output $y(t)=\sin(\pi t)$ is _____.

Choose the fastest logic family among the following:

Choose solution set $S$ corresponding to the system of two equations \[ x-2y+z=0,\qquad x-z=0 \] (Note: $\mathbb{R}$ denotes the set of real numbers).

Inductance of a coil is measured as $10\,\text{mH}$ using an LCR meter at $10\,\text{kHz}$, when no objects are near the coil. If a pure copper sheet is brought near the coil, the same LCR meter will read _________.

Which of the following flow meters offers the lowest resistance to the flow?

Pair the quantities (p) to (s) with the measuring devices (i) to (iv).

The table shows the present state $Q(t)$, next state $Q(t{+}1)$, and a single control input for a flip-flop. Identify the flip-flop.

Match the Exclusive-OR (XOR) operations (i)–(iv) with the results (p)–(s), where $X$ is a Boolean input.