Prepare for ISRO ICRB examinations with verified solutions covering Algorithms, Theory of Computation, Compiler Design, Computer Architecture, OS, Discrete Mathematics, and Computer Networks.
Marking scheme: +3.00 positive, -0.75 negative (ICRB Standard).
For $-\infty < x < \infty$ & $-1 < y < 1$, the partial differential equation
$$x^{2}\frac{\partial^{2}u}{\partial x^{2}} + (1-y^{2})\frac{\partial^{2}u}{\partial y^{2}} = 0$$
is
A CMOS digital circuit consumes $P$ watts of dynamic power while operating at 20 MHz clock frequency and 5V supply. What will be its dynamic power consumption if the clock frequency is increased to 40 MHz and supply voltage is decreased to 2.5V?
A communication channel with Additive White Gaussian Noise, has a bandwidth of 4 kHz and SNR of 31dB. Its channel capacity is
If the total power of an amplitude modulated signal is 600W and the carrier power is 400W, the modulation index is
What is the advantage of Offset QPSK (OQPSK) compared to conventional QPSK?
An angle modulated signal with carrier frequency $\omega_{c}=2\pi\times10^{5}$ is described by the equation
$$s(t)=10\cos(\omega_{c}t+5\sin(3000\pi t)+10\sin(2000\pi t))$$
What is the frequency deviation $\Delta f$?
The Fourier transform of a signal $x(t) = e^{-4|t|}$ is
What is the output waveform Vo for a sinusoidal input of peak-peak amplitude of 4V. Assume that Z1 and Z2 are two identical Zener diodes of 4.7V, and R1=10kohm and R2=20kohm.
For a particular toroidal inductor core, the inductance value obtained for 50 Turns is 200μH. If two such inductors are wired in parallel, the resulting inductance is
The magnetic equivalent of Ohm's Law is
It is required to design a class B output stage (as shown below) to deliver an average output power of 12.5W to a load of 4Ω. The power supply is selected so that Vce is 5V greater than the peak output voltage. Determine the power conversion efficiency of the circuit.
Which type of circuit has an input impedance as shown in this polar plot?
A coaxial transmission line carrying an RF signal is perfectly matched to the load. Consider the cross-section of the line, at a plane where the instantaneous voltage is at its maximum value. How will the curl of the E-field vary over this cross-section?
The continuity of the tangential field component at the interface of two media for normal incidence of a plane wave requires
Which mode of a circular waveguide will have the lowest attenuation?
If $\varphi = 2x^{2}y - xz^{3}$, then the Laplacian of $\varphi$ is
What does the following integral evaluate to?
$$\int_{0}^{\pi/2} \sin^{6}\theta \, d\theta$$
A signal with two frequency components at 6 kHz and 12 kHz, is sampled at the rate of 16 kHz and then passed through a Low Pass filter having a cut-off frequency of 16 kHz. The output signal of the filter
What is the greatest allowable PRF for unambiguous reception in a radar having a maximum range of 120 km?
A microprocessor has a cache memory with access time of 2 ns and a main memory with access time of 10 ns. If the cache miss ratio is 0.6, what is the average memory access time?
Consider the following assembly code for a hypothetical RISC processor with a 4-stage pipeline (Instruction Fetch, Decode/Register Read, Execute and Write).
add r1, r2, r3 // r1 = r2 + r3 sub r4, r1, r3 // r4 = r1 - r3 mul r5, r2, r3 // r5 = r2 * r3
Identify the possible pipeline hazard and the affected instruction.
A zero memory source emits six messages with probabilities 0.3, 0.25, 0.15, 0.12, 0.1 and 0.08. If binary Huffman coding is used, what will be the average code length?
In the circuit given below, assume that $Vcc=15V$; Z1, Z2, Z3 & Z4 are identical zener diodes with breakdown voltage of 5V; $R1=R4=5k\Omega$, $R2=R3=10k\Omega$. Find Vo when Q1 is OFF.
Assume that $Vi=2V$; $R3=10\Omega$; $\beta$ of $Q1=50$; $V_{CC}=15V$. Find $I_{\text{out}}$.
A sample and hold amplifier is connected to an ADC. The acquisition time of the sample and hold amplifier is 10 μsec and the conversion time of the ADC is 15 μsec. What is the highest possible data rate?