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).
The eigen values of the matrix are
$$\begin{bmatrix} \cos\alpha & \sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$$
The Laplace Transform of $x(t)$ formed by convolution operator is :
$$x(t) = \{t \cdot u(t)\} * \{\cos(2\pi t) \cdot u(t)\}$$
A random variable X has $\overline{X} = 0$ & $\sigma_X^2 = 1$. Form a new random variable $Y = 2X + 1$. The values of $\overline{Y}$ & $\sigma_Y^2$ are :
Person X can solve 80% of the ISRO question paper and Person Y can solve 60%. The probability that at least one of them will solve a problem from the question paper, selected at random is :
In an amplitude modulated system if the total power is 600W and the power in the carrier is 400W, the modulation index is
The channel capacity under the Gaussian noise environment for a discrete memoryless channel with a bandwidth of 4MHz and SNR of 31 is.
In satellite communication, frequency modulation is used because satellite channel has
For a 3-μm-diameter optical fiber with core and cladding indexes of refraction of 1.545 and 1.510, respectively. The cut off wavelength is.
A 12-bit ADC is operating with a 1 μs clock period and total conversion time is seen to be 14 μs always. The ADC must be of the type
Consider the analog signal $x(t) = 3\cos(100\pi t)$. If the signal is sampled at 200Hz, the discrete time signal obtained will be
In VHDL all the statements written inside a process statement are
A microprocessor with 12-bit address bus will be able to access _____ kilobytes of memory
A practical current source is usually represented by
The dominant mode in a rectangular wave guide is $\text{TE}_{10}$, because this mode has
A PN junction in series with a 100 ohm resistor is forward biased so that a current of 100 mA flows. If voltage across the combination is instantaneously reversed to 10V at time $t = 0$, the reverse current that flows through the junction at $t = 0$ is approximately given by.
Ripple factor for a half wave rectifier is
_____ is a primitive that can execute code. It contains an instruction pointer (=program counter) and sometimes has its own stack
If $\alpha$ and $\beta$ are the roots of the equation $x^2 - px + q = 0$, then $\sum \alpha^2$ is
A signal $m_1(t)$ is band limited to 3.6 kHz and the three other signals $m_2(t)$, $m_3(t)$ and $m_4(t)$ are band limited to 1.2 kHz each, and these signals are transmitted by means of TDM. Then, what will be the transmission bandwidth of the channel.
For a 10 bit PCM system the signal to quantization noise ratio is 62dB. If the number of bits is increased by 2, then the signal to quantization noise ratio will
The modulation normally used with the digital data is
The critical angle $\theta_c$ in an optical fiber is given by _____ Where $n_1$ is refractive index of medium 1 and $n_2$ is the refractive index of medium 2.
In a JK flip flop we have $J = Q'$ and $K = 1$. Assuming that the flip flop was initially cleared and clocked for 6 pulses, the sequence at the Q output will be
Which of the following system is linear
Which of the following operator cannot be synthesized by VHDL synthesis tools