List of practice Questions

Which type of charts are used in Boolean function simplification?

Which flip flop is used as a push button switch?

How many NAND gates are required to implement a full adder?

What is the product of \[ 1.11\times2^3 \] and \[ 1.0101\times2^6 ? \]

How many different strings can be made by reordering the letters of the word SUCCESS?

What is the solution of the recurrence relation \[ a_n=6a_{n-1}-9a_{n-2} \] with initial conditions \[ a_0=1,\qquad a_1=6? \]

What is \(R^3\) of \[ R=\{(1,1),(2,1),(3,2),(4,3)\}? \]

How many relations are there on a set with \(3\) elements?

What is the Four Colour Theorem?

The probability density function of a continuous random variable is \[ f(x)= \begin{cases} \dfrac35 e^{-3x/5}, & x>0 \\ 0, & x\le0 \end{cases} \] The mean of the distribution is

For a Binomial distribution, mean is \(15\) and variance is \(6\). If \[ P(X\ge2) = 1-\left(\frac25\right)^{25}k, \] then \(k=\)

Which among the following represents idempotent law?

Let \(f\) and \(g\) be the functions from the set of integers to the set of integers defined by \[ f(x)=2x+3 \] and \[ g(x)=3x+2. \] What is the composition of \(f\) and \(g\)?

Suppose that there are eight runners in a race. The winner receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. How many different ways are there to award these medals, if all possible outcomes of the race can occur and there are no ties?

On the Argand plane, eigenvalues of any unitary matrix lie on

If \(\alpha, \beta\) are two distinct eigenvalues of a matrix \(A\), then the corresponding eigenvectors are

\(f:\mathbb{R}\rightarrow\mathbb{R}\) is increasing in \((-\infty,0)\cup(1,\infty)\) and decreasing in \((0,1)\). If \(f(2)=6\) and the continuous curve \(y=f(x)\) passes through \((0,0)\), then

Evaluate \[ \int_{-1}^{1}\frac{x^{2}\sin x}{x^{4}+1}\,dx. \]

The maximum value of \(x^{4}y^{3}\) such that \(x+y=42\) exists at \(x=\alpha,\; y=\beta\). Then \(\dfrac{\alpha}{\beta}\) in its lowest form is

Given \[ P(A)=\frac{7}{20}, \quad P(B)=\frac{1}{2}, \quad P(C)=\frac{9}{20}, \] \[ P(A\cap B\cap C)=\frac{1}{20}, \quad P(A\cap B)=\frac{3}{20}, \] \[ P(A\cap C)=\frac{1}{8}, \quad P(B\cap C)=\frac{1}{5}, \] then \(P(B|\overline{A})\) is

If \(Z\) is a standard normal variable, \[ P(Z>z_1)=\alpha, \] \[ P(Z<z_2)=\beta \] and \(z_2<z_1\), then a possible value of \[ P(z_2<Z<z_1) \] is

For a lossy transmission line, the characteristic impedance does not depend on

A rectangular waveguide with dimensions \(a=2.5\) cm, \(b=1\) cm is operating below 15 GHz. If the guide is filled with a medium characterized by \(\sigma=0\), \(\epsilon=4\epsilon_0\), \(\mu_r=1\), calculate the cutoff frequency of dominant mode?

Find the maximum gain of a \(\frac{\lambda}{2}\) wire dipole operating at 30 MHz?

The S-parameters are used at microwave frequencies because of the following reasons, except