Recent questions and answers

A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited $\text{DC}$ motor with the following specifications:Rat...

​​​​​If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [talk $\rightarrow$ shout $\rightarrow$ scream] is analogous to [please $\r...

If $p, q, r, s$ are distinct integers such that:$f(p, q, r, s) = \max (p, q, r, s)$$g(p, q, r, s) = \min (p, q, r, s)$$h(p, q, r, s)$ = remainder of $(p \times q) / (r \t...

Consider the following equation in a $2-\text{D}$ real-space. $\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ Which of the following statement(s) is/a...

Let $\boldsymbol{A}=\left[\begin{array}{ccc}1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1\end{array}\right]$, and $\boldsymbol{b}=\left[\begin{array}{c}1 / 3 \\ -1 / 3 \\ 0\end...

For a given vector $\mathbf{w}=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{\mathrm{T}}$, the vector normal to the plane defined by $\mathbf{w}^{\mathrm{T}} \math...

The sum of the eigenvalues of the matrix $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{2}$ is ____________(rounded off to the nearest integer).

Let $P=\left[\begin{array}{ccc}2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$ and let $I$ be the identity matrix. Then $P^{2}$ is equal to$2 P-I$$P$$I$$P+I$

Let $v_{1}$ and $v_{2}$ be the two eigenvectors corresponding to distinct eigenvalues of a $3 \times 3$ real symmetric matrix. Which one of the following statements is tr...

Consider a matrix $A = \begin{bmatrix} 1 & 0 & 0\\ 0 & 4 & -2\\ 0 & 1 & 1 \end{bmatrix}$.The matrix $A$ satisfies the equation $6A^{-1} = A^{2} + cA + dl$, where $c$ and ...

Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$...

The three roots of the equation $f(x) = 0$ are $x = {−2, 0, 3}.$ What are the three values of $ x $ for which $f(x − 3) = 0?$$−5 , −3 , 0 $ $−2 , 0 , 3$$0 , 6 ,...

The open-loop transfer function of the system shown in the figure, is$$ G(s)=\frac{K s(s+2)}{(s+5)(s+7)}$$For $K \geq 0$, which of the following real axis point(s) is/are...

Suppose signal $y(t)$ is obtained by the time-reversal of signal $x(t)$, i.e., $y(t)=x(-t),-\infty<t<\infty$. Which one of the following options is always true for the co...

The I-V characteristics of the element between the nodes X and Y is best depicted by 

The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$$3te^{-t}+e^{-t}$$3e^{-t}$$2te^{-t}+e^{-t}$$4te^{-t}+e^{-t}$

Scores obtained by two students $P$ and $Q$ in seven courses are given in the table below. Based on the information given in the table, which one of the following stateme...

Consider the set $S$ of points $(x, y) \in \mathfrak{R}^{2}$ which minimize the real valued function$$ f(x, y)=(x+y-1)^{2}+(x+y)^{2}$$Which of the following statements is...

After Rajendra Chola returned from his voyage to Indonesia, he ________ to visit the temple in Thanjavur.Was wishingIs wishingWishedHad wished

The data given in the following table summarizes the monthly budget of an average household.$$\begin{array}{|l|c|c|} \hline \textbf{Category} & \textbf{Amount(Rs.)} \\\hl...

"The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history."Which of the following sta...

If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE?$f(a) . f(b)=0$$f(a) . f(b) < 0$$f(a) . ...

If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$$2.23$$4.33$$11.37$$27.64$

What is the value of $\left(\frac{3^{81}}{27^{4}}\right)^{\frac{1}{3}}$ ?$3^{13}$$3^{96}$$3^{23}$$3^{69}$

Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round o...

The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$

Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is$e^{-1}$$e$$1-e^{-1}$$1+e^{-1}$

The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is$20$$28$$16$$32$

Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to$-\infty$$0$$1$$\infty$

The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.

Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).

For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively...

Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right ) 0$ fo...

A function $f(x)$ is defined as$f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$Which one of the followin...

In the given figure, $EF$ and $HJ$ are coded as $30$ and $80$, respectively. Which one among the given options is most appropriate for the entries marked $(i)$ and $(ii)$...

The condensers of 30μF & 60μF capacitances are connected in series across a 180V supply. After charging they are removed from the supply and are connected in parallel wit...

​​​​In the following figure,\[\begin{array}{c}\mathrm{CD}=5 \mathrm{~cm}, \mathrm{BE}=10 \mathrm{~cm}, \mathrm{AE}=12 \mathrm{~cm}, \\\angle \mathrm{DAB}=\angle \mathrm{D...

The relationship between two variables $x$ and $y$ is given by $x+p y+q=0$ and is shown in the figure. Find the values of $p$ and $q$.Note: The figure shown is representa...