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Which one of the following figures $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, or S , correctly shows the $45^{\circ}$ clockwise-rotated version of figure $\text{(I)}$?$\text{P...

If $|9y−6| =3$, then $y^{2}-4y/3$ is .$0$$+1/3$$-1/3$undefined

Statement: There were different streams of freedom movements in colonial India carried out by themoderates, liberals, radicals, socialists, and so on.Which one of the fol...

In the summer of $2012,$ in New Delhi, the mean temperature of Monday to Wednesday was $41^{\circ}C$ and of Tuesday to Thursday was $43^{\circ}C$. If the temperature on T...

Two $n \times n$ matrices $A$ and $B$ have a common eigenvalue $2$, and the same corresponding nonzero eigenvector.Which of the following options is/are correct?(Note: $I...

Consider the system of linear equations: $A \boldsymbol{x}=\boldsymbol{b}$, where $A$ is an $n \times n$ matrix, and $\boldsymbol{x}$ and $\boldsymbol{b}$ are $n$-dimensi...

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what perce...

The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students in $2011$ and $2012$ is equal, wh...

For the circuit shown, which one of the following options correctly identifies the Thevenin's equivalent parameters between nodes Y and Z?$\mathrm{V}_{\mathrm{TH}}=100 \m...

The Laplace transform of the step response of a system is given by\[Y(s)=\frac{100}{s(s+100)}\]The rise time is defined as the time taken for the response to go from $0.1...

Instrument(s) required to synchronize an alternator to the grid is/areVoltmeterWattmeterSynchroscopeStroboscope

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

​​​​In the given text, the blanks are numbered $\text{(i)-(iv)}$. Select the best match for all the blanks.Following a row $\text{(i)}$ the shopkeeper $\text{(ii)}$_t...

Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$?$\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axi...

Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is _________________...

The integral\[\frac{1}{\pi} \int_{0}^{\infty} \frac{x^{2026}}{\left(1+x^{2026}\right)\left(1+x^{2}\right)} \mathrm{d} x\]evaluates to $\_\_\_\_$(Round off to two decimal ...

Let $(x, y) \in \Re^{2}$. The rate of change of the real valued function,$V(x, y)=x^{2}+x+y^{2}+1$at the origin in the direction of the point $(1,2)$ is $\_\_\_\_\_\_\_\_...

Let $f\left ( x \right ) = \int_{0}^{x} e^{t}\left ( t-1 \right )\left ( t-2 \right )dt$. Then $f\left ( x \right )$ decreases in the interval$x \in \left ( 1,2 \right )$...

Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its ...

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...