Recent questions and answers

In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross $(X)$ or a number, as per the given rule.\begin{array}{|l|l|l|l|}\hline 1 &...

If $y=5x^{2}+3,$ then the tangent at $x=0,y=3$passes through $x=0,y=0$has a slope of $+1$is parallel to the $x$-axishas a slope of $-1$

A system of $n$ homogeneous linear equations containing $n$ unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is$1$$-1$$0$...

For the matrix $A=\begin{bmatrix} \cos\theta &-\sin\theta \\ \sin \theta & \cos\theta \end{bmatrix}$ if $\det$ stands for the determinant and $A^{T}$ is the transpose of ...

If a matrix $M$ is defined as $M=\left[\begin{array}{cc}10 & 6 \\ 6 & 10\end{array}\right]$, the sum of all the eigenvalues of $M^3$ is equal to______________(in integer)...

Consider the matrix$$A=\left[\begin{array}{ll} 2 & 3 \\ 1 & 2\end{array}\right]$$The eigenvalues of the matrix are $0.27$ and $\_\_\_\_$ (rounded off to $2$ decimal place...

​​Schmidt number is defined as$\frac{\text { Mass Diffusivity }}{\text { Thermal Diffusivity }}$$\frac{\text { Momentum Diffusivity }}{\text { Mass Diffusivity }}$$\frac{...

​​A thin wire is used to construct all the edges of a cube of $1 \: \mathrm{m}$ side by bending, cutting and soldering the wire. If the wire is $12 \: \mathrm{m}$ long, w...

​​​A probability distribution function is given as$$p(x)=\left\{\begin{array}{ll} \frac{1}{a}, & x \in(0, a) \\ 0, & \text { otherwise } \end{array}\right.$$where $a$ is ...

A polygon is convex if, for every pair of points, $P$ and $Q$ belonging to the polygon, the line segment $PQ$ lies completely inside or on the polygon. Which one of the f...

In a 1-1 pass floating head type shell and tube heat exchanger, the tubes (od = 25 mm; id = 21 mm) are arranged in a square pitch. The tube pitch is 32 mm. The thermal co...

Pipes $\text{P}$ and $\text{Q}$ can fill a storage tank in full with water in $10$ and $6$ minutes, respectively. Pipe $\text{R}$ draws the water out from the storage tan...

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of th...

​​​​In industrial heat exchanger design, the overall heat transfer coefficient $U$ is estimated from the equation$$ \frac{1}{U}=\frac{1}{h_{i}}+\frac{1}{h_{o}}$$where $h_...

Is there any good show $\_\_\_\_\_\_$ television tonight?Select the most appropriate option to complete the above sentence.inatwithinon

​​​​As the police officer was found guilty of embezzlement, he was $\_\_\_\_\_\_$ dismissed from the service in accordance with the Service Rules.Select the most appropri...

The value of $\underset{x\rightarrow 0}{\lim}\:\frac{\tan\left ( x \right )}{x}$ is ________________.

If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________

​​​​​In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from $301$, while the house...

An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring as shown in the figure. The piston is frictionless and massless. The ...

In the elutriation leg of a commercial crystallizer containing a mixture of coarse and very fine crystals of the same material, a liquid is pumped vertically upward. The ...

​​​​A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).Which one of the following opt...