Recent questions

​​​An electricity utility company charges ₹$7$ per kWh (kilo watt-hour). If a $40$ -watt desk light is left on for $10$ hours each night for $180$ days, what would be the...

​​In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled $\text{(i), (ii), (iii)}$, and $\text{(iv...

​​​A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:The sum of Yellow balls and twice the number ...

​​​​​"His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illn...

​​​For the clock shown in the figure, if$ \begin{array}{l} \mathrm{O}^{*}=\mathrm{~O} \mathrm{~Q} \mathrm{~S} \mathrm{~Z} \mathrm{~P} \mathrm{~R} \mathrm{~T}, \text { and...

Consider a five-digit number $PQRST$ that has distinct digits $P,Q,R,S$, and $T$, and satisfies the following conditions:$$\begin{array}{c} P<Q \\ S>P>T \\ R<T \end{array...

A business person buys potatoes of two different varieties $\text{P}$ and $\text{Q}$, mixes them in a certain ratio and sells them at ₹ $192$ per kg.The cost of the varie...

​​Let $X$ and $Y$ be two random variables with mean $0$, variance $1$, and correlation coefficient $\frac{1}{3}$. Then the value of $\operatorname{Var}(X+3 Y)$ is equal t...

​​​​Consider the second order Partial Differential Equation $\textsf{(PDE)}$$$4 x^{2} \frac{\partial^{2} u}{\partial x^{2}}+4(x+y) \frac{\partial^{2} u}{\partial x \parti...

​Consider the infinite series$$ \begin{array}{l} \text { (P) }: \sum_{n=2}^{\infty} \frac{1}{(n \log n)^{1 / n}} \\\text { (Q): } \sum_{n=1}^{\infty} \frac{n^{n}}{(2 n)!}...

​​​​Suppose the polynomial $a+b x+c x^{2}+d x^{3}$ interpolates the data, $(-1,1),(0,3),(1,2)$ and $(2,4)$.Then which one of the following statements is correct?$a=-2 c, ...

​​Let $C$ be the positively oriented boundary of the domain bounded by the curves $y=2 x^{2}$ and $y^{2}=4 x$. Then the value of the line integral$$\oint_{C}\left(2 y^{2}...

Let $y(x)$ be the solution of the initial value problem,$$\begin{array}{c}x^{2} y^{\prime \prime}+x y^{\prime}-y=0, \quad x>0, \\y(1)=0, \quad y^{\prime}(1)=2 .\end{array...

Suppose that $2$ is an eigenvalue of the matrix$$\left[\begin{array}{ccc}0 & 3 & -\alpha \\0 & 1 & 0 \\1 & -1 & 3\end{array}\right]$$Then the value of $\alpha$ is equal t...

​​​​​Let $f(z)$ be an analytic function such that$$ {Re}\left(f^{\prime}(z)\right)=3 x^{2}-4 y-3 y^{2}, f(i)=0, f^{\prime}(0)=0, $$where $i=\sqrt{-1}$. Then the value of ...

​​Consider the function$$ f(x, y)=x^{2} y+2 x y^{2}-2 x^{2} y^{2}.$$Then which one of the following statements is correct?$\left(\frac{3}{2}, 0\right)$ is a point of loca...

​For $a, b \in \mathbb{R}$, consider the system of linear equations$$ \begin{array}{r} x+y+a z=2 \\ 2 y+2 z=1 \\ a x+2 z=b \end{array}$$If the system has infinitely many ...

Let $u(x, t)$ be the solution of the initial boundary value problem$$ \begin{array}{c}\frac{\partial u}{\partial t}-\frac{\partial^{2} u}{\partial x^{2}}-u=0, \quad 0< x ...

​​​Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.Which one of the following optio...

​​​A sharp flat plate of length $L$ and infinite width is immersed parallel to a fluid stream having velocity $u_{\infty}$. At a point on the plate, far away from the lea...

​Consider the following Statements $ $ and $ $.Statement $ $: The Eulerian study focusses attention on individual particle and its motion is observed as a function of tim...

​​​Statement of Reynolds Transport Theorem is given below with three blanks.The rate of change of $\_\_\_\_\_$ extensive property can be calculated by summing the rate of...

​​​For a steady and incompressible flow, the velocity field $(\vec{V})$ in Cartesian $(x, y, z)$ coordinate system is given as:$$\vec{V}=5 x i-P y j+3 k$$Here, $i, j$, an...

​​​Conservation of mass for a steady axisymmetric flow field in the cylindrical $(r, z)$ coordinates is:$$\frac{1}{r} \frac{\partial\left(r V_{r}\right)}{\partial r}+\fra...

​​$\textbf{Group-I}$ indicates different properties of fluid and $\textbf{Group-II}$ defines their basic dimensions in terms of Force $(F)$, Length ( $L$ ), and Time ( $T...

​​​Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, $\Delta P$ is the pressure drop in the direction of the...

​A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together.Which one of the following options correctly represents the natur...

​​​Figure shows two parallel plates (upper plate at $x=b$ and lower one at $x=-b$ ) of length $L$ (aligned in $z$ direction) and infinite width (in $y$ direction, normal ...

​​​​$\textbf{Group-I}$ shows different two-dimensional bodies and $\textbf{Group-II}$ mentions their total drag coefficient $\left(C_{D}\right)$ based on frontal area whi...

​​​​A solid body of uniform specific gravity floats in a deep liquid pool. Take $B, G$, and $M$ as the centre of buoyancy, centre of gravity, and metacentre of the body, ...

Figure shows the steady and incompressible flow of a fluid in the direction of arrow from section $A$ to section $D$. Three pipe connectors are to be placed between secti...

​​​A liquid flows under steady and incompressible flow conditions from station $1$ to station $4$ through pipe sections $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and $\mathrm...

Consider, $i$ and $j$ are unit vectors along $x$ and $y$ directions of a Cartesian $(x, y)$ coordinate system, respectively and $t$ is time. Temperature ($T$) and fluid v...

Driven by a pressure gradient of $100 \mathrm{kPa} / \mathrm{m}$, a fluid of dynamic viscosity $0.1 \mathrm{~Pa.s}$ flows between two fixed infinitely large parallel plat...

An incompressible fluid is flowing between two infinitely large parallel plates separated by $5 \mathrm{mm}$ distance. The bottom plate is stationary and the top plate is...

Consider, a kite weighing $100$ grams as essentially a rigid flat plate making an angle $8^{\circ}$ with the horizontal and having a planform area of $0.045 \mathrm{~m}^{...

A fixed control volume has four one-dimensional boundary sections $(1,2,3$, and $4$). For a steady flow inside the control volume, the flow properties at each section are...

A ship is to be operated in a fluid medium with kinematic viscosity $0.032 \times 10^{-3} \mathrm{~m}^{2} / \mathrm{s}$. A one-tenth scale model of the ship is built for ...

Water flows through a pipe of diameter $20 \mathrm{cm}$ at a flow rate of $0.025 \mathrm{~m}^{3} / \mathrm{s}$. A pitotstatic tube is placed at the centre of the pipe and...