Recent questions

The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine ...

Which one of the given figures $P, Q, R$ and $S$ represents the graph of the following function?$$f(x)=|| x+2|-| x-1||$$$\text{P}$$\text{Q}$$\text{R}$$\text{S}$

An opaque cylinder $\text{(shown below)}$ is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the dir...

The value of$\lim _{x \rightarrow 0} \frac{1}{x} \int_{2}^{2+x}\left(t+\sqrt{t^{2}+5}\right) d t$$0$$4$$5$$6$

Let $\mathbb{C}=\{z=x+i y: x$ and $y$ are real numbers, $i=\sqrt{-1}\}$ be the set of complex numbers. Let the function $f(z)=u(x, y)+i v(x, y)$ for $z=x+i y \in \mathbb{...

If the partial differential equation$$(x+2) \frac{\partial^2 u}{\partial x^2}+2(x+y) \frac{\partial^2 u}{\partial x \partial y}+2(y-1) \frac{\partial^2 u}{\partial y^2}-3...

Let $\Gamma$ be the positively oriented circle $x^2+y^2=9$ in the $x y$-plane. If$$\oint_{\Gamma}\left(3 y+e^{x \sin x}\right) d x+\left(7 x+\sqrt{e^y+2}\right) d y=\alph...

Let $y_{1}(x)$ and $y_{2}(x)$ be two linearly independent solutions of\[x^{2} \frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+2 y=0, \quad x>0\]Let $W\left(y_{1}, y_{2}\right...

Let $A=\left[\begin{array}{rrrr}2 & 0 & 1 & 1 \\ 1 & 2 & 5 & -5 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 1 & 3\end{array}\right]$Then the sum of the geometric multiplicities of the di...

In a cosmopolitan city, the population comprises of $30 \%$ female and $70 \%$ male. Suppose that $5 \%$ of female and $30 \%$ of male in the population are foreigners. A...

Let $f:(0, \infty) \rightarrow \mathbb{R}$ be the continuous function such that $f(x)=2+\frac{g(x)}{x}$ for all $x>0$, where $g(x)=\int_{1}^{x} f(t) d t$ for all $x>0$. T...

Let $A$ and $B$ be $n \times n$ matrices with real entries.Consider the following statements:P: If $A$ is symmetric then $\operatorname{rank}(A)=$ Number of nonzero eigen...

Let $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ be given by $f(x, y)=4 x y-2 x^{2}-y^{4}+1$. The number of critical points where $f$ has local maximum is equal to

If the quadrature rule$$\int_{-1}^1 f(x) d x \approx f(\alpha)+\gamma f(\beta),$$where $\alpha, \beta$ and $\gamma$ are real constants, is exact for all polynomials of de...

A heavy horizontal cylinder of diameter $D$ supports a mass of liquid having density $\rho$ as shown in the figure. Find out the vertical component of force exerted by th...

The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sect...

The left hand column lists some non-dimensional numbers and the right hand column lists some physical phenomena. Indicate the correct combination1. Reynolds numberi. Wave...

Which of the following statement(s) regarding a venturimeter is/are correct?In the direction of flow, it consists of a converging section, a throat, and a diverging secti...

Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?Two streamlines cannot intersect each other.Flow rate increases between tw...

A flow has a velocity potential given by $\phi=A x^{3}$ where ' $A$ ' is a non-zero constant. Which of the following statement(s) is/are true about the flow?The flow is i...

A boundary layer develops due to a two-dimensional steady flow over a horizontal flat plate. Consider a vertical line away from the leading edge which extends from the wa...

A $10 \mathrm{~kg}$ mass placed on an infinitely long horizontal massless flat platform is to be supported by a steady vertical water jet as shown in the figure. The diam...

Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe.Consider that the density of...

The speed of propagation, $c$, of a capillary wave depends on the density of the fluid, $\rho$, the wavelength of the wave, $\lambda$, and the surface tension, $\sigma$. ...

A two-dimensional flow field is described by a combination of a source of strength $m$ at the origin and a uniform flow, $U$, in the positive $x$-direction such that the ...

A typical boundary layer over a flat plate has a linear velocity profile with zero velocity at the wall and freestream velocity, $U_{\infty}$, at the outer edge of the b...

Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.

Consider steady fully developed flow of a liquid through two large horizontal flat parallel plates separated by a distance of $2 \mathrm{~mm}$. One of the plate is fixed ...

Consider two-dimensional turbulent flow of air over a horizontal flat plate of length $1 \mathrm{~m}$. Skin friction coefficient at a length $x$ from the leading edge of...

For an inviscid fluid with density } 1 \mathrm{~kg} / \mathrm{m}^{3}, \text { the Cartesian velocity field is given as:$\mathbf{u}=(-2 x+y) t \mathbf{i}+(2 x+y) t \mathbf...

Consider a lawn sprinkler with horizontal arms of radius, $a=10 \mathrm{~cm}$ which has water introduced vertically through the centre, as shown in the figure. The exit a...

A wooden cylinder $\text{(specific gravity} $=0.6$)$ of length $L$ and diameter $D$ floats in water $\text{(density}$ $1000 \mathrm{~kg} / \mathrm{m}^3)$. Find out the mi...

A wooden cylinder $\text{(specific gravity}$ $=0.6$ ) of length $L$ and diameter $D$ floats in water $\text{(density}$ $1000 \mathrm{~kg} / \mathrm{m}^3$). Find out the m...

\begin{tabular}{|l|l|}\hline Q.44 & Number of atoms per unit area of the (110) plane of a body centered cubic crystal, \\with lattice parameter ' $a$ ', is \\\hline& $\fr...

Q.45 Match the following materials with their corresponding bonding types.$\mathrm{P}-4 ; \mathrm{Q}-2 ; \mathrm{R}-3 ; \mathrm{S}-1$$\mathrm{P}-3 ; \mathrm{Q}-4 ; \mathr...

In an ideal rubber, the primary factor responsible for elasticity up to small strains isChange in both enthalpy and entropyChange in enthalpy, but no change in the entrop...

Which one of the following statements is true for an intrinsic semiconductor?Electrical conductivity increases with increasing temperature and pressureElectrical conducti...