Recent questions tagged gate1993-ec

The built-in potential (Diffusion Potential) in a $p-n$ junctionis equal to the difference in the Fermi level of the two sides, expressed in voltsincreases with the incre...

The eigenvector(s) of the matrix $\left(\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right), a \neq 0$, is (are)$(0,0, \alpha)$$(\alpha, 0,0)$$(0,0,1)...

The differential equation, $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}+\sin$ $y=0$, islinearnon-linearhomogeneousof degree two

Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$

Which of the following is (are) valid $\text{FORTRAN} 77$ statement(s)?$\mathrm{DO} \; 131=1$$\mathrm{A}=\mathrm{DIM}^{* * *} 7$$\text{READ}$ $=15.0$$\text{GOTO}$ $3=10$

Fourier series of the periodic function (period $2 \pi$ ) defined by$f(x)=\left\{\begin{array}{ll}0 & -\pi < x<0 \\ x & 0<x<\pi\end{array}\right.$ is$\frac{\pi}{4}+\sum_1...

Which of the following improper integrals is (are) convergent?$\int_{0}^{1} \frac{\sin x}{1-\cos x} d x$$\int_{0}^{\infty} \frac{\operatorname{cox} x}{1+x} d x$$\int_{0}^...

The function $f(x, y)=x^{2} y-3 x y+2 y+x$, hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum and one loca...

The radius of convergence of the power series$\sum_{0}^{\infty} \frac{(3 m) !}{(m !)^{3}} x^{3m}$ is ___________.

If the linear velocity $\overrightarrow{\mathrm{V}}$ is given by $\overrightarrow{\mathrm{V}}=x^{2} y \hat{i}+$ $x y z \hat{j}-y z^{2} k$ the anguarl velocity $\vec{w}$ a...

Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the sec...

For $\mathrm{X}=4.0$, the value of $1$ in the $\text{FORTRAN}$ $77$ statement$I=-2^{* *} 2+5.0 ^* X / X ^* 3+\frac{3}{4} \text { is}$___________.

The value of the double integral $\int_{0}^{1} \int_{x}^{1 / x} \frac{x}{1+y^{2}}$ $d x d y$ is

If $\mathrm{A}=\left(\begin{array}{cccc}1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i\end{array}\right)$the matrix $\mathrm{A}^{4}$, calculated by t...

Given, $\mathrm{V}=x \cos ^{2} y \hat{i}+x^{2} e^{x} \hat{j}+z \sin ^{2} y \hat{k}$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to...

The differential equation $y+y=0$ is subjected to the boundary conditions\[y(0)+0 y(\lambda)=0\]In order that the equation has non-trivial solution (s), the general value...

The Laplace transform of the periodic function $f(t)$ described by the curve below, i.e.$f(t)=\left\{\begin{array}{c}\sin t \text { if }(2 n-1) \pi \leq t \leq 2 n \pi(n=...

Two particles of masses $M_{1}$ and $M_{2}\left(M_{1}>M_{2}\right)$ attract each other with a force inversely proportional to the square of the distance between them. The...

The temperature of an ideal gas is held constant while its volume is increased. The pressure exerted by the gas on the walls of the container decreases because its molecu...

Although a laser beam is highly directional, its beam width increases with propagation. This increase is due tocoherencediffractionpolarizationinterference

A plane electromagnetic wave of the form $\vec{E}=\hat{y} E_{0}\left[\cos 2 \pi\left(5 \times 10^{14} \sec ^{-1}\right) t-\left(2.5 \times 10^{6} \mathrm{~m}^{-1}\right) ...

While you are listening to a programme from a radio, if a near-by electric light bulb is switched on or switched off, you hear a momentary noise in your radio. This is du...

Nuclear fusion reactions require very high temperatures so as to overcome.nuclear forcesvan der waals forcescoulomb forcesgravitational forces

In radioactive decay, the disintegration rate of the nuclei isconstant at all timesinversely proportional to half-life of the nucleiinversely proportional to the number o...

In an hydrogen atom $10.2 . \mathrm{eV}$ is given out as radiation when an electron is de-excited to the ground state. The principal quantum number of the excited state i...

Typical current voltage characteristic of a solar cell is given in the following figure bycurve $A$curve $B$curve $C$curve $D$

An optical fiber consists of a cylindrical dielectric rod of refractive index $\mathrm{n}^{1}$, surrounded by another dielectric of refractive index $n^{2}$, where $n^{2}...

For a uniformly charged sphere of radius $R$ and charge density $\rho$, the ratio of magnitude of electric fields at distances $R / 2$ and $2 R$ from the centre, i.e., $\...