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A wave travelling along the x-axis is described by the equation $y(x,t)=0.005cos(αx−βt)$. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $αandβ$ in appropriate units are

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Bakelite is obtained from phenol by reacting with

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range $0≤r<∞$, where r is the distance from the centre of the shell ?

The coodination number and the oxidation state of the element 'E' in the complex $[E(en)_{2}(C_{2}O_{4})]NO_{2}$ (where (en) is ethylene diamine) are, respectively,

Let R be the real line. Consider the following subsets of the plane $R×R$.$S={(x,y):y=x+1and0<x<2},T={(x,y):x−y$is an integer }. Which one of the following is true?

The ellipse $x_{2}+4y_{2}=4$is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

Consider a family of circles which are passing through the point $(−1,1)$and are tangent to x-axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

Given $P(x)=x_{4}+ax_{3}+cx+d$such that $x=0$is the only real root of \displaystyle{P}'{\left({x}\right)}\text{}=\text{}{0}.\text{}{I}{f}\text{}{P}

Due to the presence of the current \displaystyle{I}_{}