A potentiometer wire of length \(10 \,m\) and resistance\(20 \,\Omega\) is connected in series with a \(25 \,V\) battery and an external resistance \(30\, \Omega\). A cell of emf \(E\) in secondary circuit is balanced by \(250\, cm\) long potentiometer wire. The value of \(E\) (in volt) is \(\frac{x}{10}\). The value of \(x\) is.......

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

A helicopter is flying horizontally with a speed \('v'\) at an altitude \('{h}'\) has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

Two open organ pipes of length \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _______ \(\mathrm{Hz}\). (Velocity of sound in air \(=333 \mathrm{~m} / \mathrm{s}\) )

A bi-convex lens has radius of curvature of both the surfaces same as \(1 / 6 \mathrm{~cm}\). If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides \(\left(R_1 \neq R_2\right)\), without any change in lens power then possible combination of \(R_1\) and \(R_2\) is :

In the figure shown, what is the current (in Ampere) drawn from the battery ? You are given \(R_1 = 15\,\Omega \)\(,R _2 = 10\,\Omega ,\)\( R_3 = 20\,\Omega ,\)\( R_4 = 5\,\Omega ,\)\(R_5 = 25\,\Omega ,\)\(R_6 = 30\,\Omega , \)\(E = 15\,V\)

Four identical particles of mass \(M\) are located at the corners of a square of side \(‘a’\). What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by \(4\, \%\), will be ......... \(\%\)

A bag contains \(30\) white balls and \(10\) red balls. \(16\) balls are drawn one by one randomly from the bag with replacement. If \(X\) be the number of white balls drawn, then \(\left( {\frac{{{\rm{mean\, of\, X}}}}{{{\rm{standard\, deviation\, of\, X}}}}} \right)\) is equal to

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

The position vectors of two 1 kg particles, (A) and (B), are given by
\(\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m}\) and \(\overrightarrow{\mathrm{r}}_{\mathrm{B}}=(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}\) \(+\beta_3 \mathrm{t} \hat{k}) \mathrm{m}\), respectively; \((\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s},\) \(\alpha_3=2 \mathrm{~m} / \mathrm{s},\) \(\beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{pm} / \mathrm{s})\), where t is time, n and p are constants. At \(t=1 \mathrm{~s},\left|\overrightarrow{V_A}\right|=\left|\vec{V}_B\right|\) and velocities \(\vec{V}_A\) and \(\vec{V}_B\) of the particles are orthogonal to each other. At \(t=1 \mathrm{~s}\), the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is \(\sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}\). The value of L is _______ .

Consider the differential equation \({y^2}dx + \left( {x - \frac{1}{y}} \right)dy = 0\) . If value of \(y\) is \(1\) when \(x = 1\), then the value of \(x\) for which \(y = 2\), is

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46\  \Omega\). The power consumed in it is :