The effective current \(I\) in the given circuit at very high frequencies will be \(.......A\)

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

If the distance between object and its two times magnified virtual image produced by a curved mirror is \(15 \mathrm{~cm}\), the focal length of the mirror must be _______.

The heat extracted out of \(x\) gram of water initially at \(50°C\) to cool it down to \(0°C\) is sufficient to evaporate \((1000 - x)\) gram of water also initially at \(50°C\). The value of \(x\) (closest integer) is _______.
(Take latent heat of water \(2256\text{ kJ/kg.K}\), specific heat capacity of water \(4200\text{ J/kg.K}\))

Three charged particle \(A, B\) and \(C\) with charges \(-4 q,  2 q\) and \(-2 q\) are present on the circumference of a circle of radius \(d\). the charged particles \(A, C\) and centre \(O\) of the circle formed an equilateral triangle as shown in figure. Electric field at \(O\) along \(x-\)direction is

A radioactive sample has an average life of \(30\, {ms}\) and is decaying. A capacitor of capacitance \(200\, \mu\, {F}\) is first charged and later connected with resistor \(^{\prime}{R}^{\prime}\). If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of \(^{\prime}R^{\prime}\) should be \(....\,\Omega\)

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10 th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be _________ mm .

A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is

A long straight wire of radius ' \(a\) ' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(\frac{a}{2}\) and \(2\)a from axis of the wire is _______.

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)

A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit).

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \(10\text{ V}\) and \(5\text{ A}\), respectively. The least counts of voltmeter and ammeter are \(500\text{ mV}\) and \(200\text{ mA}\), respectively. The estimated error in the resistance measurement is _______ \(\Omega\).

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \(5^{\text {th}}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^{+}\) is _______.