A capacitor P with capacitance \( 10\times10^{-6} F \) is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance \( 20\times10^{-6} F \). The charge on capacitor Q when equilibrium is established will be \( \alpha\times10^{-5} C \).(assume capacitor \(Q\) does not have any charge initially),The value of \( \alpha \) is __________ .

The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will be

A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)

The \(AC\) voltage across a resistance can be measured using a

A square loop of sides \(a=1 \mathrm{~m}\) is held normally in front of a point charge \(\mathrm{q}=1 \mathrm{C}\). The flux of the electric field through the shaded region is \(\frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}\), where the value of p is _____.

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency \(512\,Hz\) produces first resonance when the tube is filled with water to a mark \(11\,cm\) below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency \(256\,Hz\) which produces first resonance when water reaches a mark \(27\,cm\) below the reference mark. The velocity of sound in air, obtained in the experiment, is close to .... \(ms^{-1}\)

The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer 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 _______.

A force of \(F=(5 y+20) \hat{j} \,N\) acts on a particle. The work done by this force when the particle is moved from \(y=0 \,m\) to \(y=10 \,{m}\) is \(...\,{J}.\)

Mach List-\(I\) with List - \(II\) :

List - \(I\)	List - \(II\)
\((a)\) Ultraviolet rays	\((a)\) Study crystal structure
\((b)\) Microwaves	\((b)\) Greenhouse
\((c)\) Infrared waves	\((c)\) sterilizing surgical instrument
\((d)\) \(x\)-rays	\((d)\) Radar system

Choose the correct answer from the options given below

A thin strip \(10\, cm\) long is on a \(U\) shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5\,Nm^{-1}\) (see figure). The assembly is kept in a uniform magnetic field of \(0.1\, T\). If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of \(e\) is \(N\). If the mass of the strip is \(50\, grams\), its resistance \(10\,\Omega \) and air drag negligible, \(N\) will be close to

In the figure shown below, a resistance of \(150.4 \Omega\) is connected in series to an ammeter A of resistance \(240 \Omega\). A shunt resistance of \(10 \Omega\) is connected in parallel with the ammeter. The reading of the ammeter is _____ mA.