A closed organ pipe \(150 \mathrm{~cm}\) long gives \(7\) beats per second with an open organ pipe of length \(350 \mathrm{~cm}\), both vibrating in fundamental mode. The velocity of sound is_________ \(\mathrm{m} / \mathrm{s}\).

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V _{ Z }=5 V\) and the desired current in load is 5 mA . The unregulated voltage source can supply upto 25 V . Considering the Zener diode can withstand four times of the load current, the value of resistor \(R _{ S }\) (shown in circuit) should be ___________ \(\Omega\).

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

A plane electromagnetic wave of frequency \(500\, MHz\) is travelling in vacuum along \(y-\)direction. At a particular point in space and time, \(\overrightarrow{ B }=8.0 \times 10^{-8} \hat{ z } \;T\). The value of electric field at this point is (speed of light \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\) \(\hat{ x }, \hat{ y }, \hat{ z }\) are unit vectors along \(x , y\) and \(z\) direction.

The radius of a sphere is measured to be \((7.50 \pm 0.85) \,cm .\) Suppose the percentage error in its volume is \(x\). The value of \(x\), to the nearest integer is .....\(\%\)

An ideal capacitor of capacitance \(0.2\, μF\) is charged to a potential difference of \(10\,V\). The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance \(0.5\,mH\). The current at a time when the potential difference across the capacitor is \(5\,V\), is.....\(A\)

The wavelength of an \(X-\)ray beam is \(10 \, \mathring A\). The mass of a fictitious particle having the same energy as that of the \(X-\)ray photons is \(\frac{ x }{3} h \,kg\). The value of \(x\) is ....... . \((h =\) Planck's constant \()\)

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to

The energy required to ionise a hydrogen like ion in its ground state is \(9\) Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?  ........\(nm\)

In the circuit, the logical value of \(A =1\) or \(B =1\) when potential at \(A\) or \(B\) is \(5\,V\) and the logical value of \(A=0\) or \(B=0\) when potential at \(A\) or \(B\) is \(0\,V\). The truth table of the given circuit will be :

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)