Three charges \(Q, +q\) and \(+q\) are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) is

A pendulum of length \(2 \; m\) consists of a wooden bob of mass \(50 \; g\). A bullet of mass \(75 \; g\) is fired towards the stationary bob with a speed \(v\). The bullet emerges out of the bob with a speed \(\frac{v}{3}\) and the bob just completes the vertical circle. The value of \(v\) is \(\dots \; ms ^{-1}\). (if \(g =10 \; m / s ^{2}\) )

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\((a)\) \({R}_{{H}}\) (Rydberg constant)	\((i)\) \({kg} {m}^{-1} {s}^{-1}\)
\((b)\) \(h\) (Planck's constant)	\((ii)\) \({kg} {m}^{2} {s}^{-1}\)
\((c)\) \(\mu_{{B}}\) (Magnetic field energy density)	\((iii)\) \({m}^{-1}\)
\((d)\) \(\eta\) (coefficient of viscocity)	\((iv)\) \({kg} {m}^{-1} {s}^{-2}\)

Choose the most appropriate answer from the options given below:

A single slit of width \(b\) is illuminated by a coherent monochromatic light of wavelength \(\lambda \). If the second and fourth minima in the diffraction pattern at a distance \(1\,m\) from the slit are at \(3\, cm\) and \(6\, cm\) respectively from the central maximum, what is the width of the central maximum ?......\(cm\) (i.e. distance between first minimum on either side of the central maximum)

To light, a \(50\,W , 100\,V\) lamp is connected, in series with a capacitor of capacitance \(\frac{50}{\pi \sqrt{ x }} \mu F\), with \(200 V , 50 Hz AC\) source. The value of \(x\) will be........

The mean intensity of radiation on the surface of the Sun is about \(10^{8}\,W/m^2.\) The \(rms\) value of the corresponding magnetic field is closet to

Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

Given below are two statements: one is labelled as Assertion \(\mathrm{A}\) and the other is labelled as Reason \(\mathrm{R}\) Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is \(\frac{1}{2} \mathrm{mgR}\), where R is the radius of earth.
Reason \(\mathrm{R}\) : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below

Consider the sound wave travelling in ideal gases of \(\mathrm{He}, \mathrm{CH}_4\), and \(\mathrm{CO}_2\). All the gases have the same ratio \(\frac{P}{\rho}\), where \(P\) is the pressure and \(\rho\) is the density. The ratio of the speed of sound through the gases \(\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_4}: \mathrm{v}_{\mathrm{CO}_2}\) is given by

In a photoelectric effect experiment the threshold wavelength of incident light is \(380\, nm\), If the wavelength of the incident light is \(260\,nm\), the maximum kinetic energy of emitted electrons will be: .............. \(eV\) Given \(E\) (in \(eV\)) \( = \frac{{1237}}{{\lambda \left( {in\,nm} \right)}}\)