A wire of \(1 \,\Omega\) has a length of \(1\, m\). It is stetched till its length increases by \(25\, \%\). The percentage change in resistance to the neartest integer is .....\(\%\)

If the deBroglie wavelength of an electron is equal to \(10^{-3}\) times the wavelength of a photon of frequency \(6\,\times 10^{14}\,Hz,\) then the speed of electron is equal to: (Speed of light \(=3\times 10^8\,m/s\,;\) Planck’s constant \(=6.63\times 10^{-34}\,J.s\,;\) Mass of electron \(=9.1\times 10^{-31}\,kg\) )

The equivalent resistance between \(A\) and \(B\) of the network shown in figure

A proton and an \(\alpha -\) particle (with their masses in the ratio of \(1 : 4\) and charges in the ratio of \(1:2\) are accelerated from rest through a potential difference \(V\). If a uniform magnetic field \((B)\) is set up perpendicular to their velocities, the ratio of the radii \(r_p : r_{\alpha }\) of the circular paths described by them will be

A parallel plate capacitor with air between the plate has a capacitance of \(15 pF\). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \(3.5.\) Then the capacitance becomes \(\frac{ x }{4}\,pF\).The value of \(x\) is \(............\)

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).

In a Young's double slit experiment, an angular width of the fringe is \(0.35^{\circ}\) on a screen placed at \(2\,m\) away for particular wavelength of \(450\,nm\). The angular width of the fringe, when whole system is immersed in a medium of refractive index \(7 / 5\), is \(\frac{1}{\alpha}\). The value of \(\alpha\) is ..............

As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^{\circ}\) to the vertical. It hits another bob \(B\) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)

If two metallic plates of equal thicknesses and thermal conductivities \({K_1}\) and \({K_2}\) are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

A small square loop of wire of side \(\ell\) is placed inside a large square loop of wire of side \(L\) \(\left(\mathrm{L}=\ell^2\right)\). The loops are coplanar and therr centers coinside. The value of the mutual inductance of the system is \(\sqrt{\mathrm{x}} \times 10^{-7} \mathrm{H}\), where X = _______.

\(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material :
Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains.
Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
In the light of the above statements, choose the correct answer from the options given below :