The radius ( \(\mathrm{r})\), length \((l)\) and resistance \((\mathrm{R})\) of a metal wire was measured in the laboratory as \(\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}\) \(\mathrm{R}=(100 \pm 10) \mathrm{ohm}\) \(l=(15 \pm 0.2) \mathrm{cm}\) The percentage error in resistivity of the material of the wire is _______.

A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\)

The ratio of the equivalent resistance of the network (shown in figure) between the points \(a\) and \({b}\) when switch is open and switch is closed is \({x}: 8 .\) The value of \({x}\) is ..... .

A wire of length \(10 \mathrm{~cm}\) and radius \(\sqrt{7} \times 10^{-4} \mathrm{~m}\) connected across the right gap of a meter bridge. When a resistance of \(4.5 \ \Omega\) is connected on the left gap by using a resistance box, the balance length is found to be at \(60 \mathrm{~cm}\) from the left end. If the resistivity of the wire is \(\mathrm{R} \times 10^{-7} \Omega \mathrm{m}\), then value of \(\mathrm{R}\) is :

Two particles, of masses \(M\) and \(2M\), moving as shown, with speeds of \(10\, m/s\) and \(5\, m/s\), collide elastically at the origin. After the collision, they move along the indicated directions with speeds \(v_1\) and \(v_2\) respectively. The value of \(v_1\) and \(v_2\) are nearly

A lens having refractive index 1.6 has focal length of 12 cm , when it is in air. Find the focal length of the lens when it is placed in water.
(Take refractive index of water as 1.28)

In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm, the angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is _______.

A small soap bubble of radius \(4\,cm\)  is trapped inside another bubble of radius \(6\,cm\) without any contact. Let \(P_2\)  be the pressure inside the inner bubble and \(P_0\)  the pressure outside the outer bubble. Radius of another bubble with pressure difference \(P_2 - P_0\)  between its inside and outside would be....... \(cm\)

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

A bullet of mass \(0.1\, kg\) is fired on a wooden block to pierce through it, but it stops after moving a distance of \(50\, cm\) into it. If the velocity of bullet before hitting the wood is \(10\) \(m / s\) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \('x' N.\) The value of \('x'\) to the nearest integer is................. \(N\)

The energy required to remove the electron from a singly ionized Helium atom is \(2.2\, times\) the energy required to remove an electron from Helium atom . The total energy required to ionize the Helium atom completely is......\(eV\)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.
Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.
In the light of the above statements, chose the most appropriate answer from the options given below :

Name the logic gate equivalent to the diagram attached