The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively \(1.5\%\) and \(1\%\), the maximum error in determining the density is   ........ \(\%\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is 

In a meter bridge, the wire of length \(1\, m\) has a nonuniform cross-section such that, the variation \(\frac{{dR}}{{d\ell }}\) of its resistance \(R\) with length \(\ell \) is \(\frac{{dR}}{{d\ell }} \propto \frac{1}{{\sqrt \ell  }}\) Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point \(P\). What is the length \(AP\) ? ................ \(m\)

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

List \(I\)	List \(II\)
\(A\) Spring constant	\(I\) \((T ^{-1})\)
\(B\) Angular speed	\(II\) \((MT ^{-2})\)
\(C\) Angular momentum	\(III\) \((ML ^2)\)
\(D\) Moment of Inertia	\(IV\) \((ML ^2 T ^{-1})\)

Choose the correct answer from the options given below

For three low density gases \(A, B, C\) pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point ' \(K\) ' is \(...........\,{}^{\circ}\,C\)

The \(B-H\) curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with \(1000\, turns/cm\) . The current that should be passed in the solenoid to demagnetise the ferromagnet completely is

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter \(0.1\, \mu m\). If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that :

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

A \(2 \mathrm{~kg}\) brick begins to slide over a surface which is inclined at an angle of \(45^{\circ}\) with respect to horizontal axis. The co-efficient of static friction between their surfaces is _______.

Figure here shows \(P\) and \(Q\) as two equally intense coherent sources emitting radiations of wavelength \(20 \,m\). The separation \(PQ\) is \(5.0 \,m\) and phase of \(P\) is ahead of the phase of \(Q\) by \(90^{0}\). \(A, B \) and \( C\) are three distant points of observation equidistant from the mid-point of \(PQ\). The intensity of radiations at \(A, B, C\)  will bear the ratio

A particle of charge \(16\times10^{-16}\, C\) moving with velocity \(10\, ms^{-1}\) along \(x-\) axis enters a region where magnetic field of induction \(\vec B\) is along the \(y-\) axis and an electric field of magnitude \(10^4\, Vm^{-1}\) is along the negative \(z-\) axis. If the charged particle continues moving along \(x-\) axis, the magnitude of \(\vec B\) is

For a charged spherical ball, electrostatic potential inside the ball varies with \(r\) as \(V =2 ar ^2+ b\). Here, \(a\) and \(b\) are constant and \(r\) is the distance from the center. The volume charge density inside the ball is \(-\lambda a \varepsilon\). The value of \(\lambda\) is \(...........\). \(\varepsilon=\) permittivity of medium.