The \(AC\) voltage across a resistance can be measured using a

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______.

A current carrying circular loop of radius \(2\) cm with unit normal \(\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field, \(\vec{B} = B_0(3\hat{i}+2\hat{k})\). If \(B_0 = 4\times 10^{-3}\) T and current \(I=100\sqrt{2}\) A, the torque experienced by the loop is ________ Wb·A. (\(\pi=3.14\))

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is \(\frac{\sqrt{x}}{2}\). Then, the value of \(x\) is .... .

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

The charge stored by the capacitor C in the given circuit in the steady state is _________ \(\mu C\).

A point charge of \(+\,12 \,\mu C\) is at a distance \(6 \,cm\) vertically above the centre of a square of side \(12\, cm\) as shown in figure. The magnitude of the electric flux through the square will be ....... \(\times 10^{3} \,Nm ^{2} / C\)

The integral \(\int {\frac{{2{x^3} - 1}}{{{x^4} + x}}} \,dx\) is equal to (Here \(C\) is a constant of integration)

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason \(R:\) Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

If for some \(\alpha \in R ,\) the lines \(L _{1}: \frac{ x +1}{2}=\frac{ y -2}{-1}=\frac{ z -1}{1}\) and \(L _{2}: \frac{ x +2}{\alpha}=\frac{ y +1}{5-\alpha}=\frac{ z +1}{1}\) are coplanar, then the line \(L _{2}\) passes through the point

Let \(\mathrm{a} \in \mathbf{R}\) and A be a matrix of order \(3 \times 3\) such that \(\operatorname{det}(A)=-4\) and \(A+I=\left[\begin{array}{lll}1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2\end{array}\right]\), where \(I\) is the identity matrix of order \(3 \times 3\).
If \(\operatorname{det}((a+1) \operatorname{adj}((a-1) A))\) is \(2^m 3^n, m, n \in\) \(\{0,1,2, \ldots .20\}\), then \(\mathrm{m}+\mathrm{n}\) is equal to :

Let \(\mathrm{ABC}\) be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle \(\mathrm{ABC}\) and the same process is repeated infinitely many times. If \(\mathrm{P}\) is the sum of perimeters and \(Q\) is be the sum of areas of all the triangles formed in this process, then :

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm.