Class 12th

Given below are two statements:

Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only

Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.

In light of above statements choose the most appropriate answer from the options given below:

The equivalent capacitance of the system shown in the following circuit is:

If ${\text{∮}\mathrm{}}_{\mathrm{s}}\vec{\mathrm{E}}\cdot \overrightarrow{\mathrm{d}\mathrm{S}}=0$  over a surface, then:

An electric dipole is placed at an angle of ${30}^{?}$ with an electric field of intensity $2*{10}^5{\mathrm{N}\mathrm{C}}^{-1}$ . It experiences a torque equal to $4\mathrm{N}\mathrm{m}$ . Calculate the magnitude of charge on the dipole, if the dipole length is $2\mathrm{c}\mathrm{m}$ .

When two monochromatic lights of frequency, $v$ $$ and $\frac{v}{2}$ $\frac{}{}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_S}{2}$ $\frac{{}_{}}{}$ and $V_S$ ${}_{}$ respectively. The threshold frequency for this metal is

When light propagates through a material medium of relative permittivity ${\epsilon }_{\mathrm{r}}$ and relative permeability ${\mu }_{\mathrm{r}}$ , the velocity of light, $\mathrm{v}$ is given by : ( $\mathrm{c}$  - velocity of light in vacuum)

A square loop of side $1\mathrm{m}$ $$ and resistance $1\mathrm{\Omega }$ $$ is placed in a magnetic field of $0.5\mathrm{T}$ $$ . If the plane of loop is perpendicular to the direction of a magnetic field, the magnetic flux through the loop is

Let P = [[-30, 20, 56],,] and A = [[2, 7, ω²], [-1, -ω, 1], [0, -ω, -ω+1]] where ω = (-1 + i√3)/2, and I be the identity matrix of order 3. If the determinant of the matrix (P?¹AP - I)² is αω², then the value of α is equal to.

The total number of 3 x 3 matrices A having entries from the set {0,1,2,3} such that the sum of all the diagonal entries of AA? is 9, is equal to.

Let f: (0, 2) → R be defined as f(x) = log?(1 + tan(πx/4)). Then, lim (n→∞) (2/n) [f(1/n) + f(2/n) + . + f(1)] is equal to.