During transmission of electrical energy by transformer, near the consumer

"The nucleus \( ^{23}_{10}\text{Ne} \) decays by \(\beta\)^- emission. The maximum kinetic energy of the emitted electrons is :
Given that : \( m(^{23}_{10}\text{Ne}) = 22.994466 \text{ u} \), \( m(^{23}_{11}\text{Na}) = 22.989770 \text{ u} \) and \( 1 \text{ u} = 931 \text{ MeV/c}^2 \)

A current of 2 A is maintained in a long straight conductor placed in air. Calculate the magnitude of the magnetic field at a distance of 2 m from the conductor.

Positively charged particles are projected into a magnetic field. If the direction of magnetic field is along the direction of motion of the charged particles, the particles will experience

A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance \( R_1 \) in series with the coil. If a resistance \( R_2 \) is connected in series with it, then it can measure the \( \frac{V}{3} \) volts. Find the resistance \( R_3 \) in terms of \( R_1 \) and \( R_2 \) required to be connected to convert it into a voltmeter that can read upto 3V volts :

A conducting circular loop is placed in a uniform magnetic field of 10 T with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate 5 mm/s. When the radius is 5 cm then the induced emf is

Match List-I with List-II

List-I	List-II
(A) Rutherford	(I) Nuclear model of atom
(B) A.H. Becquerel	(II) Plum-Pudding Model of atom
(C) Niels Bohr	(III) Radioactivity
(D) J.J. Thomson	(IV) Hydrogen atom model

Choose the correct answer from the options given below :

The total number of sigma bonds present in \(P _4 O _{10}\) are:

If \(A\) is a non-singular square matrix of order 3 such that \(A^3=4 A^2\), then the value of \(|A|\) is:

Process of formation of new species due to change in allele frequency in a population is called:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar
conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The plot between \(\Lambda_m\) and \(c^{1 / 2}\) is a straight line with

The transverse nature of light is shown by

\[\int e^x\left(1+x^2\right) d x=\]