In an experiment with Meter Bridge, with unknown resistance R in the left gap, the null point is obtained at \( l_1 = 40 \text{ cm} \) from the left end. Now a resistance of \( R' = 10 \Omega \) is connected in series with resistance R, the null point is obtained at \( l_2 = 70 \text{ cm} \) from the left end. The value of resistance R is

Interference was observed in a chamber where air was present. Now, the chamber is evacuated and the same light is used. A careful observer will note :

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of \( 3 \times 10^{10} \text{ Hz} \) and its amplitude is 30 V/m. The amplitude of the oscillating magnetic field is:

A charged particle moves along a circle under the action of constant electric and magnetic fields. Which of the following is possible?

In Rutherford's scattering experiment, if impact parameter \( b = 0 \), then the value of the scattering angle will be :

A diver at a depth of 1.2 m in clear water (n = 4/3) sees the sky in a cone of semi-vertical angle :

A TV tower has a height of 160 m. How much population is covered by the television broadcast, if the average population density around the tower is 1000 per km^2? Given radius of the earth is 6400 km.

Observe the given diagram representing global biodiversity and answer the question.

Global Bio-diversity
Identify which is not represented in the figure?

\(\int_1^2 \frac{1}{x(x+1)} d x, x>0\) equals

Read the passage carefully and answer the questions.
Electrochemistry is the study involving two types of processes. One type involves the production of electricity from the energy released during a spontaneous chemical reaction. Galvanic cells like Daniel cells are used to produce electricity from the redox reaction. Nernst equation of a galvanic cell gives the relation between the standard cell potential and the concentration of the species involved in the redox reaction. The second type of study involves the cells in which electrical energy is used to bring about the chemical reactions in a non-spontaneous process. The conductance of electrolytic solution depends on many factors including the nature of the electrolyte and the dimensions of the electrolytic cell.
The following equation represents the reaction taking place in a Galvanic cell:
Mg(s) + 2Ag\(^+\)(0.001 M) \(\rightarrow\) Mg\(^2+\)(0.01 M) + 2Ag(s)
Calculate its \(E_{\text {cell }}\) at 298 K if \(E_{\text {cell }}^{\circ}=2.91 \mathrm{~V}\).

The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer function, is continuous at \(x=\)
(A) 2.9
(B) 5
(C) -3
(D) 6.5
Choose the correct answer from the options given below:

Electromagnetic wave carries

By using the determinants the area of the triangle with vertices \((0,0),(0,1)\) and \((1,0)\) is :