Match List-I with List-II

List-I (Materials)	List-II (Band Gap (eV))
(A) Germanium	(I) 1.42 eV
(B) Gallium Arsenide	(II) > 3 eV
(C) Insulator	(III) 1.1 eV
(D) Silicon	(IV) 0.7 eV

Choose the correct answer from the options given below :

Magnetic susceptibility \(X\) of a given material is \(- 0 . 5\). Identify the magnetic material.

Choose the correct statement regarding dependence of electric potential at a point due to an electric dipole:

The frequency of a photon whose energy is 66.3 eV would be
(Given \( h = 6.63 \times 10^{-34} \text{ Js} \))

If 200 MeV energy is released in the fission of a single nucleus of uranium-235, how many fissions per second will produce a power of 32 kW?

In the circuit diagram, the battery, diodes \( D_1 \) and \( D_2 \), bulbs \( B_1 \) and \( B_2 \) are connected as shown. Which of the following statements is true regarding bulbs \( B_1 \) and \( B_2 \)?

Three concentric metallic spherical shells of radii \( R, 2R \), and \( 3R \) are given charges \( Q_1, Q_2 \) and \( Q_3 \), respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells \( Q_1 : Q_2 : Q_3 \) is:

The general solution of the differential equation \(\frac{d y}{d x}+y \tan x=\sec x\) is :
(Where \(C\) is constant of integration)

For \(x>y>0\), if \(x^5 y^6=(x+y)^{11}\), then \(\frac{d^{2} y}{d x^2}\) is

Two charges, \(+ 20 \, μC\) and \(+ 40 \, μC\) are placed at a separation of 4 cm. The electric potential due to the pair at the middle point of the line joining the two charges is:

Read the following passage carefully and answer the given questions.
Productivity in the Ecosystem The flow of energy through a terrestrial ecosystem starts with the harnessing of sunlight by autotrophs. The radiant energy is converted by photosynthesis to organic compounds is known as productivity. The productivity is expressed in units of energy per unit of area per unit time. The amount of organic matter present at any given time is biomass. The productivity of any ecosystem is affected by many parameters like weather conditions, nutrient availability etc. The productivity of any ecosystem does vary seasonally and yearly.
The Net Primary Productivity of an ecosystem are represented by:

For the given linear programming problem \(z=a x+b y, a, b>0\) subject to the constraint
\(2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0\). If the corner points are \((0,0),(5,0),(3,4)\) and \((0,5)\) and \(z\) is maximum at both \((3,4)\) and \((0,5)\), then the relationship between \(a\) and \(b\) is

Which of the following microbe serves as an important biofertiliser in paddy field?