The kinetic energy of an electron in the 2nd excited state in a hydrogen atom, if its ground state energy is \(-13.6 \text{ eV}\), will be:

Match List-I with List-II

List-I	List-II
(A) Light	(I) 1 mm to \(10^{-3} nm\)
(B) Infra-red	(II) 700 nm to 400 nm
(C) X-rays	(III) 400 nm to 1 nm
(D) UV rays	(IV) 1 mm to 700 nm

Choose the correct answer from the options given below :

The electric field in a region is given by \( E = \frac{E_0 x}{b} \). Find the charge contained in the cubical volume bounded by the \( x = 0, x = a, y = 0, y = a \) and \( z = 0, z = a \). Take \( E_0 = 6 \times 10^3 \text{ N/C}, a = 1 \text{ cm} \) and \( b = 2 \text{ cm} \)

A common emitter amplifier has a current gain 75. The collector resistance is 4 \( k\Omega \) and the input resistance is 500 \( \Omega \). The voltage gain of amplifier is:

Choose the correct relation between drift velocity (\( v_d \)) and current density (\( J \)) from the following:

A current I flows through an infinitely long, straight copper walled pipe. Then:

A p-n junction diode can be used :

Read the passage carefully and answer the given questions.
Recombinant DNA Technology
Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
In Recombinant DNA Technology, what is the role of the "selectable marker gene"?

In an experiment, a student measures the terminal potential difference (\( V \)) of a cell (emf \( E \) and internal resistance \( r \)) as a function of current \( I \) and plots a graph with \( V \) on the y-axis and \( I \) on the x-axis.
The slope of the graph between \( V \) and \( I \) is:

Identify the correct statement in the context of Rutherford scattering of \( \alpha \)-particles by a target nucleus:

If \(\vec{a}=5 \hat{i}+\hat{j}+3 \hat{k}\) then the sum of projections of \(\vec{a}\) on \(x\)-axis, \(y\)-axis and \(z\)-axis is:

Which of the following is NOT a basic step in the genetic modification of an organism?

The general solution of the differential equation \(\frac{x d y}{d x}+4 y=x^3,(x \neq 0)\) is :