Two resistances are connected in two gaps of a metre bridge. The balance point is 20 cm from the zero end. A resistance of \(3 \Omega\) is connected in series with the smaller resistance, then the null point shifts to 40 cm. The value of the smaller resistance is:

Two capacitors of capacitances C and 4C at potentials 40 V and 60 V, respectively are connected in parallel. The common potential of the combination is

A spherical conductor placed in vacuum has capacitance of \( 3.14 \times 10^{-9} \, \text{F} \). Its radius will be:

A charge q is enclosed by a spherical Gaussian surface of radius R. If the radius of the sphere is doubled, how will the outward electric flux change?

The wavelength range of X-rays is:

A 50 cm long air core solenoid has a 2 cm radius and 500 turns. The self-inductance of the solenoid would be (given \(\mu_0=4 \pi \times 10^{-7} \operatorname{Tm} * A^{-1}\) and \(\pi^2=10\) )

The charge flowing in a conductor varies with time as \(q(t) = (8t^2 - 4t + 5)C\). Then the current changes at the rate of :

Arrange the halogens in the increasing order of bond dissociation enthalpy :
(A) \(F_2\)
(B) \(Cl_2\)
(C) \(Br_2\)
(D) \(I_2\)
Choose the correct answer from the options given below :

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.
Which one of the following is not used as a vector in recombinant DNA
technology?

The degree of the differential equation
\(\left[1+\left(\frac{d y}{d x}\right)\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is :

The necessary conditions for total internal reflection are
(A) Light must travel from denser to rarer medium.
(B) The angle of incidence in the denser medium must be less than the critical angle for the two media.
(C) Light must travel from rarer to denser medium.
(D) The angle of incidence in the denser medium must be greater than the critical angle for the two media.
Choose the correct answer from the options given below:

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 3 MHz. The frequency of the resultant signal are:

If \(A\) is a non-singular matrix of order 3 such that \(|\operatorname{adj}(A)|=121\), then \(\left|A A^T\right|\) is equal to :