In a Young's double slit experiment, the \( n^{\text{th}} \) bright fringe for a light of wavelength 5000 \( \text{\AA} \) coincides with the \( (n+1)^{\text{th}} \) bright fringe for light of wavelength 4000 \( \text{\AA} \). The value of \( n \) is :

The velocity and acceleration vectors of a particle moving in a magnetic field are given by : \(\vec{v}=3 \hat{i}+4 \hat{j}\) and \(\vec{a}=2 \hat{i}+\hat{j}\) respectively, Then :
(A) the magnetic field is along \(z\)-direction
(B) \(v=3\)
(C) the kinetic energy of the particle is constant
(D) the acceleration is in x-z plane
(E) the particle is moving in \(x-y\) plane

Which of the following statements are correct?
(A) Metals obey Ohms law at constant temperature.
(B) The resistivity of the metals depends on temperature.
(C) The conductivity of the metals is independent of temperature.
(D) The number of electrons per unit volume in a metal is independent of temperature.
Choose the correct answer from the options given below:

The output frequency of a (i) half-wave rectifier and (ii) full-wave rectifier, if the input frequency is 50 Hz are, respectively

The magnitude of the magnetic field due to a short bar magnet having a magnetic moment of 0.2 \( \text{Am}^2 \), at a distance of 50 cm from the centre of the magnet on its axial line will be:

What is the radius of the path of an electron moving with velocity of \(3 \times 10^7\) m/s in a magnetic field of \(6 \times 10^{-4}\) T perpendicular to it?

A wire of resistance 4 R is bent in the form of a circle. The equivalent resistance between two points diametrically opposite on the circle will be

Read the passage carefully to answer the questions given below
Some strains of `Bacillus thuringiensis` produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). In `Bacillus thuringiensis` the toxin is coded by a gene `crylAc` named cry. There are a number of them, for example, the proteins encoded by the genes `crylAc` and `cryllAb` control the cotton bollworms, that of `crylAb` controls corn borer. Using conventional methods of diagnosis (serum and urine analysis, etc.) early detection is not possible. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. The disorder is caused due to the deletion of the gene for adenosine deaminase. `RNAi` takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific `mRNA` due to a complementary `dsRNA` molecule that binds to and prevents translation of the `mRNA`.
Which of the following Bt toxin gene controls the corn borer?

The diagonal elements of a skew symmetric matrix are all

Arrange the following in the increasing order of their energy gap between their conduction and valence bands:
(A) Si
(B) C (diamond)
(C) Ge
(D) Sn
choose the correct answer from the options given below:

A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is \(4 \times 10^{-3} Wb\). The self-inductance of the solenoid is

Identify the incorrect statement/s:
(A) Intestinal perforation and death may occur in severe cases of typhoid infection.
(B) Common cold is caused by Rhinoviruses.
(C) Lips and fingernails may turn grey to bluish colour in severe cases of pneumonia.
(D) Pneumonia is caused by Salmonella.
(E) Typhoid fever could be confirmed by Widal test.
Choose the answer from the options given below:

The limiting molar conductivities for \(\mathrm{H}^{+}, \mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{CH}_3 \mathrm{COO}^{-}\)are \(349.6,50.1,76.3,40.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\), respectively, in water at 298 K.
Match List-l and List-II

List-I	List-II
Electrolyte	\(\Lambda_m^o\)
(A) HCl	(I) \(390.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(B) NaCl	(II) \(126.4 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(C) \(\mathrm{CH}_3 \mathrm{COONa}\)	(III) \(425.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)
(D) \(\mathrm{CH}_3 \mathrm{COOH}\)	(IV) \(91.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\)

Choose the correct answer from the options given below: