A potentiometer wire has a uniform potential gradient. The specific resistance of the material of the wire is \(10^{-7} \text{ ohm-m}\), the current passing through it is 0.1 A and its cross-sectional area is \(10^{-6} \text{ m}^2\). What is the value of the potential gradient?

A region has a uniform magnetic field in it. A proton enters the region with a velocity, making an angle of \( 45^\circ \) with the direction of the magnetic field. In this region the proton will move in :

The maximum power drawn out of cell is given by : (E is emf, r is internal resistance)

A radioactive substance decays to \( \frac{1}{32} \text{th} \) of its initial activity in 30 days. Its half life period will be:

Equipotential surfaces at a great distance from a collection of charges whose total sum is not zero are approximately:

The optical length of an astronomical telescope with magnifying power of 10 for normal adjustment is 55 cm. What is the focal length of the objective ?

The size of the atom is of the order of:

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Fe(II) octahedral complexes can show different 'spin only' magnetic moments for arrangements in the presence of weak and strong ligands. The 'spin only' magnetic moments of these complexes with weak and strong ligands, respectively, are

If the line \(\vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}+2 \hat{k})\)
is parallel to the plane \(\vec{r} \cdot(3 \hat{i}-2 \hat{j}+a \hat{k})=11\), then \(a\) is equal to :

Which one of the following is a correct statement about dormancy?

Which one of the given sacred groves is not found in Madhya Pradesh?

Read the following passage carefully and answer the given questions.
Immune System in the Body
The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The primary lymphoid organs are bone marrow and thymus where immature lymphocytes differentiate into antigen-sensitive lymphocytes. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells. The bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Hence, an antibody is represented as H2L2. Different types of antibodies are produced in our body. IgA, IgM, IgE, IgG are some of them. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs.
The site of interaction of lymphocytes with antigen is

In a Binomial distribution, the probability of getting a success is \(\frac{3}{4}\) and the variance is \(\frac{3}{8}\) then the probability of no success is: