A proton of charge \(1.6 \times 10^{-19} C\) is moving with a velocity of \(5 \times 10^3 m / s\) in a magnetic field of 4 T. The work done by the magnetic field on the proton is :

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at \(30^{\circ}\) with the horizontal. The horizontal component of the earth's magnetic field at the place is B . The strength of the earth's magnetic field at the place is :

The de-Broglie wavelength of neutron at \( 127^\circ \text{C} \) is : (Given Boltzmann constant, \( k = 1.38 \times 10^{-23} \text{ J mole}^{-1} \text{K}^{-1}, h = 6.63 \times 10^{-34} \text{ Js} \), mass of neutron \( m = 1.66 \times 10^{-27} \text{ kg} \))

A 10 V battery of negligible internal resistance is connected with a 200 V battery and a set of parallel resistances as shown in the figure. The value of current in the circuit.

The objective of a reflecting telescope is a :

In an experiment with Meter Bridge, with unknown resistance R in the left gap, the null point is obtained at \( l_1 = 40 \text{ cm} \) from the left end. Now a resistance of \( R' = 10 \Omega \) is connected in series with resistance R, the null point is obtained at \( l_2 = 70 \text{ cm} \) from the left end. The value of resistance R is

Which of the following is NOT correct in the case of the output obtained from a full wave rectifier?

The Mediterranean orchid Ophrys employs 'sexual deceit mechanism to get pollination done by

Read the passage given below and answer the question.
The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7 . The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence \(( Cu , Zn )\). Thus early in the series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti (III) or Ti (II). At the other end, the only oxidation state of zinc is \(+ 2\) (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum of the s - and d-electrons upto manganese ( \(Ti ^{I V} O _2, V^V O _2^{+}, Cr ^{V I} O _4^{2-}\), \(Mn ^{\text {VII }} O _4\) ) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe ^{I I, I I I}, Co ^{I I, I I I}, Ni ^{I I}, Cu ^{I, I I}, Zn ^{I I}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g. \(V ^{I I}, V^{I I I}, V^{I V}, V^V\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit of two.
An interesting feature in the variability of oxidation states of the d-block elements is noticed among the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of dblock. For example, in group 6, \(Mo ( VI )\) and \(W ( VI )\) are found to be more stable than \(Cr ( VI )\). The \(Cr ( VI )\) in the form of dichromate in acidic medium is a strong oxidising agent, whereas \(MoO _3\) and \(WO _3\) are not.
Low oxidation states are found when a complex compound has ligands capable of \(\pi\)-acceptor character in addition to the \(\sigma\)-bonding. For example, in \(Ni ( CO )_4\) and \(Fe ( CO )_5\), the oxidation state of nickel and iron is zero.
Identify the stable pair of ions :

Let \(X\) denote the number of tails in two tosses of a coin. If the mean and the variance of \(X\) are \(\mu\) and \(\sigma^2\) respectively, then \(\mu+\sigma^2\) is equal to:

In the following differential equation \(\frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^2=2 x^2 \log \left(\frac{d^2 y}{d x^2}\right)\) order and degree is:

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:

What is the formula of following coordination compound: Potassium trioxalatoaluminate(III)