A proton is accelerated by a potential V and the de-Broglie wavelength associated with it is \(\lambda\). By how much potential a deuteron should be accelerated to acquire the same de-Broglie wavelength as that of a proton?

The wavelength range of X-rays is:

Which of the followings should be doped with pure silicon to get an n-type and p-type semiconductors respectively?

Which of the following statements are true about electromagnetic waves?
(A) Accelerated charges radiate electromagnetic waves.
(B) The frequency of the electromagnetic wave equals the frequency of oscillation of the charge.
(C) No material medium is involved in the vibrations of the electric and magnetic fields.
(D) Electromagnetic waves of different wavelengths have different velocities in free space/vacuum.
Choose the correct answer from the options given below:

The kinetic energy of an electron in the H-atom in the second excited state is k units. Its total energy and potential energy, respectively, in the ground state will be

According to Bohr's theory, the angular momentum of an electron revolving in the second orbit of the hydrogen atom will be:

In a Wheatstone Bridge, all the four arms have equal resistance r. If the resistance of the galvanometer arm is also equal to r, the equivalent resistance of the combination will be

Given below are the steps involved in the process of zone refining for removing impurities which are more soluble in the melt than solid state of the metal.
A. Impurities get concentrated at one end.
B. As the heater moves forward, the pure metal crystallises out of the melt left behind and the impurities pass to the next zone.
C. A mobile heater surrounding the rod of impure metal is fixed at its one end.
D. The end is cut off.
E. The molten zone moves along with the heater which is moved forward.
Choose the correct answer from the options given below:

The area (in square units) of the region bounded by the curve \(x^2=y\) and the straight line \(y=4\) in the first quadrant is equal to

Every year the price of a motorcycle depreciates by Rs. 15,000. After 12 years its price has become Rs. 50,000. Then its original cost was:

The solution of the differential equation \((x+1) \frac{d y}{d x}+1-2 e^{-y}=0 ; y(0)=0\) is

To prepare \(2 5 0 ~ m L\) standard solution of \(M / 2 0 ~ N a C l\), amount of NaCl required is :

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.
Which amongst the following is a better oxidising agent than other ?