The relation \(R\) on the set \(A\) of points in a plane, given by \(R=\{(P, Q)\) : Distance of the point \(P\) from the origin is same as the distance of

If the matrix \(\left[\begin{array}{ccc}2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4\end{array}\right]\) is not invertible, then the value of \(\lambda\) is :

If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :

If the points \((2,1),(-1,4)\) and \((a, 3)\) are collinear then the value/(s) of a is/(are) :

A boat covers a distance of 24 km upstream and returns to the same point in a total time of 4 hours. If the speed of the boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identify matrix of the same order as \(A\) then \((I+2 A)^3-6 A\) is equal to

The order and degree of the differential equation \(x\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2-3 \frac{d y}{d x}+y=0\) respectively, are:

The energy released in fusion reaction \( ^2_1H + ^2_1H \rightarrow ^3_2He + n \) where Binding Energy of \( ^2_1H = 2.23 \text{ MeV} \) and of \( ^3_2He = 7.73 \text{ MeV} \), would be

Which of the following is incorrect?

Why must the reacting molecules have a minimum energy for an effective collision?

Identify the incorrect statement about the human genome -

If a copper wire carries a direct current, the magnetic field associated with the current would be:

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 (\(TiO_2, VVO^+, CrVIO_4^{2-}, MnVIIO_4\)) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe^{II,III}, Co^{II,III}, Ni^{II}, Cu^{I,II}, Zn^{II}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitaIs 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.
Highest oxidation state shown by 'Mn' is :