The increase in the sale of shawls during winters is an example of :

Let \(P=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix and let \(Q=\left[b_{i j}\right]\) be a \(3 \times 3\) matrix,
where \(b_{i j}=2^{i+j} a_{i j}\) for \(1 \leq i, j \leq 3\).
If the determinant of \(P\) is 2 , then the determinant of the matrix \(Q\) is ___________ .

If \(x, y\) and \(z\) are real numbers such that \(x+y+z=0\), then the value of \(\left|\begin{array}{ccc} 3 x & -x+y & -x+z \\ x-y & 3 y & z-y \\ x-z & y-z & 3 z \end{array}\right| \) is

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000 ?

If \(A^T=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}-1 & 0 \\ 1 & 2\end{array}\right]\), then the matrix \((A+2 B)^T\) is

The value of \(\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|\) is:

If A and B are two events such that \(P(B) = \frac{3}{5}\), \(P(A|B) = \frac{1}{2}\) and \(P(A \cup B) = \frac{4}{5}\), then P(A) is equal to:

A heater boils \( x \) amount of water in time \( t_{1} \) and another heater boils the same water in time \( t_{2} \) having resistances \( R_{1} \) and \( R_{2} \) respectively. The ratio \( \frac{t_{1}}{t_{2}} \) will be:

Two cards are drawn without replacement. The probability distribution of number of aces is given by :

The complex \(\left[ Co \left( NH _3\right)_4\left( NO _2\right)_2\right] Cl\) exhibits:
A. Coordination isomerism
B. Linkage isomerism
C. Solvate isomerism
D. Ionisation isomerism
E. Geometrical isomerism
Choose the correct answer from the options given below:

Fertilization in human female takes place in -

A vessel contains 56 litres of mixture of milk and water in the ratio \(5: 2\). How much water should be mixed with it so that the milk to water ratio becomes 4:5.

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complez to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_0\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{\circ}\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_0\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octabedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Which of the following relations is correct for the splitting of \(d\) orbitals in octahedral and tetrahedral crystal fields, considering same metal, the same ligands and metal-ligand distances?