Two positive numbers whose sum is 60 and the product of the square of one number and other number is maximum are:

The statement "all tax payers above 60 years in India" is an example of
(A) Sample
(B) Finite population
(C) Infinite population
(D) Statistical Interference

The value of \(k\) for which the lines \(\frac{2 x-3}{4}=\frac{3-y}{k}=\frac{z-2}{-2}\) and \(\frac{x-2}{1}=\frac{y}{4}=\frac{5-z}{3}\) are perpendicular to each other 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:

Match the Matrix in List - I with its Adjoint's Determinant in List - II.
List - I (Matrix A) :

LIST 1	LIST 2
(A) \(\left[\begin{array}{ll}3 & 1 \\ 4 & 2\end{array}\right]\)	(I) 9
(B) \(\left[\begin{array}{cc}5 & -1 \\ 4 & 2\end{array}\right]\)	(II) 8
(C) \(\left[\begin{array}{cc}6 & -1 \\ 2 & 1\end{array}\right]\)	(III) 14
(D) \(\left[\begin{array}{ll}4 & 1 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below:

The domain of the function f(x) = \(\frac{x^2+1}{x^2-3 x+2}\) is

Consider the function \(f(x)=\sin x\) in the interval \([\pi, 2 \pi]\), then which of the following statements are correct?
(A) \(x=\frac{3 \pi}{2}\) is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at \(\pi\) and \(2 \pi\)
Choose the correct answer from the options given below:

The projection of the vector \(\hat{i}+\hat{j}+\hat{k}\) on the vector \(\hat{j}\) is:

HIV attacks which one of the following cells?

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 \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_0\) 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 \(\Delta_{\circ}\) 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 octahedral 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.
Choose the correct statement from the following:

Let \(A\) be a square matrix of order 2 such that \(\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] A\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\) Then \(A\) is :

India has a history of religious and cultural traditions to emphasise protection of nature. In related with this such sacred groves are found in _________

The order of kinetics of \(\mathrm{S}_{\mathrm{N}} 1\) reactions is: