In a 100 metre race, \(A\) beats \(B\) by 10 metres and \(C\) by 13 metres. By how many meters will \(B\) beat \(C\) in a 180 metre race?

\(\int \frac{\sin 2 x d x}{\sqrt{9-\cos ^4 x}}\) equals

If \(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}3 & 5 \\ -1 & 3\end{array}\right]=\left[\begin{array}{cc}m & 14 \\ 2 & n\end{array}\right]\), then m + n is equal to:

Area lying in the first quadrant and bounded by the circle \(x^2+y^2=4\) and the lines x = 0 and x = 2 is:

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

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then \(\lambda\) is equal to

The intervals for which \(f(x)=x^4-2 x^2\) is increasing are:

Two coherent monochromatic light beams of intensities 16I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are-

Which of the following can be an objective function for a Linear Programming problems in two variables x and y?

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In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Fe(II) octahedral complexes can show different 'spin only' magnetic moments for arrangements in the presence of weak and strong ligands. The 'spin only' magnetic moments of these complexes with weak and strong ligands, respectively, are

The following reaction of benzene with carbon monoxide and hydrogen chloride in the presence of aluminum trichloride to give benzaldehyde is known as

The maximum value of \(f(x)=\frac{1}{4 x^2+2 x+1}\) is

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When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a dior polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following is a chelate complex?