If \(A=\left|\begin{array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|\) and \(B=\left|\begin{array}{cc}x & 1 \\ 1 & x\end{array}\right|\), then \(\frac{d A}{d x}\) is equal to

Domain of the function \(f\), given by \(f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}\) is

The value of \(\int e^{\sin x} \sin 2 x d x\) is

On the set of positive rationals, a binary operation * is defined by \( a^{*} b=\frac{2 a b}{5} \). If \( 2^{*} x=3^{-1} \)
then \( x= \)

If the volume of the parallelopiped formed by three non-coplanar vectors \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) is 4 cu units, then \([\mathbf{a} \times \mathbf{b} \mathbf{b} \times \mathbf{c} \mathbf{c} \times \mathbf{a}]\) is equal to

If \(\alpha, \beta\) and \(\gamma\) are the roots of the equation \(x^{3}+4 x+2=0\), then \(\alpha^{3}+\beta^{3}+\gamma^{3}\) is equal to

The total number of common tangents of \(x^{2}+y^{2}-6 x-8 y+9=0\) and \(x^{2}+y^{2}=1\) is

The property which is not true about Fluorine is,

The correct order for wavelengths of light absorbed in the complex ions \(\left[\operatorname{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+},\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) and \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) is

If the function \( g(x) \) is defined by
\[
g(x)=\frac{\chi^{200}}{200}+\frac{\chi^{199}}{199}+\frac{\chi^{198}}{198}+\ldots \ldots+\frac{\chi^{2}}{2}+\chi+5, \text { then } g^{\prime}(0)=
\]

Match List-I with List-II
\begin{array}{|l|l|l|l|}\hline & \text{List-I (Types of redox reactions)} & & \text{List-II (Examples)} \\\hline \text{a}. & \text{Combination reaction} & \text{(i)} & \mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{Br}_{(\mathrm{aq})}^{-} \rightarrow 2 \mathrm{Cl}_{(\mathrm{aq})}^{-}+\mathrm{Br}_{2(\mathrm{l})} \\\hline \text{b.} & \text{Decomposition reaction} & \text{(ii)} & 2 \mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow 2 \mathrm{H}_2 \mathrm{O}_{(1)}+\mathrm{O}_{2(\mathrm{~g})} \\\hline \text{c.} & \text{Displacement reaction} & \text{(iii)} & \mathrm{CH}_{4(\mathrm{~g})}+2 \mathrm{O}_{2(\mathrm{~g})} \xrightarrow{\Delta} \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(1)} \\\hline \text{d.} & \text{Disproportionation reaction} & \text{(iv)} & \mathrm{H}_2 \mathrm{O}_{(1)} \xrightarrow{\Delta} 2 \mathrm{H}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \\\hline\end{array}

Choose the correct answer from the options given below.

The angles \(A, B\) and \(C\) of a triangle \(A B C\) are in AP. If \(\mathrm{b}: \mathrm{c}=\sqrt{3}: \sqrt{2}\), then the angle \(\mathrm{A}\) is

Which of the following monomers can undergo condensation polymerisation?