If \(\alpha, \beta, \gamma\) are the mean deviations about the mean, median and mode of the data 1, 2, 2, \(3,3,3,4,6\) respectively, then

If $\alpha$ and $\beta$ are the greatest divisors of $n\left(n^2-1\right)$ and $2n\left(n^2+2\right)$ respectively for all $n\in N$, then $\alpha \beta =$

If \(\frac{x^2+x+1}{x^2+2 x+1}=A+\frac{B}{x+1}+\frac{C}{(x+1)^2}\), then \(A-B\) is equal to

If a man throws a die until he gets a number bigger than 3, then the probability that he gets a 5 in his last throw is

The line \(4 x-3 y+2=0\) intersects the circle \(x^2+y^2-2 x+6 y+c=0\) at two points A, B and \(\mathrm{AB}=8\). If \((1, \mathrm{k})\) is a point on the given circle and \(\mathrm{k}>0\), then \(\mathrm{k}=\)

A fair coin is tossed $15$ times. The probability that the tail will appear atleast thrice is

If \(A\) is a non singular matrix, then \(\operatorname{Adj}\left(A^{-1}\right)=\)

Consider the following three resonance structures

The correct order of their stabilities is:

Let \(\alpha \neq 1\) be a real root of the equation \(x^3-a x^2+a x-1=0\), where \(a \neq-1\) is a rea number. Then, a root of this equation, among the following, is

Let \(\bar{a}\) and \(\bar{b}\) be two vectors such that \(|\bar{a}|=|\bar{b}|\) and \(|\bar{a}+2 \bar{b}|=|2 \bar{a}-\bar{b}|\). If \(\bar{c}\) is a vector parallel to \(\bar{a}\) then the angle between \(\bar{b}\) and \(\bar{c}\) is

Which among the following is the strongest acid?

\[ \begin{aligned} & \text { Given } \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(l) ; \Delta \mathrm{H}=-285 \mathrm{~kJ} \ & \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_3(l) ; \Delta \mathrm{H}=-76.6 \mathrm{~kJ} \ & \mathrm{~N}_2(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{HNO}_3(l) ; \Delta \mathrm{H}=-348.2 \mathrm{~kJ} \ & \text { Calculate the } \Delta \mathrm{H} \text { of } 2 \mathrm{~N}_2(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \end{aligned} \] Calculate the \(\Delta \mathrm{H}\) of \(2 \mathrm{~N}_2(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g})\).

The following reaction occurs in acidic medium \(\mathrm{KMnO}_4+8 \mathrm{H}^{+}+5 e^{-} \longrightarrow \mathrm{K}^{+}+\mathrm{Mn}^{2+}+4 \mathrm{H}_2 \mathrm{O}\) What is the equivalent weight of \(\mathrm{KMnO}_4\) ? (Molecular weight of \(\mathrm{KMnO}_4=158\))