If \(A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]\), then \(A+2 A^{-1}=\)

\(x=\frac{1}{2}\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right)\), then \(\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}\) is equal to

Suppose the pairs of straight lines \(2 x^2+a x y+3 y^2=0\) and \(2 x^2+b x y-3 y^2=0\) are such that they have one common line with the other two remaining perpendicular. Then the values of \(a\) and \(b\) respectively are

If the roots of the equation \(x^3-13 x^2+\mathrm{K} x-27=0\) are in geometric progression then \(\mathrm{K}=\)

If in $∆ABC,a\tan A+b\tan B=(a+b)·\tan \left(\frac{A+B}{2}\right)$, then which of the following holds?

In the binomial expansion of \((p-q)^{14}\), if the sum of \(7^{\text {th }}\) term and \(8^{\text {th }}\) term is zero, then \(\frac{p+q}{p-q}=\)

If $f\left(x\right)=2x^3+{mx}^2- 13x+n$ and $2, 3$ are roots of the equation $f\left(x\right)=0$ , then the values of $m$ and $n$ are -

Let \(X\) be a random variable with probability distribution function,
\(P(X=x)=K\left(\frac{2}{5}\right)^x, x=1,2,3, \ldots \ldots\) Then, value of \(K\) is

If \(\alpha\) is the maximum value and \(\beta\) is the minimum value of \(\cos ^2 \frac{x}{4}+\sin \frac{x}{4}\), \(x \in R\), then \(\alpha-\beta=\)

The plates of a parallel plate capacitor are charged upto \(100 \mathrm{~V}\). A \(2 \mathrm{~mm}\) thick insulator sheet is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by \(1.6 \mathrm{~mm}\). The dielectric constant of the insulator is

Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) and \(\mathrm{d}\) be non-zero numbers. If the point of intersection of the lines \(4 a x+2 a y+c=0\) and \(5 b x+2 b y\) \(+\mathrm{d}=0\) lies in the fourth quadrant and is equidistant from the two coordinate axes, then

If the straight lines \(2 x+3 y-1=0\), \(x+2 y-1=0\) and \(a x+b y-1=0\) form a triangle with orthocentre at the origin, then \((a, b)=\)

Observe the following statements :
a. The thermal stability of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
b. Acidic nature of hydrides of group 16 elements follow the order :
\(\mathrm{H}_2 \mathrm{O}>\mathrm{H}_2 \mathrm{~S}>\mathrm{H}_2 \mathrm{Se}>\mathrm{H}_2 \mathrm{Te}\)
c. The reducing nature of \(\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{Se}\) and \(\mathrm{H}_2\) Te follow the order :
\(\mathrm{H}_2 \mathrm{~S} < \mathrm{H}_2 \mathrm{Se} < \mathrm{H}_2 \mathrm{Te}\)
The correct statement are: