If \(x+\mathrm{y}=6, x \geqslant 0, y \geqslant 0\), then the maximum value of \(x^2 \mathrm{y}\) is

Which of the following matrix is invertible?
\(A_{1}=\left[\begin{array}{ll}4 & 2 \\ 2 & 1\end{array}\right]\)
\(A_{2}=\left[\begin{array}{ccc}-1 & -2 & 3 \\ 4 & 5 & 7 \\ 2 & 4 & -6\end{array}\right]\)
\(A_{3}=\left[\begin{array}{lll}1 & 0 & 0 \\ 5 & 2 & 1 \\ 7 & 2 & 1\end{array}\right]\)
\(A_{4}=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1\end{array}\right]\)

If the vector \(\overline{\mathrm{c}}\) lies in the plane of \(\overline{\mathrm{a}}\) and \(\bar{b}\), where \(\bar{a}=\hat{i}-\hat{j}+2 \hat{k}, \bar{b}=\hat{i}+\hat{j}+\hat{k}\) and \(\overline{\mathrm{c}}=x \hat{\mathrm{i}}-(2-x) \hat{\mathrm{j}}-\hat{\mathrm{k}}\), then the value of \(x\) is

If the line \(b x+m y+n=0\) is tangent to the parabola \(y^{2}=4 a x\), then

If \(\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}\), then the angle between the vectors \((2 \bar{a}+\bar{b})\) and \((\bar{a}+2 \bar{b})\) is

If \(\bar{x}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \bar{y}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) and \(\overline{\mathrm{z}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) where \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors, then value of \(\bar{x} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})+\bar{y} \cdot(\overline{\mathrm{~b}}+\overline{\mathrm{c}})+\overline{\mathrm{z}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})\) is

\(\int \frac{x \mathrm{~d} x}{(x-1)^2(x+2)}=\)

Which of following monomers is used in preparation of PAN?

The molar specific heat of an ideal gas at constant pressure and constant volume is $C_p$ and $C_{\upsilon }$ respectively. If $R$ is the universal gas constant and the ratio of $C_p$ to $C_{\upsilon }$ is $\gamma$ then $C_{\upsilon }=$

During DNA replication, the term leading template is applied to the one which replicates itself in A and the replication is B.

What is the position of transition elements from \(\mathrm{Sc}\) to \(\mathrm{Zn}\) in long form of periodic table?

At the same conditions of pressure, volume and temperature, work done is maximum for which gas if all gases have equal masses?

The value of \(\cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} x\right)\right)\right)\) is