Which of the following is NOT a corner point of the feasible region determined by the constraints:
\(x + 2y \leq 4\) ;
\(x + y \geq 2\) ;
\(x \geq 0\) and \(y \geq 0\)

\(\int_\limits0^{\dfrac{\pi}{2}} \dfrac{\cos x}{1+\cos x+\sin x} d x=\)

If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]\), then \(A \cdot \operatorname{adj}(A)\) is equal to

\(\text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is }\)

Find the distance of a point \((1,2,3)\) from the plane \(3 y+4 z+4=0\).

The line \(21 x+5 y=116\) is a tangent to the hyperbola \(7 x^{2}-5 y^{2}=232\). Its point of contact is

\(\text { The function } f(x)=\tan ^{-1}(\sin x+\cos x) \text { is an increasing function in }\)

In a container of height \(21 \mathrm{~cm}\), certain transparent liquid is taken to a height of \(12 \mathrm{~cm}\). When seen from above, it appears half filled. The refractive index of the liquid is

Choose the incorrect statement from the following.

If \(C\) be the capacitance and \(V\) be the electric potential, then the dimensional formula of \(\mathrm{CV}^2\) is

The metal hydroxide which is soluble in excess of ammonium hydroxide is

Match the coordination compounds in Column I having the given type of hybridisation of \(\mathrm{M}^{\mathrm{n}+}\) ion and magnetic moment as given in Column II.
\(\begin{array}{|l|l|l|l|} \hline & \text { Coordination compounds. } & & \text { Hybridisation \& Magnetic nature. } \\ \hline \text { A } & \mathrm{Ni}(\mathrm{CO})_4 & \text { P } & \mathrm{sp}^3, \quad \mu=5.92 \mathrm{BM} \\ \hline \text { B } & {\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}} & \text { Q } & \mathrm{sp}^3, \quad \mu=2.84 \mathrm{BM} \\ \hline \text { C } & {\left[\mathrm{Ni}(\mathrm{Cl})_4\right]^{2-}} & \text { R } & \mathrm{sp}^3, \quad \mu=0 \\ \hline \text { D } & {[\mathrm{MnBr}]^{2-}} & \text { S } & \mathrm{dsp}^2, \quad \mu=0 \\ \hline \end{array}\)

The enthalpies of combustion of \(\mathrm{H}_2, \mathrm{C}\) (graphite) and \(\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})\) are \(-286.0,-394.0\) and \(-1560.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at \(25^{\circ} \mathrm{C}\) and 1 atm pressure. The enthalpy of formation of ethane is: