The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is:

$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases.

$A$ tank with vertical walls is mounted so that its base is at a height $H$ above the horizontal ground. The tank is filled with water to a depth $h$. $A$ hole is punched in the side wall of the tank at a depth $x$ below the water surface. To have maximum range of the emerging stream,the value of $x$ is

Total number of secondary amines (excluding stereoisomers) possible with the molecular formula $C_5H_{13}N$ is

Which of the following statements is correct?

The formation of the oxide ion $O^{2-}_{(g)}$ requires first an exothermic and then an endothermic step as shown below:
$O_{(g)} + e^- \to O^-_{(g)}; \Delta H = -142 \ kJ/mol$
$O^-_{(g)} + e^- \to O^{2-}_{(g)}; \Delta H = 844 \ kJ/mol$
This is because: