The common bottle cork is a product of .......... .

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:

Two simple pendulums whose lengths are $1\,m$ and $121\,cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum will the two be in phase again?

$A$ metal ball of mass $2 \ kg$ moving with a velocity of $36 \ km/h$ has a head-on collision with a stationary ball of mass $3 \ kg$. After the collision,if both balls move together,the loss in kinetic energy due to the collision is: (in $J$)

Using the Trapezoidal rule,find the approximate value of $\int_1^4 y \, dx$ based on the following table:

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

(in $.1833$)

Suppose $A$ and $B$ are the points at which the line $x+y-\lambda=0$ meets the pair of straight lines $x^2+y^2-2x-4y+2=0$. If $\angle AOB=90^{\circ}$,then a value of $\lambda$ is