$A$ large tank is filled with water to a height $H$. $A$ small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $H/\eta$ (where $\eta > 1$); and it takes $T_2$ time to drain the rest of the water. If $T_1 = T_2$,then the value of $\eta$ is:

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$,$y=\cos x$ and the $x$-axis $(0 \leq x \leq \frac{\pi}{2})$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)

$3$ moles of an ideal monoatomic gas perform an $A B C D A$ cyclic process as shown in the figure. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J / mol K)$. (in $ \, kJ$)

Assign $A, B, C, D$ from the given type of reaction.
$4KCN + Fe(CN)_2 \downarrow \longrightarrow K_4[Fe(CN)_6]$

Suppose $E$ and $F$ are two events of a random experiment. If the probability of occurrence of $E$ is $1/5$ and the probability of occurrence of $F$ given $E$ is $1/10$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is

One turn of insulated wire in the form of a planar square frame with side $l = 0.2\,m$ and resistance $R = 1\,\Omega$ is placed in a uniform magnetic field perpendicular to the plane of the frame. The current passing through the turn when the magnetic field starts to decrease at a constant rate of $0.1\,T/s$ is......$mA$.