If $a$ and $b$ are unit vectors such that $(a + 2b)$ and $(5a - 4b)$ are perpendicular to each other,then the angle between $a$ and $b$ is ................... $^o$.

In the circuit shown,a potential difference of $60\,V$ is applied across $AB$. The potential difference between the points $M$ and $N$ is.....$V$

$A$ weak acid $HA$ has a $K_a$ of $1.00 \times 10^{-5}$. If $0.100 \ mol$ of this acid is dissolved in one litre of water,the percentage of acid dissociated at equilibrium is closest to.....$\%$

$A$ point charge $+q$ is placed at the centre of a cube of side $L$. The electric flux emerging from the cube is

$A$ finite ladder is constructed by connecting several sections of $2\,\mu F$ and $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between? (Answer in $\mu F$)

The function $f: R \rightarrow R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$. Then the range $f(R)$ is equal to