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 ................... $^o$.

$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strikes the rod with a velocity $v_0$ at point $C$ at a distance $x$ from the centre $O$. The particle comes to rest after the collision. The value of $x$,so that point $A$ of the rod remains stationary just after the collision,is:

An expression of energy density is given by $u = \frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{kt}\right)$,where $\alpha$ and $\beta$ are constants,$x$ is displacement,$k$ is the Boltzmann constant,and $t$ is the temperature. The dimensions of $\beta$ will be $-$

What is absent in yeast?

If the lines,joining the origin to the points of intersection of the curve $2x^2 - 2xy + 3y^2 + 2x - y - 1 = 0$ and the line $x + 2y = k$,are at right angles,then $k^2$ equals

In the adjoining circuit diagram,the readings of the ammeter and voltmeter are $2 \ A$ and $120 \ V$,respectively. If the value of $R$ is $75 \ \Omega$,then the voltmeter resistance will be $\Omega$.