If $\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} = 3,$ then $\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} = $

$4 \ g$ of an ideal gas occupies $5.6035 \ L$ of volume at $546 \ K$ and $2 \ atm$ pressure. What is its molecular weight?

$A$ sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of the wire is '$n_1$'. When the bob is completely immersed in water,the frequency of vibration of the wire becomes '$n_2$'. The relative density of the metal of the bob is

Identify the incorrect pair for Gymnosperms from the following:

$\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \\ & \Rightarrow A+C= \end{aligned}$

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: (in $kg$)