If the two circles $2x^2 + 2y^2 - 3x + 6y + k = 0$ and $x^2 + y^2 - 4x + 10y + 16 = 0$ cut orthogonally,then the value of $k$ is

In a pseudo first order hydrolysis of ester in water,the following results were obtained.

$t/s$	$0$	$30$	$60$	$90$
$Ester/mol\, L^{-1}$	$0.55$	$0.31$	$0.17$	$0.085$

What will be the average rate of reaction between the time interval $30$ to $60$ seconds?

Two semicircular rings of linear mass densities $\lambda$ and $3 \lambda$ and of radius $R$ each,are joined to form a complete ring. The distance of the centre of mass of the complete ring from its geometrical centre is

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be

Assertion : Bond angle of $H_2S$ is smaller than $H_2O$.
Reason : Electronegativity of the central atom increases,bond angle decreases.

If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$, then $f(9)$ is equal to