The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$,then the time at which the population becomes zero is

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

How many $g$ of a dibasic acid (Mol. wt. $= 200$) should be present in $100 \ ml$ of its aqueous solution to give a decinormal strength?

The enthalpy of combustion of benzene from the following data will be
$(i) \ 6C_{(s)} + 3H_{2(g)} \to C_6H_{6(l)}; \Delta H = + 45.9 \ kJ$
$(ii) \ H_{2(g)} + \frac{1}{2}O_{2(g)} \to H_2O_{(l)}; \Delta H = - 285.9 \ kJ$
$(iii) \ C_{(s)} + O_{2(g)} \to CO_{2(g)}; \Delta H = - 393.5 \ kJ$
........$kJ$

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $C$ is equal to (in $^{\circ}$)

On stretching a wire,the elastic energy stored per unit volume is