An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

On addition of $1 \ mL$ solution of $10\% \ NaCl$ to $10 \ mL$ gold sol in the presence of $0.025 \ g$ of starch,the coagulation is just prevented. The gold number of starch is:

Which insecticide is lipophilic in nature?

Which of the following ethers cannot be produced by Williamson ether synthesis?

The figure shows a plot of binding energy per nucleon $E_b$ against the nuclear mass $M$. $A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:
$(i)$ $A + B \to C + \varepsilon$
$(ii)$ $C \to A + B + \varepsilon$
$(iii)$ $D + E \to F + \varepsilon$
$(iv)$ $F \to D + E + \varepsilon$
where $\varepsilon$ is the energy released. In which reactions is $\varepsilon$ positive?