$\begin{array}{1 1}(a)\;rate=k[X]\\(b)\;rate=k[X]^2\\(c)\;rate=k[X][Y]\\(d)\;rate=k[X]^2[Y]\end{array}$

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Answer: Rate=$k[X]^2$

From the given diagram, when time $= 50s,\; \large\frac{1}{[X]}$$ = 6 \rightarrow $ Equation of line=$\large\frac{1}{[X]}$$-2=\large\frac{6-2}{50}$$(t-0)$

$\large\frac{1}{[X]}$$=2+\large\frac{4t}{50}$

$\large\frac{1}{[X]}$$=2+\large\frac{2}{25}$$t$

Differentiating w.r.t [X]

$-\large\frac{-1}{[X]^2}=\frac{2}{25}\frac{dt}{d[X]}$

$\large\frac{d[X]}{dt}=-\frac{2}{25}$$[X]^2$

rate=$-\large\frac{d[X]}{dt}=\frac{2}{25}$$[X]^2=k[X]^2$

Rate=$k[X]^2$

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