Statement-1 : For PCℓ5 Image not present PCl3 + Cl2 reaction, equilibrium constant increases on increasing temperature. Statement-2 : Rate of forward reaction increases and rate of backward reaction decreases on increasing temperature. (1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation of statement-1. (2) Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1. (3) Statement-1 is true, statement-2 is false. (4) Statement-1 is false, statement-2 is true.

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- 1 :

0 < x < y \Rightarrow {log}_{a} x > {log}_{a} y

a > 1

- 2 :

a > 1, {log}_{a} x

H_{3} P O_{4}

H_{3} P O_{4}, H_{3} P O_{3} and H_{3} P O_{2}

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} = (n + 2) 2^{n - 1} .

\sum_{r = 0}^{n} (r + 1)^{n} C_{r} x^{r} = (1 + x)^{n} + n x (1 + x)^{n - 1} .

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

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