1. Use the Arrhenius equation

$k = A e^{-E_a/(RT)}$

Taking logarithm:

$\ln k = \ln A - \frac{E_a}{RT}$

This shows how the rate constant $k$ depends on temperature $T$ and activation energy $E_a$.

2. Interpret temperature dependence

From Arrhenius equation, for larger $E_a$, the exponential term changes more strongly with temperature. Hence, greater temperature dependence of $k$ means larger activation energy.

So:

• (A) Correct
• (C) Incorrect

3. Check statement (B)

If $E_a = 0$, then

$k = A e^0 = A$

So $k$ becomes independent of temperature provided $A$ is taken constant in the Arrhenius form, which is the standard interpretation in such questions.

Hence:

• (B) Correct

4. Check statement (D)

If there is no correlation between temperature and rate constant, then effectively $k$ does not change with $T$.

From Arrhenius equation, that corresponds to:

$E_a = 0$

not negative activation energy.

For negative activation energy, rate constant typically decreases with increasing temperature, so there is still a temperature dependence, just opposite in sign.

Therefore:

• (D) Incorrect

5. Count correct statements

Correct statements are:

$A, B$

So the number of correct statements is:

$2$