Assertion (A):

$\dfrac{1}{2}$ log₂₅ $5+\dfrac{1}{3}$ log₈2 = $\dfrac{13}{36}$.

Reason (R):

$\dfrac{1}{2}$ log₂₅ $5+\dfrac{1}{3}$ log₈2 = $\dfrac{1}{4}+\dfrac{1}{9}=\dfrac{13}{36}$

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): log_x (m x n x p) = log_x m + log_x n + log p.

Reason (R): The logarithm of a product at any non-zero base is equal to the sum of the logarithms of its factors at the same base.

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): Using the information in the given figure; we get BD = CE.

Reason (R):

∵ △BDC ≅ △CEB (By AAS or ASA)
BD = CE

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): Using the information in the given figure, we get AM = CN.

Reason (R):

∠NDC = $\dfrac{1}{2}$∠ADC
and, ∠MBC = $\dfrac{1}{2}$∠ABC
Since. ∠ADC = ∠ABC
⇒ ∠NDC = ∠MBC
⇒ ∠AM = CN

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.