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): log₁₀₀(1000) = $\dfrac{3}{2}$.

Reason (R): log_b a = $\dfrac{log_{x}a}{log{x}b}$, for all a, b, x.

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.

Assertion (A): The straight line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side.

Reason (R): If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.

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.