Assertion (A):

$\dfrac{8^{x+2}+8^{x+1}}{8^{x+2}-8^{x+1}} \\[1em] = \dfrac{x + 2 + x + 1}{x + 2 - x - 1} \\[1em] = 2x + 3$

Reason (R):

$\dfrac{8^{x+2}+8^{x+1}}{8^{x+2}-8^{x+1}} \\[1em] = \dfrac{8^{(x+2+x+1)}}{8^{(x+2-x-1)}} \\[1em] = \dfrac{x + 2 + x + 1}{x + 2 - x - 1} \\[1em] = 2x + 3$

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):

4^x= 8^y x 16⁰
⇒ 2x = 3y

Reason (R):

4^x= 8^y x 16⁰
⇒ 2^2x = 2^3y
⇒ 2x = 3y
and 2x - 3y = 0

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): $\sqrt\dfrac{1}{4}+\dfrac{1}{\sqrt{0.01}}- \sqrt[3]{27^2} = \dfrac{1}{2}$

Reason (R): $\sqrt[n]{a^m}=a^\dfrac{m}{n}$, where a ≠ 0.

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): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ 5x = 20 and x = 4

Reason (R): If log₁₀x $\times$ log₁₀5 = log₁₀20
⇒ x + 5 = 20 and x = 15

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.