Question

If the equation \[ \sin^2x - (p+2)\sin x - (p+3) = 0 \] has a solution, then \( p \) must lie in:

• A. \( [-3,-2] \)
• B. \( (-3,-2) \)
• C. \( (2,3) \)
• D. \( [-5,-3] \)

Hint:

For trig-substituted quadratics: Replace with bounded variable.  Check interval constraints.

Answer 1

The Correct Option is A

Concept:
Parallel combination:
- Resistor gives linear I–V relation.
- Diode gives exponential current in forward bias.

Step 1: Forward bias (positive V)
Diode conducts strongly ⇒ exponential rise.

Step 2: Reverse bias (negative V)
Diode blocks current ⇒ only resistor conducts ⇒ linear I–V.

Step 3: Resulting graph
- Linear in negative region
- Exponential in positive region
Matches option (B).