Question:
If the equation
\[
\sin^2x - (p+2)\sin x - (p+3) = 0
\]
has a solution, then \( p \) must lie in:
If the equation
\[
\sin^2x - (p+2)\sin x - (p+3) = 0
\]
has a solution, then \( p \) must lie in:
Show Hint
For trig-substituted quadratics: Replace with bounded variable. Check interval constraints.
Updated On: Mar 2, 2026
- \( [-3,-2] \)
- \( (-3,-2) \)
- \( (2,3) \)
- \( [-5,-3] \)
Show Solution
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The Correct Option is A
Solution and Explanation
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).
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).
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