In a $\triangle \mathrm{ABC}, \mathrm{A} \equiv(\alpha, 2 \alpha+3), \mathrm{B} \equiv(1,2), \mathrm{C} \equiv(2,3)$. If the area of $\triangle \mathrm{ABC}$ be $\Delta$ such that $[\Delta]=2$, where [.] denotes the greatest integer function, then the number of all possible integral values of $\alpha$ is

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

In a

\triangle \mathrm{ABC}, \mathrm{A} \equiv(\alpha, 2 \alpha+3), \mathrm{B} \equiv(1,2), \mathrm{C} \equiv(2,3)

. If the area of

\triangle \mathrm{ABC}

\Delta

such that

[\Delta]=2

, where [.] denotes the greatest integer function, then the number of all possible integral values of

\alpha

View answer and explanation

Correct option: A

Option A (4) is correct because solving the inequality derived from the area condition yields four possible integer values for alpha.