"The probability of selecting integers a$\\in$[$-$ 5, 30] such that x2 + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\\in$R, is :"

"D < 0 $\\Rightarrow$ 4(a + 4) 2 $-$ 4($-$5a + 64) < 0 $\\Rightarrow$ a 2 + 16 + 8a + 5a $-$ 64 < 0 $\\Rightarrow$ a 2 + 13a $-$ 48 < 0 $\\Rightarrow$ (a + 16) (a $-$ 3) < 0 $\\Rightarrow$ a $\\in$ ($-$16, 3) $\\therefore$ Possible a : {$-$5, $-$4, ............., 3} $\\therefore$ Required probability = ${8 \\over {36}}$ = ${2 \\over {9}}$"

Medium MCQ +4 / -1 PYQ · JEE Mains 2021

The probability of selecting integers a$\in$[$-$ 5, 30] such that x² + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, is :

A ${7 \over {36}}$
B ${2 \over {9}}$ Correct answer
C ${1 \over {6}}$
D ${1 \over {4}}$

Solution

D < 0 $\Rightarrow$ 4(a + 4)2 $-$ 4($-$5a + 64) < 0 $\Rightarrow$ a2 + 16 + 8a + 5a $-$ 64 < 0 $\Rightarrow$ a2 + 13a $-$ 48 < 0 $\Rightarrow$ (a + 16) (a $-$ 3) < 0 $\Rightarrow$ a $\in$ ($-$16, 3) $\therefore$ Possible a : {$-$5, $-$4, ............., 3} $\therefore$ Required probability = ${8 \over {36}}$ = ${2 \over {9}}$

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Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability

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The probability of selecting integers a$\in$[$-$ 5, 30] such that x2 + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, is :

Solution

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The probability of selecting integers a$\in$[$-$ 5, 30] such that x² + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, is :