JEE MAIN - Mathematics (2019 - 11th January Evening Slot - No. 21)

All x satisfying the inequality (cot–1 x)2– 7(cot–1 x) + 10 > 0, lie in the interval :
(cot 2, $$\infty $$)
(–$$\infty $$, cot 5) $$ \cup $$ (cot 2, $$\infty $$)
(cot 5, cot 4)
(– $$\infty $$, cot 5) $$ \cup $$ (cot 4, cot 2)

Explanation

cot$$-$$1 x > 5,    cot$$-$$1 x < 2

$$ \Rightarrow $$  x < cot5,   x > cot2

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