1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If $$\alpha = {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$, $$\beta = {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$ where $$0 < \alpha ,\beta < {\pi \over 2}$$ , then $$\alpha$$ - $$\beta$$ is equal to :
A
$${\tan ^{ - 1}}\left( {{9 \over {14 }}} \right)$$
B
$${\sin ^{ - 1}}\left( {{9 \over {5\sqrt {10} }}} \right)$$
C
$${\cos ^{ - 1}}\left( {{9 \over {5\sqrt {10} }}} \right)$$
D
$${\tan ^{ - 1}}\left( {{9 \over {5\sqrt {10} }}} \right)$$
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Considering only the principal values of inverse functions, the set
A = { x $$\ge$$ 0: tan$$-$$1(2x) + tan$$-$$1(3x) = $${\pi \over 4}$$}
A
contains two elements
B
contains more than two elements
C
is an empty set
D
is a singleton
3
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
All x satisfying the inequality (cot–1 x)2– 7(cot–1 x) + 10 > 0, lie in the interval :
A
(cot 2, $$\infty$$)
B
(–$$\infty$$, cot 5) $$\cup$$ (cot 2, $$\infty$$)
C
(cot 5, cot 4)
D
(– $$\infty$$, cot 5) $$\cup$$ (cot 4, cot 2)
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The value of $$\cot \left( {\sum\limits_{n = 1}^{19} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{p = 1}^n {2p} } \right)} \right)$$ is :
A
$${{22} \over {23}}$$
B
$${{23} \over {22}}$$
C
$${{21} \over {19}}$$
D
$${{19} \over {21}}$$
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