1
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha$$,where –1 $$\le$$ x $$\le$$ 1, – 2 $$\le$$ y $$\le$$ 2, x $$\le$$ $${y \over 2}$$ , then for all x, y, 4x2 – 4xy cos $$\alpha$$ + y2 is equal to :
A
4 sin2 $$\alpha$$
B
2 sin2 $$\alpha$$
C
4 sin2 $$\alpha$$ - 2x2y2
D
4 cos2 $$\alpha$$ + 2x2y2
2
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
$${\tan ^{ - 1}}\left( {{9 \over {5\sqrt {10} }}} \right)$$
3
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
4
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)
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