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Questions
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1
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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