1
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
If $$\alpha$$, $$\beta$$ and $$\gamma$$ are three consecutive terms of a non-constant G.P. such that the equations $$\alpha$$x 2 + 2$$\beta$$x + $$\gamma$$ = 0 and x2 + x – 1 = 0 have a common root, then $$\alpha$$($$\beta$$ + $$\gamma$$) is equal to :
A
$$\alpha$$$$\gamma$$
B
0
C
$$\beta$$$$\gamma$$
D
$$\alpha$$$$\beta$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
The number of real roots of the equation
5 + |2x – 1| = 2x (2x – 2) is
A
2
B
1
C
3
D
4
3
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
All the pairs (x, y) that satisfy the inequality
$${2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1$$
also satisfy the equation
A
sin x = |sin y|
B
sin x = 2sin y
C
2 sin x = sin y
D
2 |sin x | = 3 sin y
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation,
x2 + x sin $$\theta$$ - 2 sin $$\theta$$ = 0, $$\theta \in \left( {0,{\pi \over 2}} \right)$$, then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right).{{\left( {\alpha - \beta } \right)}^{24}}}}$$ is equal to :
A
$${{{2^{12}}} \over {{{\left( {\sin \theta - 8} \right)}^6}}}$$
B
$${{{2^6}} \over {{{\left( {\sin \theta + 4} \right)}^{12}}}}$$
C
$${{{2^{12}}} \over {{{\left( {\sin \theta + 8} \right)}^{12}}}}$$
D
$${{{2^{12}}} \over {{{\left( {\sin \theta - 4} \right)}^{12}}}}$$
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