1
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

Let $$\lambda x - 2y = \mu$$ be a tangent to the hyperbola $${a^2}{x^2} - {y^2} = {b^2}$$. Then $${\left( {{\lambda \over a}} \right)^2} - {\left( {{\mu \over b}} \right)^2}$$ is equal to :

A
$$-$$2
B
$$-$$4
C
2
D
4
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The number of real roots of the equation

$${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$$ is :
A
2
B
4
C
1
D
0
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
A box open from top is made from a rectangular sheet of dimension a $$\times$$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :
A
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over {12}}$$
B
$${{a + b - \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
C
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over 6}$$
D
$${{a + b + \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :
A
$${5 \over {2 + \sqrt 3 }}$$
B
$${{10} \over {2 + 3\sqrt 3 }}$$
C
$${5 \over {3 + \sqrt 3 }}$$
D
$${{10} \over {3 + 2\sqrt 3 }}$$
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