1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2 / sec) at which the wet conical surface area of the vessel increases is

A
5
B
$${{\sqrt {21} } \over 5}$$
C
$${{\sqrt {26} } \over 5}$$
D
$${{\sqrt {26} } \over {10}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

If the angle made by the tangent at the point (x0, y0) on the curve $$x = 12(t + \sin t\cos t)$$, $$y = 12{(1 + \sin t)^2}$$, $$0 < t < {\pi \over 2}$$, with the positive x-axis is $${\pi \over 3}$$, then y0 is equal to:

A
$$6\left( {3 + 2\sqrt 2 } \right)$$
B
$$3\left( {7 + 4\sqrt 3 } \right)$$
C
27
D
48
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by $${{{x^2}} \over {xy - {x^2}{y^2} - 1}}$$. If the curve passes through the point (1, 1), then e . y(e) is equal to

A
$${{1 - \tan (1)} \over {1 + \tan (1)}}$$
B
tan(1)
C
1
D
$${{1 + \tan (1)} \over {1 - \tan (1)}}$$
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let $$\lambda$$$$^ *$$ be the largest value of $$\lambda$$ for which the function $${f_\lambda }(x) = 4\lambda {x^3} - 36\lambda {x^2} + 36x + 48$$ is increasing for all x $$\in$$ R. Then $${f_{{\lambda ^ * }}}(1) + {f_{{\lambda ^ * }}}( - 1)$$ is equal to :

A
36
B
48
C
64
D
72
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