1
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
$${{1 + \tan (1)} \over {1 - \tan (1)}}$$
2
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
3
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1 The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

A
9
B
10
C
11
D
12
4
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1 If the tangent at the point (x1, y1) on the curve $$y = {x^3} + 3{x^2} + 5$$ passes through the origin, then (x1, y1) does NOT lie on the curve :

A
$${x^2} + {{{y^2}} \over {81}} = 2$$
B
$${{{y^2}} \over 9} - {x^2} = 8$$
C
$$y = 4{x^2} + 5$$
D
$${x \over 3} - {y^2} = 2$$
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