1
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1
Out of Syllabus

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

For the function

$$f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$$, which one of the following is NOT correct?

A
f is increasing in (1, 2) and decreasing in (2, $$\infty$$)
B
f(x) = $$-$$1 has exactly two solutions
C
$$f'(e) - f''(2) < 0$$
D
f(x) = 0 has a root in the interval (e, e + 1)
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