1
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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)
2
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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
$${x \over 3} - {y^2} = 2$$
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of absolute maximum and absolute minimum values of the function $$f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$$ in the interval [0, 1] is :

A
$$3 + {{\sin (1){{\cos }^2}\left( {{1 \over 2}} \right)} \over 2}$$
B
$$3 + {1 \over 2}(1 + 2\cos (1))\sin (1)$$
C
$$5 + {1 \over 2}(\sin (1) + \sin (2))$$
D
$$2 + \sin \left( {{1 \over 2}} \right)\cos \left( {{1 \over 2}} \right)$$
4
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

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
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