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
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
$$2 + \sin \left( {{1 \over 2}} \right)\cos \left( {{1 \over 2}} \right)$$
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\{ {a_i}\} _{i = 1}^n$$, where n is an even integer, is an arithmetic progression with common difference 1, and $$\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120} $$, then n is equal to :

A
48
B
96
C
92
D
104
4
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If x = x(y) is the solution of the differential equation

$$y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0$$; then x(e) is equal to :

A
$${e^3}({e^e} - 1)$$
B
$${e^e}({e^3} - 1)$$
C
$${e^2}({e^e} + 1)$$
D
$${e^e}({e^2} - 1)$$
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