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1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let $$f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$$, $$x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$$. Then, f is :
A
increasing in $$\left( { - {\pi \over 6},{\pi \over 2}} \right)$$
B
decreasing in $$\left( {0,{\pi \over 2}} \right)$$
C
increasing in $$\left( { - {\pi \over 6},0} \right)$$
D
decreasing in $$\left( { - {\pi \over 6},0} \right)$$
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let f : R $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ {{{\lambda \left| {{x^2} - 5x + 6} \right|} \over {\mu (5x - {x^2} - 6)}},} & {x < 2} \cr {{e^{{{\tan (x - 2)} \over {x - [x]}}}},} & {x > 2} \cr {\mu ,} & {x = 2} \cr } } \right.$$

where [x] is the greatest integer lss than or equal to x. If f is continuous at x = 2, then $$\lambda$$ + $$\mu$$ is equal to :
A
e($$-$$e + 1)
B
e(e $$-$$ 2)
C
1
D
2e $$-$$ 1
3
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let f : R $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.$$. Then f is increasing function in the interval
A
$$\left( { - {1 \over 2},2} \right)$$
B
(0,2)
C
$$\left( { - 1,{3 \over 2}} \right)$$
D
($$-$$3, $$-$$1)
4
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let f : R $$\to$$ R be defined as $$f(x) = \left\{ {\matrix{ {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{1 + 2x{e^{ - 2x}}} \over {{{(1 - x{e^{ - x}})}^2}}}} \right),} & {x \ne 0} \cr {\alpha ,} & {x = 0} \cr } } \right.$$

If f is continuous at x = 0, then $$\alpha$$ is equal to :
A
1
B
3
C
0
D
2
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