1
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

Let $$\beta=\mathop {\lim }\limits_{x \to 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}$$ for some $$\alpha \in \mathbb{R}$$. Then the value of $$\alpha+\beta$$ is :

A
$$\frac{14}{5}$$
B
$$\frac{3}{2}$$
C
$$\frac{5}{2}$$
D
$$\frac{7}{2}$$
2
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

Let f : R $$\to$$ R be a continuous function such that $$f(3x) - f(x) = x$$. If $$f(8) = 7$$, then $$f(14)$$ is equal to :

A
4
B
10
C
11
D
16
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

If the function $$f(x) = \left\{ {\matrix{ {{{{{\log }_e}(1 - x + {x^2}) + {{\log }_e}(1 + x + {x^2})} \over {\sec x - \cos x}}} & , & {x \in \left( {{{ - \pi } \over 2},{\pi \over 2}} \right) - \{ 0\} } \cr k & , & {x = 0} \cr } } \right.$$ is continuous at x = 0, then k is equal to:

A
1
B
$$-$$1
C
e
D
0
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

If $$f(x) = \left\{ {\matrix{ {x + a} & , & {x \le 0} \cr {|x - 4|} & , & {x > 0} \cr } } \right.$$ and $$g(x) = \left\{ {\matrix{ {x + 1} & , & {x < 0} \cr {{{(x - 4)}^2} + b} & , & {x \ge 0} \cr } } \right.$$ are continuous on R, then $$(gof)(2) + (fog)( - 2)$$ is equal to :

A
$$-$$10
B
10
C
8
D
$$-$$8
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