1
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be defined as :

$$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4\end{cases}$$

where $$\mathrm{b} \in \mathbb{R}$$. If $$f$$ is continuous at $$x=4$$, then which of the following statements is NOT true?

A
$$f$$ is not differentiable at $$x=4$$
B
$$f^{\prime}(3)+f^{\prime}(5)=\frac{35}{4}$$
C
$$f$$ is increasing in $$\left(-\infty, \frac{1}{8}\right) \cup(8, \infty)$$
D
$$f$$ has a local minima at $$x=\frac{1}{8}$$
2
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \int\limits_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x \text { is equal to } $$

A
$$10(\pi+4)$$
B
$$10(\pi+2)$$
C
$$20(\pi-2)$$
D
$$20(\pi+2)$$
3
JEE Main 2022 (Online) 26th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area bounded by the curves $$y=\left|x^{2}-1\right|$$ and $$y=1$$ is

A
$$\frac{2}{3}(\sqrt{2}+1)$$
B
$$\frac{4}{3}(\sqrt{2}-1)$$
C
$$2(\sqrt{2}-1)$$
D
$$\frac{8}{3}(\sqrt{2}-1)$$
4
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is $${{364} \over 3}$$, is equal to :

A
3
B
5
C
7
D
9
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