1
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$I_{n}(x)=\int_{0}^{x} \frac{1}{\left(t^{2}+5\right)^{n}} d t, n=1,2,3, \ldots .$$ Then :

A
$$50 I_{6}-9 I_{5}=x I_{5}^{\prime}$$
B
$$50 I_{6}-11 I_{5}=x I_{5}^{\prime}$$
C
$$50 I_{6}-9 I_{5}=I_{5}^{\prime}$$
D
$$50 I_{6}-11 I_{5}=I_{5}^{\prime}$$
2
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area enclosed by the curves $$y=\log _{e}\left(x+\mathrm{e}^{2}\right), x=\log _{e}\left(\frac{2}{y}\right)$$ and $$x=\log _{\mathrm{e}} 2$$, above the line $$y=1$$ is:

A
$$2+\mathrm{e}-\log _{\mathrm{e}} 2$$
B
$$1+e-\log _{e} 2$$
C
$$e-\log _{e} 2$$
D
$$1+\log _{e} 2$$
3
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x)=2+|x|-|x-1|+|x+1|, x \in \mathbf{R}$$.

Consider

$$(\mathrm{S} 1): f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2$$

$$(\mathrm{S} 2): \int\limits_{-2}^{2} f(x) \mathrm{d} x=12$$

Then,

A
both (S1) and (S2) are correct
B
both (S1) and (S2) are wrong
C
only (S1) is correct
D
only (S2) is correct
4
JEE Main 2022 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region enclosed by $$y \leq 4 x^{2}, x^{2} \leq 9 y$$ and $$y \leq 4$$, is equal to :

A
$$\frac{40}{3}$$
B
$$\frac{56}{3}$$
C
$$\frac{112}{3}$$
D
$$\frac{80}{3}$$
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