1
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$f(\alpha)=\int\limits_{1}^{\alpha} \frac{\log _{10} \mathrm{t}}{1+\mathrm{t}} \mathrm{dt}, \alpha>0$$, then $$f\left(\mathrm{e}^{3}\right)+f\left(\mathrm{e}^{-3}\right)$$ is equal to :

A
9
B
$$\frac{9}{2}$$
C
$$\frac{9}{\log _{e}(10)}$$
D
$$\frac{9}{2 \log _{e}(10)}$$
2
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
$$50 I_{6}-11 I_{5}=I_{5}^{\prime}$$
3
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The minimum value of the twice differentiable function $$f(x)=\int\limits_{0}^{x} \mathrm{e}^{x-\mathrm{t}} f^{\prime}(\mathrm{t}) \mathrm{dt}-\left(x^{2}-x+1\right) \mathrm{e}^{x}$$, $$x \in \mathbf{R}$$, is :

A
$$-\frac{2}{\sqrt{\mathrm{e}}}$$
B
$$-2 \sqrt{\mathrm{e}}$$
C
$$-\sqrt{\mathrm{e}}$$
D
$$\frac{2}{\sqrt{\mathrm{e}}}$$
4
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
JEE Main Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12