1
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

Let $$A$$ be the area bounded by the curve $$y=x|x-3|$$, the $$x$$-axis and the ordinates $$x=-1$$ and $$x=2$$. Then $$12 A$$ is equal to ____________.

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2
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

$$A(2,6,2), B(-4,0, \lambda), C(2,3,-1)$$ and $$D(4,5,0),|\lambda| \leq 5$$ are the vertices of a quadrilateral $$A B C D$$. If its area is 18 square units, then $$5-6 \lambda$$ is equal to __________.

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3
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

If $$f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)$$ and $$g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)$$, then the value of $$f(4)-g(4)$$ is equal to ____________.

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4
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
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Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_{I}, E_{I I}$$ and $$E_{I I I}$$ are:

JEE Main 2023 (Online) 1st February Morning Shift Physics - Electrostatics Question 51 English

A
$$\vec{E}_{I}=0, \vec{E}_{I I}=\frac{\sigma}{\epsilon_{0}} \hat{n}, E_{I I I}=0$$
B
$$\vec{E}_{I}=\frac{\sigma}{2 \epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{\sigma}{2 \epsilon_{0}} \hat{n}$$
C
$$\vec{E}_{I}=-\frac{\sigma}{\epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{\sigma}{\epsilon_{0}} \hat{n}$$
D
$$\vec{E}_{I}=\frac{2 \sigma}{\epsilon_{0}} \hat{n}, \vec{E}_{I I}=0, \vec{E}_{I I I}=\frac{2 \sigma}{\epsilon_{0}} \hat{n}$$
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