1
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the local maximum value of the function $$f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right)$$ , is $$\frac{k}{e}$$, then $$\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}$$ is equal to

A
$$e^{3}+e^{6}+e^{10}$$
B
$$e^{3}+e^{5}+e^{11}$$
C
$$e^{3}+e^{6}+e^{11}$$
D
$$e^{5}+e^{6}+e^{11}$$
2
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the plane P: $$4 x-y+z=10$$ be rotated by an angle $$\frac{\pi}{2}$$ about its line of intersection with the plane $$x+y-z=4$$. If $$\alpha$$ is the distance of the point $$(2,3,-4)$$ from the new position of the plane $$\mathrm{P}$$, then $$35 \alpha$$ is equal to :

A
126
B
105
C
85
D
90
3
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region enclosed by the curve $$y=x^{3}$$ and its tangent at the point $$(-1,-1)$$ is :

A
$$\frac{23}{4}$$
B
$$\frac{19}{4}$$
C
$$\frac{27}{4}$$
D
$$\frac{31}{4}$$

4
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

In a triangle ABC, if $$\cos \mathrm{A}+2 \cos \mathrm{B}+\cos C=2$$ and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then $$\mathrm{\cos A-\cos C}$$ is equal to

A
$$\frac{3}{7}$$
B
$$\frac{9}{7}$$
C
$$\frac{10}{7}$$
D
$$\frac{5}{7}$$
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