1
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of all the roots of the equation $$\left|x^{2}-8 x+15\right|-2 x+7=0$$ is :

A
$$11+\sqrt{3}$$
B
$$9+\sqrt{3}$$
C
$$9-\sqrt{3}$$
D
$$11-\sqrt{3}$$
2
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $$\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^{\mathrm{n}}$$ is $$\sqrt{6}: 1$$, then the third term from the beginning is :

A
$$30 \sqrt{2}$$
B
$$60 \sqrt{3}$$
C
$$60 \sqrt{2}$$
D
$$30 \sqrt{3}$$
3
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$2 x^{y}+3 y^{x}=20$$, then $$\frac{d y}{d x}$$ at $$(2,2)$$ is equal to :

A
$$-\left(\frac{3+\log _{e} 16}{4+\log _{e} 8}\right)$$
B
$$-\left(\frac{2+\log _{e} 8}{3+\log _{e} 4}\right)$$
C
$$-\left(\frac{3+\log _{e} 8}{2+\log _{e} 4}\right)$$
D
$$-\left(\frac{3+\log _{e} 4}{2+\log _{e} 8}\right)$$
4
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1
Change Language

Let $$y=y(x)$$ be a solution of the differential equation $$(x \cos x) d y+(x y \sin x+y \cos x-1) d x=0,0 < x < \frac{\pi}{2}$$. If $$\frac{\pi}{3} y\left(\frac{\pi}{3}\right)=\sqrt{3}$$, then $$\left|\frac{\pi}{6} y^{\prime \prime}\left(\frac{\pi}{6}\right)+2 y^{\prime}\left(\frac{\pi}{6}\right)\right|$$ is equal to ____________.

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