1
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

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
$$-\left(\frac{3+\log _{e} 4}{2+\log _{e} 8}\right)$$
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

If $$y(x)=x^{x},x > 0$$, then $$y''(2)-2y'(2)$$ is equal to

A
$$4(\log_{e}2)^{2}+2$$
B
$$8\log_{e}2-2$$
C
$$4\log_{e}2+2$$
D
$$4(\log_{e}2)^{2}-2$$
3
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

Let $$f(x) = 2x + {\tan ^{ - 1}}x$$ and $$g(x) = {\log _e}(\sqrt {1 + {x^2}} + x),x \in [0,3]$$. Then

A
there exists $$\widehat x \in [0,3]$$ such that $$f'(\widehat x) < g'(\widehat x)$$
B
there exist $$0 < {x_1} < {x_2} < 3$$ such that $$f(x) < g(x),\forall x \in ({x_1},{x_2})$$
C
$$\min f'(x) = 1 + \max g'(x)$$
D
$$\max f(x) > \max g(x)$$
4
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

Let $$y=f(x)=\sin ^{3}\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^{3}+5 x^{2}+1\right)^{\frac{3}{2}}\right)\right)\right)$$. Then, at x = 1,

A
$$2 y^{\prime}+\sqrt{3} \pi^{2} y=0$$
B
$$y^{\prime}+3 \pi^{2} y=0$$
C
$$\sqrt{2} y^{\prime}-3 \pi^{2} y=0$$
D
$$2 y^{\prime}+3 \pi^{2} y=0$$
EXAM MAP
Medical
NEET