1
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

For the differentiable function $$f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$$, let $$3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10$$, then $$\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|$$ is equal to

A
13
B
$$\frac{29}{5}$$
C
$$\frac{33}{5}$$
D
7
2
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1

Let $$f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$$. Then $$f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$$ is equal to

A
$$\frac{2}{3 \sqrt{3}}$$
B
$$\frac{2}{9}$$
C
$$\frac{-1}{3 \sqrt{3}}$$
D
$$\frac{-2}{3}$$
3
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
$$-\left(\frac{3+\log _{e} 4}{2+\log _{e} 8}\right)$$
4
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
$$4(\log_{e}2)^{2}-2$$
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