1
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

$$\text { Let } y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1 < x<1 \text {. Then at } x=\frac{1}{2} \text {, the value of } 225\left(y^{\prime}-y^{\prime \prime}\right) \text { is equal to }$$

A
732
B
736
C
742
D
746
2
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

Suppose $$f(x)=\frac{\left(2^x+2^{-x}\right) \tan x \sqrt{\tan ^{-1}\left(x^2-x+1\right)}}{\left(7 x^2+3 x+1\right)^3}$$. Then the value of $$f^{\prime}(0)$$ is equal to

A
$$\pi$$
B
$$\sqrt{\pi}$$
C
0
D
$$\frac{\pi}{2}$$
3
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
4
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
$$\frac{-2}{3}$$
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