1
JEE Main 2025 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f:(0, \infty) \rightarrow \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^2 f^{\prime}(x)=2 x f(x)+3$, with $f(1)=4$. Then $2 f(2)$ is equal to :

A
19
B
23
C
29
D
39
2
JEE Main 2024 (Online) 9th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\log _e y=3 \sin ^{-1} x$$, then $$(1-x^2) y^{\prime \prime}-x y^{\prime}$$ at $$x=\frac{1}{2}$$ is equal to

A
$$9 e^{\pi / 2}$$
B
$$9 e^{\pi / 6}$$
C
$$3 e^{\pi / 2}$$
D
$$3 e^{\pi / 6}$$
3
JEE Main 2024 (Online) 9th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x)=a x^3+b x^2+c x+41$$ be such that $$f(1)=40, f^{\prime}(1)=2$$ and $$f^{\prime \prime}(1)=4$$. Then $$a^2+b^2+c^2$$ is equal to:

A
54
B
51
C
73
D
62
4
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Suppose for a differentiable function $$h, h(0)=0, h(1)=1$$ and $$h^{\prime}(0)=h^{\prime}(1)=2$$. If $$g(x)=h\left(\mathrm{e}^x\right) \mathrm{e}^{h(x)}$$, then $$g^{\prime}(0)$$ is equal to:

A
4
B
5
C
3
D
8
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