1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$\mathrm{f}$$ be a differential function with $$\lim _\limits{x \rightarrow \infty} \mathrm{f}(x)=0$$. If $$\mathrm{y}^{\prime}+\mathrm{yf}^{\prime}(x)-\mathrm{f}(x) \mathrm{f}^{\prime}(x)=0$$, $$\lim _\limits{x \rightarrow \infty} y(x)=0$$ then

A
$$\mathrm{y}+1=\mathrm{e}^{\mathrm{f}(x)}+\mathrm{f}(x)$$
B
$$\mathrm{y}+1=\mathrm{e}^{-\mathrm{f}(x)}+\mathrm{f}(x)$$
C
$$\mathrm{y}+2=\mathrm{e}^{-\mathrm{f}(\mathrm{x})}+\mathrm{f}(x)$$
D
$$\mathrm{y}-1=\mathrm{e}^{-\mathrm{f}(x)}+\mathrm{f}(x)$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$x y^{\prime}+y-e^x=0, y(a)=b$$, then $$\lim _\limits{x \rightarrow 1} y(x)$$ is

A
$$e+2 a b-e^a$$
B
$$e^2+a b-e^{-a}$$
C
$$\mathrm{e}-\mathrm{ab}+\mathrm{e}^{\mathrm{a}}$$
D
$$\mathrm{e}+\mathrm{ab}-\mathrm{e}^{\mathrm{a}},\left(\mathrm{y}^{\prime}=\frac{\mathrm{dy}}{\mathrm{d} x}\right)$$
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The area bounded by the curves $$x=4-y^2$$ and the Y-axis is

A
16 sq. unit
B
$$\frac{32}{3}$$ sq. unit
C
$$\frac{16}{3}$$ sq. unit
D
32 sq. unit
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

$$f(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}$$ Then $$\mathrm{f}(x)$$ is

A
decreasing function
B
increasing function
C
neither increasing nor decreasing
D
constant $$\forall x>0$$
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