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

For any integer $$\mathrm{n}, \int_\limits0^\pi \mathrm{e}^{\cos ^2 x} \cdot \cos ^3(2 n+1) x \mathrm{~d} x$$ has the value :

A
$$\pi$$
B
1
C
0
D
$$\frac{3 \pi}{2}$$
2
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
$$\mathrm{y}-1=\mathrm{e}^{-\mathrm{f}(x)}+\mathrm{f}(x)$$
3
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
$$\mathrm{e}+\mathrm{ab}-\mathrm{e}^{\mathrm{a}},\left(\mathrm{y}^{\prime}=\frac{\mathrm{dy}}{\mathrm{d} x}\right)$$
4
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
EXAM MAP