1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

$$\lim _\limits{n \rightarrow \infty} \frac{1}{n^{k+1}}[2^k+4^k+6^k+\ldots .+(2 n)^k]=$$

A
$$\frac{2^k}{k}$$
B
$$\frac{2^{k+1}}{k+1}$$
C
$$\frac{2^k}{k+1}$$
D
$$\frac{2^{\mathrm{k}}}{\mathrm{k}-1}$$
2
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

The acceleration f $$\mathrm{ft} / \mathrm{sec}^2$$ of a particle after a time $$\mathrm{t}$$ sec starting from rest is given by $$\mathrm{f}=6-\sqrt{1.2 \mathrm{t}}$$. Then the maximum velocity $$\mathrm{v}$$ and time $$\mathrm{T}$$ to attend this velocity are

A
$$\mathrm{T}=20 \mathrm{~sec}$$
B
$$\mathrm{v}=60 \mathrm{~ft} / \mathrm{sec}$$
C
$$\mathrm{T}=30 \mathrm{~sec}$$
D
$$\mathrm{v}=40 \mathrm{~tt} / \mathrm{sec}$$
3
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

Let $$\Gamma$$ be the curve $$\mathrm{y}=\mathrm{be}^{-x / a}$$ & $$\mathrm{L}$$ be the straight line $$\frac{x}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$$ where $$\mathrm{a}, \mathrm{b} \in \mathbb{R}$$. Then

A
$$\mathrm{L}$$ touches the curve $$\Gamma$$ at the point where the curve crosses the axis of $$y$$.
B
$$\mathrm{L}$$ does not touch the curve at the point where the curve crosses the axis of $$\mathbf{y}$$.
C
$$\Gamma$$ touches the axis of $$x$$ at a point.
D
$$\Gamma$$ never touches the axis of $$x$$.
4
WB JEE 2024
MCQ (More than One Correct Answer)
+2
-0
Change Language

If $$n$$ is a positive integer, the value of $$(2 n+1){ }^n C_0+(2 n-1){ }^n C_1+(2 n-3){ }^n C_2 +\ldots .+1 \cdot{ }^n C_n$$ is

A
$$(n+1) 2^n$$
B
$$3^{\mathrm{n}}$$
C
$$f^{\prime}(2)$$ where $$f(x)=x^{n+1}$$
D
$$(\mathrm{n}+1) 2^{\mathrm{n}+1}$$
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