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

Let $$\mathrm{I}(\mathrm{R})=\int_\limits0^{\mathrm{R}} \mathrm{e}^{-\mathrm{R} \sin x} \mathrm{~d} x, \mathrm{R}>0$$. then,

A
$$I(R)>\frac{\pi}{2 R}\left(1-e^{-R}\right)$$
B
$$I(R)<\frac{\pi}{2 R}\left(1-e^{-R}\right)$$
C
$$I(R)=\frac{\pi}{2 R}\left(1-e^{-R}\right)$$
D
$$I(R) \text { and } \frac{\pi}{2 R}(1-e^{-R}) \text { are not comparable }$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Consider the function $$\mathrm{f}(x)=x(x-1)(x-2) \ldots(x-100)$$. Which one of the following is correct?

A
This function has 100 local maxima
B
This function has 50 local maxima
C
This function has 51 local maxima
D
Local minima do not exist for this function
3
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

In a plane $$\vec{a}$$ and $$\vec{b}$$ are the position vectors of two points A and B respectively. A point $P$ with position vector $$\overrightarrow{\mathrm{r}}$$ moves on that plane in such a way that $$|\overrightarrow{\vec{r}}-\vec{a}| \sim|\vec{r}-\vec{b}|=c$$ (real constant). The locus of P is a conic section whose eccentricity is

A
$$\frac{|\vec{a}-\vec{b}|}{c}$$
B
$$\frac{|\vec{a}+\vec{b}|}{c}$$
C
$$\frac{|\vec{a}-\vec{b}|}{2 c}$$
D
$$\frac{|\vec{a}+\vec{b}|}{2 c}$$
4
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

A
160
B
140
C
180
D
150
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