The following bodies |RIGID BODY DYNAMICS| JEE-Main-2021

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The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ______. [Mark the body as per their respective numbering given in the question]

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Given below are two statements :

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The value of the integral $\int_{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$ is :

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Match List - I with List - II.

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Let a, ar, $a r^{2^2} \ldots \ldots .$. be an infinite G.P. If $\sum_{n=0}^{\infty} a^n=57$ and $\sum_{n=0}^{\infty} a^3 r^{3 n}=9747$,...

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The metal atom present in the complex MABXL (where $\mathrm{A}, \mathrm{B}, \mathrm{X}$ and L are unidentate ligands and M is...

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The integral $\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}$ is equal to:

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Given below are two statements:

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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 :

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Let $B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$ and $A$ be a $2 \times 2$ matrix such that $\mathrm{AB}^{-1}=\mathrm{A}^{-1}$. If...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

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$\lim _{x \rightarrow \frac{x}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos \left(t^{1 / 3}\right)\right) d t}{\left(x-\frac{\pi}{2}\right)^2}\right)$ is equal to :

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Between the following two statements :
Statement-I : Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$ and $\vec{b}=2 \hat{\imath}+\hat{\jmath}-\hat{k}$. Then the vector $\overrightarrow{\mathrm{r}}$...

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The correct nomenclature for the following compound is:

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Let the range of the function $f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \mathrm{IR}$ be $[a, b]$. If $\alpha$ and...

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