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JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
A ball of mass 4 kg, moving with a velocity of 10 ms$$-$$1, collides with a spring of length 8 m and force constant 100 Nm$$-$$1. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.
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JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s2)

The value of 'x' to the nearest integer is __________. 3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
A boy pushes a box of mass 2 kg with a force $$\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N$$ on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.
$$U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3$$
where, $$\alpha$$ and $$\beta$$ are positive constants. The equilibrium distance between two atoms will be $${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$$, where a = ___________.