JEE Advanced Mi...

A sphere of mass m and radius r is placed inside a rotating horizontal cylinder of radius R. As the cylinder's angular acceleration, β, gradually increases, find the maximum value of β that enables the sphere to reach from A to the horizontal point B.

Imagine you have a cup of Starbucks coffee in a moving car. If the car suddenly brakes

A square frame is constructed from four uniform rods. The rods, AB, BC, CD, and DA, have masses 2m, 3m, 4m, and 5m respectively, and each has a length of 2a.  Where is the center of mass of this frame located in the x-y plane, specifically, which quadrant or region defined by x and y coordinates.

A ball of 8 kg, moving at 15 m/s, enters a 22 kg spring gun at rest. If the surfaces are frictionless and the spring is massless, determine the gun's speed after the ball stops moving relative to the gun.

Gold number of haemoglobin is 0.03. Hence, 100mL of gold sol will require how much haemoglobin so that gold is not coagulated by 10mL of 10% NaCl solution?

The EAN of metal atoms in [Fe(CO)₂(NO⁺)₂] and Co₂(CO)₈ respectively are :

Given that  out of these three vectors two are equal in magnitude and the magnitude of the third vector  times as that of either of the two having equal magnitude. Then the angles between vectors are given by :-

A box contains the following three coins.

I. A fair coin with head on one face and tail on the other face.

II. A coin with heads on both the faces.

III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is