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Physics
In the figure, masses m₁, m₂ and M are 20kg, 5kg and 50kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between m₁ and M and that between m₂ and ground is 0.3. The pulleys and the strings are mass less. The string is perfectly horizontal between P₁ and m₁ and also between P₂ and m₂. The string is perfectly vertical between P₁ and P₂. An external horizontal force F is applied to the mass M Take g = 10 m/s². Draw a free body diagram for mass M, clearly showing all the forces. Let the magnitude of the force of friction between m₁ and M be f₁ and that between m₂ and ground be f₂. For a particular F it is found that f₁ = 2f₂. Find f₁ and f₂. Write equations of motion of all the masses. Find F, tension in the string and acceleration of the masses.
Chemistry
Which of the following statement(s) is (are) correct? The coordination number of each type of ion in CsCl crystal is 8. A metal that crystallizes in bcc structure has a coordination number of 12. A unit cell of an ionic crystal shares some of its ions with other unit cells. The length of the unit cell in NaCl is 552 pm.
Mathematics
If log (a+c), log (a-c), log (a-2b+c) are in A.P, then a, b, c are in A.P. a², b², c² are in A.P. a, b, c are in G.P. a, b, c are in H.P.

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