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In given question below are two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seen to be at variance from commonly know facts. Read the conclusions logically follows the two given statement, disregarding commonly know facts. Statements : Some doctors are nurses. All nurses are patients Conclusions: I. All doctors are patients. II. Some patients are doctors.

Suppose that f is a function such that 2x^(2)<=f(x)<=x(x^(2)+1) for all x that are near to 1 but not equal to 1. Show that this fact contains enough information for us to find lim_(x rarr1)f(x). Also,find this limit.

A horizontal force Facts on the lower block which is connected with another block kept on it. The two blocks are connected by a light, smooth inextensible string that passes over a fixed pulley. If the co-efficient of friction between all contact surfaces is u , then minimum value of F so that the block starts moving.

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