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The number of carbon atoms in exactly 12 g C^(12) is called Avogadro's number , N_(A) (6.022 xx 10^(23)) . One mole is the amount of material which contains Avogradro's number of particle. These definitions emphasize that the mole refers to a fixed number of NA^(+) b Avogadro's number of atoms , electrons to refer to a mole of helium , a mole of electrons , or a mole of NA^(+) by Avogadro's number of atoms, electrons or ions respectively. On the other hand, phrases like "one mole of hydrogen" can be ambiguous , and should be restated as "one mole of hydroden atoms" or " one mole fo hydrogen molecules." But it is a matter of common practice among chemists , however , to let the name of the element stand for its mos common form. Thus one mole of O_(2) is frequently referred to as one mole of oxygen , whereas one moles of O is called one mole of oxygen atoms. Suppose if we take one mole molecules fo H_(2)SO_(4) then it contain 2 moles of H atom 1 mole of S atom and 4 moles of O atom. It can also be said that moles of oxygen molecules is (4)/(2) =2 mole. From a mixture of 4 moles Ca_(3)(PO_(4))_(2) , 5 moles of p_(4)O_(10) and 6 moles of H_(3)PO_(3) , all the phosphourus atoms are removed . Then moles of P_(4) molecules formed from all these atoms are:

Students I_(1),J_(1), J_(3) and I_(2) perform an experiment for measuring the acceleration due to gravity (g) using a simple predulum, they use different lengths of the pendulum and record time for different number of oscillations. The observations are shown in the table. Least count for length = 0.1 cm , least count for time = 1s {:("Students",underset("pendulum (cm)")("Length of the"),underset("oscillations(n)")("No.of"),underset("of pendulum (s)")("Time period")),(I_(1),100.0,20,20),(J_(1),400.0,10,40),(J_(1),100.0,10,20),(I_(1),400.0,20,40):} If P_(1),P_(2),P_(3) and P_(4) are the % error in g for students I_(1),J_(1),J_(3) and I_(2) respectively then -

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement system and others do not understands it. Instead of taking 1kg, 1m and 1 sec, as basic unit they took unit of mass as alpha kg , the unit of length as beta m and unit of times as gamma second. They called power in new system as ACME then match the two columns. {:(,"Column-I",,"Column-II"),((a),"1N in new system",(p),alpha^(-1) beta^(-2) gamma^(2)),((b),"1J in new system",(q),alpha^(-1) beta^(-1) gamma^(2)),((c),"1 pascal (SI unit of pressure) in new system",(r),alpha^(-1)beta gamma^(2)),((d),alpha "ACME in watt",(s),alpha^(2) beta^(2) gamma^(-3)):}