In a quiz, team A scored -40, 10,0 and tema B scored 10,0,-40 in three successive rounds. Which team socred more? Can we say that we can add integers in any order?

We know that 3+5=5+3=8 that is the whole numbers can be added in any order . In other words , addition is commutative for whole numbers Can we say the same fot integers also ? We have 5+(-6)=(-6)+5 Are the following equal ? (i) (-8)+(-9)and(-9)+(-8) (ii) (-23)+32and32+(-23) (iii) (-45)+0and0+(-45) Try this with five other pairs of inegers .Do you find any pairs of intergers for which the sums are different when the order is changed ?

The runs scored by 11 members of a cricket team are: 10,30,43,15,35,55,20,0,58,32. find the median score.

The gold numbers of protective colloids A,B,C and D are 0.04, 0.004, 10 and 40 respectively . The protective powers of A,B,C and D are in the orders .

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev.//min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

To find the sum of three numbers 14, 27 and 13. We can have two ways. We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus This can be done for any three numbers. This property is known as the associativity of the addition of numbers. Express this property which we have already studied in the chapter on Whole Numbers, in a general way, by using variables a,b and c.

When we add zero to any whole number we get the same whole number Zero is called the additive identity for whole numbers .Is it an additive identity again for integers also Observe the following and fill in the blanks (i) (-8)+0=-8 (ii) 0+(-8)=-8 (iii) (-23) +0= (iv) 0+(-37)=-37 (v) 0+(-59)=... (vi) 0+...=-43 (vii) -61 +....=-43 (vii) -61 +...=-61 (viii) ..+0= ..... The above examples shows that zero is an additive identity for integers . you can verify it by a adding zero to any other five integers . In general , for any integer a , a+0=0+a=a

Solution of a weak acid and its anion (that is,its conjugate base) or of a base and its common cation are buffered. When we add a small amount of acid or base to any one of the, the pH of solution change very little. pH of buffer solution can be computed as for acidic buffer : pH=pK_(a)+ log.(["Conjugate base"])/(["Acid"]) for basic buffer : pOH=pK_(b)+log.(["Conjugate acid"])/([Base]) It is generly accepted that a has useful buffer cpacity (pH change resisting power) provided that the value of [salt or conjugate base] /[acid] for acidic buffer lies within the range of 1 : 10 to 1. Buffer capacity is maximum when [conjugate base] = [acid] Calculater the pH of a solution made by adding 0.01 mole of HCl in 100 mL of a solution which is 0.2 M in NH_(3)(pK_(b)=4.74) and 0.3 M in NH_(4)^(+) : (Assuming no change in volume )

A current balance is a device to measure magnetic forces. It is constructed from two parallel coils, each with an average radius of 12.5 cm. The lower coil rests on a balance, it has 20 turns and carries a constant current of 4.0 A. The upper coil, suspended 0.314 cm above the lower coil, has 50 turns and a current that can be varied. The reading of the balance changes as the. magnetic force on the lower coil changes. What current is needed in the upper coil to exert a force of 1.0 N on the bottom coil?

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be consider as spheres of radius 1 Aoverset0 ).