Exams

Hardness can be removed by adding sodium carbonate (washing soda) or by passing the water through an ion-exchange column.

Hardness in water is caused by dissolved magnesium ions and calcium ions. These can get into the water when it comes into contact with limestone and other rocks that contain calcium compounds. This can happen, for example, when rainwater flows over these rocks on its way to a reservoir.

Hardness in water is of two types. They are :

1. Temporary hardness

2. Permanent hardness

1. Temporary hardness:: Temporary hardness is caused by dissolved calcium hydrogen carbonate.

2. Permanent hardness:: Permanent hardness is caused by dissolved calcium sulfate. Unlike temporary hardness, it is not removed by boiling the water.

Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years

Let the Father be x years when he died

Average Age 10 years ago be A

Total Age 10 years ago = 6*A

Total Age after 10 years(Just before father's Death) = 6A + 6*10 = 6A + 60

Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0

(6A +60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60

Therefore we can conclude that the father was 60 years old when he died.

Annie Besant (1847-1933) – political reformer, women's rights activist, theosophist and Indian nationalist is known as the grand old lady of Indian nationalism.

ASSISTANT→AAINSSSTT

STATISTICS→ACIISSSTTT

Here N and C are not common and same letters can be A, I, S, T. Therefore

 Probability of choosing A =  2C19C1×1C110C1 = 1/45 

 Probability of choosing I = 19C1×2C110C1 = 1/45

Probability of choosing S = 3C19C1×3C110C1 = 1/10

Probability of choosing T = 2C19C1×3C110C1 = 1/15

Hence, Required probability =   145+145+110+115= 1990 

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither

78 = (41-9) + (22-9) + 9 + neither.

Not enrolled students = 24

let 'b' be the Length of bridge from cow to the near end of the bridge and 'a' be the distance of the train from the bridge.
'x' be speed of cow => '4x' speed of train
Then the total length of the bridge 2b + 10.
(a-2)/4x = b/x
=> a-2 = 4b........(1)
Now if it had run in opposite direction
(a+2b+10-2)/4x = (b+10-2)/x
=> a - 2b = 24......(2)
Solving (1) and (2)
b = 11 ,
Therefore length of the bridge is 2 x 11 + 10 = 32mts.