**Explanation:**

by ohms law

v = ir

so r = v/i

so r = 80/20 = 4

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) =n(E)/n(S)=9/20

No of ways of selecting 2 from hotel (6 choices) = 6C2

And from home (2 choices) = 2C2

2C2 x 6C2 = 1 x 15 = 15 ways

One number be x and other y, then x - y = 9

(x - y)2 = 81

x2 + y2 = 81 + 2xy = 109

(x+y)2 = x2 + y2 + 2xy = 109 + 28 = 137

So answer is 137

a: b = 3:5

b: c = 8: 5

a:b:c = 24 : 40 : 25 and total is 24+40+25 = 89

(40/89) x 35 = 15.73

(3/4)t=1

t=4/3=1+1/3

She will have to increase her speed by 33.333% to run the same distance in 3/4s of the time

1= 5^4-1=125, n= no of digits

1 2

2 4

3 2

4 4

5 2

The first two digits in the place can be filled in 5 x 5 ways.

So there are totally 25 x 5 = 125 ways

Have 6 mice for testing,

Give each mice contents from 5 cans each

5 5 5 5 5 5

After 14 hours, one of the mice will die

So, we will know which 5 cans must have the poison

Then , take the contents of these 5 cans and give to the remaining 5 mice each.

We will know in due time which can is poisoned

5C1+5C2+5C3+5C4 = 5 + 10 + 10 + 5 = 30

Let the age be the friends be 2x and 3x. Sum of their ages = 55

2x + 3x = 55 => 5x=55 => x=11

Their ages are 22 and 33

After k years both of them will be 22+k and 33+k years old

Ratio of their age at that time will me 4:5

(22+k)/(33+k)=4/5

5(22+k)=4(33+4) => 110 + 5k = 132+4k

K=132-110 = 22

Distance between the starting and end point is 37 + 17 = 54.

Probability for the bacteria to be dying = 1/3

Hence probability of survival = 1/5

if they survive, they will be split into 3 more bacteria hence, p = (1/3) + (3* 1/5)

12 x 11 / 2 = 66 Handshakes.

Probability of bacteria to die is 1/3

or its get tripled, hence the probability of getting tripled is (2/3)*p*p*p that is (2/3)*p^3

so both the probability combined as P=1/3+(2/3*p^3)

Let the capacity of the tank be 6 litre.

Then time to fill this tank is 6 hour ,when there is no leakage .

so in 1 hour it fills 1 litre.

when leakage is there then it takes 6.5 hour to fill 6 litre

so in 1 hour it fills 6/6.5 litre.

Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour

time to vacate 1 litre will be 13 hour.

For 6 litre it will be 13*6 =78

Area = 20 x 30 = 600 cm^2

Bricks = 600 x 35 = 21000

Speed = 54 x5/18 m/sec = 15 m/sec.

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,x + 300/36 = 15

x + 300 = 540

x = 240 m.

Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream = (68/17)hrs = 4 hrs.

Dimensions = 4 x 5 x 2

TSA = 2 (4 x 5 + 5 x 2 + 4 x 2) = 2(20+10+8)=2x38 = 76 sq m

So bricks required = 76 x 17 = 1292

For 5 rooms 1292 x5 = 6460

Let the age of eldest child is E , that of elder child is M and that of youngest child is Y, then according to the given conditions

E = 3Y (1) and E = 2 + M + Y (2)

Third condition is somewhat complicated, according to this condition two of the age difference is 3 so three cases will arise

1) E - M = 3, ......(3)

2) M - Y = 3, ......(4)

3) E - Y = 3, ......(5)

if we take first of the 3 conditions then on solving (1), (2) and (3) we will get E = 3, M = 0, Y = 1 which is wrong now on solving (1), (2) and (4) we will get E = 15, M = 8, Y = 5

similarity on solving (1), (2) and (5) we will get E = 4.5, M = 1, Y = 1.5

only E = 15, M = 8, Y = 5 is correct so age of elder child is 8 years.

Mohans speed = 35 Km/hr

Rohit speed = 4 x Mohan speed = 4 x 35 = 140 Kmph

Time taken =Distance / Speed = 490 / 140 = 49/14 = 7/2

FEB. 14, 2005 IS A MONDAY

From Feb. 14, 2005 to Feb. 14 2006, there will be 365 days which means one odd day.

So, FEB. 14, 2006 WILL BE A TUESDAY

From Feb. 14, 2006 to Feb. 14 2007, there will be 365 days which means one odd day.

So, FEB. 14, 2007 WILL BE A WEDNESDAY

From Feb. 14, 2007 to Feb. 14 2008, there will be 365 days which means one odd day.

So, FEB. 14, 2008 WILL BE A THURSDAY

From Feb. 14, 2008 to Feb. 14 2009, there will be 366 days

- add one more odd day for Feb.2@Total is 2 odd days.

So FEB. 14, 2009 WILL BE A SATURDAY

From Feb. 14, 2009 to Feb. 14 2010, there will be 365 days

one odd day .

So FEB. 14, 2010 WILL BE A SUNDAY

d = 4*(t-9)

Given r = 12 mm

So, d = 24 mm

So,

24 = 4t - 36

4t = 60

t = 15 years

Tank B is filled in geometric progression, so after 22 hrs water in tank will be = 10 * 2^21 = x/8

where x = volume of tank x = 10 * 2^24 thus by geometric progression we get that n-1 = 24

so n = 25, hence time required is 25 hrs.

Horse covers = 81*3 = 243 kms

So ponies speed = 243/(2+3) = 243/5 = 48.6

Let the age of two friends be 6x and 5x

Sum of their ages 66 => 6x + 5x = 66 => 11x = 66 => x=6

The ages will be 36 and 30

(36+k)/(30+k) = 7/6 => 36 x 6 + 6k = 210 + 7k

216 + 6k = 210 + 7k => 6 = k

After 6 years their ages will be in the ratio 7:6