### Question 1:

There are five couples attending a party ( all couple has a husband and a wife ).The probability associated with each quantity below with condition is provided**The probability associated with arranging the couples such that male and females are alternate**

__Quantity I :__**the probability associated with the case when all male are together.**

__Quantity II :__a) quantity I > quantity II

b)quantity II > quantity I

c) quantity I quantity II

d) quantity I quantity II

e)no relation can be established or quantity I = quantity II

### Question 2:

There are 65 cards (numbered 1,2,3,4, …… 65) in a box. Two cards are picked at random .**Probability that both cards show 2 digit numbers which increase by 36 when its digit are reversed**

__Quantity I:__**Probability that both cards show a number divisible by 8 but not 16**

__Quantity II:__a) quantity I > quantity II

b)quantity II > quantity I

c) quantity I quantity II

d) quantity I quantity II

e)no relation can be established or quantity I = quantity II

### Question 3:

There are two stations P and Q which are 516 km apart, Train A starts from station P at 9.45 am and goes towards Q and train B starts from Q 30min after train A towards P and they meet at 12.55. Train B speed is 1.5 times train A. Then Relative speed of A to B in m/sa) 45m/s

b)55m/s

c)50m/s

d)60 m/s

e)none

### Question 4:

There are two stations P and Q which are 516 km apart, Train A starts from station P at 9.45 am and goes towards Q and train B starts from Q 30min after train A towards P and they meet at 12.55. Train B speed is 1.5 times train A. Then If B travels in the same direction as A. what time B will take to catch train A ?a) 45 min later

b) 50 min later

c) 60 min later

d) 35min later

e)none

## Answers With Solution:

#### 1) a

__Quantity I :__**Males have to be together , so we can take them as one unit while arranging both male and females ( but they will arrange internally among themselves )**

__Quantity II :__they arrange themselves in 6 places in 6! Ways x 5! ( males arrangement )

__Quantity II :__Comparing both quantity

Quantity I is greater than II

#### 2) a

**5c₂ / 65 c₂**

__Quantity I :__**numbers divisible by 8 will be 8, 16, 24,32,40,48,56 ,64**

__Qunatity II :__But numbers divisible by 16 should not be taken so 16 ,32 ,48,64 are eliminated

Only four numbers i.e. 8 ,24, 40 , 56 are considered , we have to choose any two out of these

So 4C₂ / 65C₂ is the quantity II

Clearly :Quantity I > Quantity II

**(a) is the right answer.**

#### 3) c

Given speed ratio x : 1.5 x

Relative speed(opposite direction) = (x + y) km/hr = ( 1 x+ 1.5 x = 2.5 x )When opposite direction given ,we can make starting time same by chossing either A or B ‘s timing

Train A starts before 30 min , and covers 1/2 * X In that duration and the rest distance will be

516 - 1/2 * X

From B’s side :

Distance / relative speed = time

(516 - 1/2 * X ) / 2.5x = 8/3 ( 2hrs. 40 min )

X = 12* 6

We need to find what is 2.5 x , so relative speed = 2.5 * 12*6 * (as asked in meters)

**Relative speed = 50 m/s**

#### 4) c

If both travel in same direction then relative speed will be subtraction of both speeds

Relative speed = 1.5x – 1x = 0.5x

B will have to takeover by travelling ½ x

Time taken by B to overtake A = ½ x / 0.5x = 1hour =

Relative speed = 1.5x – 1x = 0.5x

B will have to takeover by travelling ½ x

Time taken by B to overtake A = ½ x / 0.5x = 1hour =

**60 min later .**

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