**1. Give the synonym: ABYSMAL**

__Sol__: deep

**2. Find the least number which when divided by 35,leaves remainder 25,when divided by45,leaves remainder 35 and when divided by 55,leaves remainder 45?**

__Sol:__ 3455

**Hint:** l.c.m of(35,45,55) minus 10

l.c.m is 3465.Hence the answer is 3455.

**3. What is the remainder left after dividing 1!+2!+3!+...+100! By 7?**

__Sol:__ 5

**Hint**: 7! Onwards all terms are divisible by 7 as 7 is one of the factor. So there is no remainder left for those terms. i.e. remainder left after dividing 7!+8!+9!+..+100! Is 0.The only part to be consider is=1!+..+6!=873;

The remainder left after dividing 873 by 7 is 5.Hence the remainder is 5.

**4. Two identical pack of cards A and B are shuffled thoroughly.**

**One card is picked from A and shuffled with B. The top card from pack A is turned up. If this is the Queen of hearts, what are the chances that the top card in B will be the King of hearts?**

__Sol:__ 52/2703

**Hint**: There are two cases to be considered.

__Case1:__ King of hearts is drawn from pack A and shuffled with pack B.

Probability of drawing king of hearts from pack A=1/51(as queen of hearts is not to be drawn. Probability of having King of hearts on the top of the pack B=2/53

So, total probability of case 1=(1/51)*(2/53)=2/(51*53)

__Case 2:__ King of hearts is not drawn from pack A

Probability of not drawing king of hearts from pack A=50/51(as queen of hearts is not to be

drawn).Probability of having king of hearts on the top of the pack B=1/53

So total probability, the required probability is=2/(51*53)+50/(51*53)

=52/2703

**5. When do you get a .PLL extension?**

__Sol:__ save the library file.