having some basic conceptual doubts in Permutation,Combi n Probablity...pls guide me...thanks in advance

Q.
A student is allowed to select at most n books from a collection of 2n+1 books. If the total number of ways in which he can select at least one book is 63. Find value of n?

1. 4
2. 3
3. 5
4. 6

Q.There are 3 rooms in a motel: one single, one double and one for 4 persons.How many ways are there to house 7 persons in these room?
1. 7!/ 2!4!
2. 7!
3. 7!/3
4. 7!/3!

Q.How many 7 digit nos are there having digit 3 three times and digit 0 four times?
1.15
2.3^3*4^4
3.30

I think its a annuity based concept...can any1 guide me how to solve such problems

Q.
An amount of $12820 due 3 yrs hence, is fully repaid in three annual installments starting after 1 year. The 1st instalment is 1/2 the 2nd instalment and 2nd instalment is 2/3rd of the 3rd. If the rate of interest is 10% per annum, find the 1st installment.

1.$2400
2.$1800
3.$2000

consider base as 10
If log 242=a, log 80=b, log 45= c
Q1.express log 36 in terms of a,b,c

a. (c-1)(3c+b-4)/2
b. (c-1)(3c+b-4)/3
c. (c-1)(3c-b-4)/2
d. none of these

Q2.express log 66 in terms of a,b,c
a. /6
b. /6
c. 3(c-1)(3c+b-4)/6

Q.
log (16/15) + 5 log (25/24) + 3 log( 81/80)= log x
x=?

a. 2
b. 3
c. 0
d. none of these

Pls explain

Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?
1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

1. Pls explain
   
2. Q.
   Each of A,B and C need a certain unique time to do a certain work.C needs 1 hr less than A to complete the work.Working together, they require 30 minutes to complete 50% of the job.The work also gets completed if A and B start working together and A leaves after 1 hr and B works for further 3 hrs.How much work does C do per hour?
   
   1] 16.66%
   2] 33.33%
   3] 50%
   4] 66.66%
   

Pls expalin
Q.
Mini and Vinay are quiz masters preparing for a quiz.In 'x' minutes, Mini makes 'y' questions more than Vinay. If it were possible to reduce the time needed by each to make a question by 2 mins, then in 'x' minutes Mini would make '2y' questions more than Vinay. How many questions does Mini make in 'x' minutes?
1] 1/4[ 2(x+y) - ( 2 x^2 + 4 y^2 )^1/2 ]
2] 1/4[ 2(x-y) - ( 2 x^2 + 4 y^2 )^1/2 ]
3] Either option 1 or 2
4] 1/4[ 2(x-y) - ( 2 x^2 - 4 y^2 )^1/2 ]

Pls Explain
Q.
Each of A,B and C need a certain unique time to do a certain work.C needs 1 hr less than A to complete the work.Working together, they require 30 minutes to complete 50% of the job.The work also gets completed if A and B start working together and A leaves after 1 hr and B works for further 3 hrs.How much work does C do per hour?

1] 16.66%
2] 33.33%
3] 50%
4] 66.66%

Pls guide

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
1] 3 times
2] 4 times
3] 5 times
4] 6 times
5] 7 times

It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
1] 3 times
2] 4 times
3] 5 times
4] 6 times
5] 7 times