A+B+C=N (N Fixed), with Lower Limit

Q. Find the number of integral solutions to |x| + |y| + |z| = 15.

1. 900
2. 901
3. 902
4. 903
5. none of these

Q.

Out of 7 crew members, 3 particular members can sit only on the left side. Another 2 particular members can sit only on the right side. Find the number of ways in which the crew can be arranged if a maximum of four men can sit on each side.

1. 6*3!*4!

2. None of these

3. 5*3!*4!

4. 2*3!*4!

5. 3*3!*4!

Q. Let $x_1,x_2,x_3,...,x_n$ be a sequence of integers such that:
i) -1 $\le$ $x_i$ $\le$ 2 for i = 1, 2 ..., n
ii) $x_1+x_2+x_3+...+x_n$ = 19
iii) $x_1^2+x_2^2+x_3^2+...+x_n^2$ = 99
Determine the minimum and maximum possible values of $x_1^3+x_2^3+x_3^3+...+x_n^3$

1. 20, 99
2. 19, 133
3. 0, 391
4. 4, 99

Q. How many solutions are there for the equation A+B+3C = 10 if A, B, C are whole numbers?

1. 25
2. 24
3. 23
4. 26
5. 22

Q. How many integral solutions are there for the equation A+B+C = 10 where A $\ge$ 1, B $\ge$ 2, C $\ge$ 3 ?

1. ⁵C₂
2. ⁶C₂
3. None of these
4. ¹²C₂
5. ⁸C₂

Q. How many solutions are there for the equation A+B+3C = 10 if A, B, C are whole numbers?

1. 24
2. 23
3. 22
4. 26
5. 25

Q. To set up a farm, a farmer goes to buy some animals. He selects from cows, sheep, goats, chickens and pigs. In how many ways can he select 15 animals such that he selects atleast 1 cow, 2 sheep, 2 goats and 3 chicken.

1. 1215
2. 1306
3. 210
4. 330
5. 420

Q. How many numbers (N) can we have, such that 100<N<1000 with the sum of the digits of these numbers as 10?

1. 55
2. 66
3. 78
4. 27
5. 52

Q. State the following statement is True or False:

1. True
2. False

Q. How many ways a person can buy 13 fruits of three types, mangoes , apples and oranges. He can buy a maximum of 7 of any type and minimum of 1.

1. 21
2. 36
3. 66
4. 26
5. None of these