Quiz 1
Question 1
In how many ways can one travel in the xy-plane from $(1,2)$ to $(5,9)$ if each move is one of the following types: $(R): (x,y) \rightarrow (x+1, y); (U)L (x, y) \rightarrow (x, y+ 1)$?
A. 11!/7!
B. 10!/(4! 5!)
C. 11!/(4! 7!)
D. 11!
Answer
C. 11!/(4! 7!)Question 2
In how many ways can the letter in UNUSUAL be arranged?
A. 7!
B. 7! + 3!
C. 7!/4!
D. 7!/3!
Answer
D. 7!/3!Question 3
Suppose that Mr. and Mrs. Riggs want to name their new daughter so that her initials (first, middle, and last) will be in alphabetical order with no repeated initial. How many such triples of initials can occur under these circumstances? Note: the last initial must be an R.
A. 68
B. 325
C. 136
D. 680
Answer
C. 136Question 4
In how many ways can a teacher loan 12 different science books to 16 students so that no student gets more than one book?
A. $P(12, 16)$
B. $P(16, 12)$
C. $P(12, 4)$
D. $P(16, 1)$
Answer
B. $P(16, 12)$Question 5
For $n$ distinct objects, an arrangement (with repetitions allowed) of size 3 can be obtained in how many ways?
A. $3^{n}$
B. $n^{3}$
C. $n^{2}$
D. $3 \log_{2}(n)$
Answer
B. $n^{3}$Question 6
Assume $n$ is an integer greater than 0, which of the following are equal to $n$?
A. $C(n, n+1)$
B. $C(n, n-1)$
C. $C(n, 0)$
D. $C(n, n)$
Answer
B. $C(n, n-1)$Question 7
What is the value of the following sum?
\[{n \choose 0} + {n \choose 1} + {n \choose 2} + \ldots + {n \choose n}\]A. $n^{2}$
B. $2^{n}$
C. $\log_{2}(n)$
D. $2n$
Answer
B. $2^{n}$Question 8
How many times is the cout statement executed in the C++ code below?
1
2
3
4
for (i=0;i<10;i++){
for (j=0;j<=10;j++){
for (k=0;k<=10;k++){
cout << i+j+k; }}}
A. 495
B. 220
C. 360
D. 165
Answer
B. 220Question 9
Which of the following correct expression for the number of times that the line count++; is executed in the code below? Pay attention to the range of values for the indices i and j.
1
2
3
4
count=0;
for (i=0;i<=n;i++){
for (j=0;j<=i;j++){
count++; }}
A. $C(n, 2)$
B. $C(n-1, 2)$
C. $C(n+2, 2)$
D. $C(n+1, 2)$
Answer
C. $C(n+2, 2)$Question 10
Which of the following is the coefficient for $x^{3}y^{2}$ in the expansion of $(x+y)^{5}$?
A. $C(5, 3)$
B. $C(2, 5)$
C. $C(3, 5)$
D. $C(5, 4)$