Answer the following questions by applying the pigeonhole principle. For each blank, write in the number in numeral form. For example, if the answer is ten, simply write 10. a) What is the minimum number of integers that you must pick between 0 and 9 (inclusive), such that two of them add up to 9?

b) In a class of 30 students, each student can pick between 10 different home-works. What is the minimum number of students needed to ensure that two students get the same home-work?

c) I have 9 pairs of socks of different colors in a box. How many must I grab to ensure that I'll have at least one matching set?

d) I also have 9 sets of gloves of different colors in the same box. How many different objects must I grab to ensure that I have one matching set of gloves or socks?

e) What is the minimum number of rooks from a chess game that we must place on an 7X7 grid, such that at least two of them threaten each other?

An npn transistor is correctly biased and turned on if the a. base is negative. b. collector is negative. c. collector is positive with respect to the emitter and negative with respect to the base. d. collector is the most positive lead followed by the base.

Write a program to analyze student’s scores. each student’s id and 4 original test scores are saved in the attached file “student_id_scores.txt”. assume there are exactly 15 students in the class.• the program first opens the file, reads student’s ids and scores from the file and saves them in two arrays: o create a one-dimensional string array “ids” to store the student’s ids.o create a (parallel) two-dimensional int array “scores” to store student’s original test scores. this array has 5 columns, the original 4 test scores should be saved in the first 4 columns, and the last column will be used to save the average score after the calculation in next step.• the program then retrieves test scores from the array “scores”, calculates average score and determines the final letter grade based on the rules in the table below for each student. assume average score is integer value.average score = (score1 + score2 + score3 + score4) / 4average score letter grade90 ~ 100 a80 ~ 89 b70 ~ 79 c60 ~ 70 d0 ~ 60 f• the average score should be saved back in the 5th column of “scores” array.• create a new parallel one-dimensional char array “grades” to save each student’s letter grade.• program also needs to find the number of a, number of b, number of c, number of d and number of f grade. as well as the highest, lowest and average score of the class.• finally, program will display all of the original scores and all results on the computer screen using the format shown as the sample output below.• the program must contain at least the following functions: (1) a function “getscores” to read and store data into “ids” and “scores” arrays.(2) a function “analyzescores” to calculate student’s average score, determine letter grade, get the number of a, b, c, d and f, find the highest, lowest and average score of the class.(3) a function “displayresults” to display all of the results

Which of the following best describe how the depth-limited search works. a normal depth-first search is performed but the number of ply/depths is limited. a normal breadth-first search is performed but the number of ply/depths is limited. a normal breadth-first search is performed but values above a specific value will be ignored. a normal depth-first search is performed but values above a specific value will be ignored.