05 - PERMUTATIONS AND COMBINATIONS ( Answers at the end of all questions ) Page 1 (1) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary‚ then the word ‘SACHIN’ appears at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602 [ AIEEE 2005 ] (2) The value of 50 C4 + 55 r =1 ∑ 6 56 -r C 3 is ( a ) 55 C 4 (b) C3 ( c ) 56 C 3 (d) 56 C4 [ AIEEE 2005 ] (3) How many ways are here to arrange the letters in the word GARDEN
Premium Integer Numerical digit Natural number
Emil: thavamaniprem@yahoo.co.in D.S.T.Ramesh Department of Mathematics‚ Margocis College‚ Nazareth‚ Tuticorin‚ Tamilnadu‚ India Abstract A labeling of a simple graph G is an assignment of integers to the edges subject to certain conditions. A bijection f: E P where P is a set of positive integers is called an edge function of the graph G. The smallest number r is called the edge product number G‚ so that G∪rK2 becomes an edge product graph. In this paper we prove some results on edge product
Premium Natural number Graph theory Integer
Algorithm 1. Design a while loop that lets the user enter a number. The number should be multiplied by 10‚ and the result stored in a variable named products. The loop should iterate as long as product contains a value less than 100. Dim product as integer While product < 100 Display “What is your number” Input number Product = number * 10 Display “Your number is”‚ product End While 2. Design a Do-While loop that asks the user to enter two numbers. The numbers should be added and the sum displayed
Premium Real number Addition Integer
Chapter 1 - Section 1.1 Write the interval of real numbers in interval notation and graph it. See Example 5. 50. The set of real numbers less than or equal to -4 Consider the following nine integers: -4‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚ 4 94. Which of these integers has an absolute value greater than 1? Solution: -4‚ -3‚ -2‚ 2‚ 3‚ 4 Write the interval notation for the interval of real numbers shown in the graph. __________________ -50 -40 -30 -20
Premium Real number Mathematics Integer
BUDGET OF WORK IN MATHEMATICS VI FIRST GRADING PERIOD 1. WHOLE NUMBERS A. Comprehension of Whole Numbers (Pre-requisite Skills Before BEC) 1. Reads and writes numbers through billions 2. Identifies the properties of addition/multiplication of numbers 3. Expresses a number in simple form to expanded notation and vice-versa 4. Rounds numbers to the place value specified 5. adds five or more digit numbers with four or more addends with sums through
Premium Elementary arithmetic Number Real number
SAT Math 1 & 2 Subject Tests Jonathan Spaihts Revised by Morgan Chase Cracking the * 2009–2010 Edition PrincetonReview.com Random House‚ Inc. New York The Independent Education Consultants Association recognizes The Princeton Review as a valuable resource for high school and college students applying to college and graduate school. John Katzman‚ Chairman‚ Founder Michael J. Perik‚ President‚ CEO Stephen Richards‚ COO‚ CFO John Marshall‚ President‚ Test Preparation Services
Premium Prime number Integer Real number
GRADUATE RECORD EXAMINATIONS® Practice General Test #1 Section 3: Quantitative Reasoning Section 4: Quantitative Reasoning Copyright © 2010 by Educational Testing Service. All rights reserved. ETS‚ the E T S logo‚ GRADUATE RECORD EXAMINATIONS‚ and GRE are registered trademarks of Educational Testing Service (E T S) in the United States and other countries. Revised Graduate Record Examinations® General Test Practice Test Number 1 Instructions for the Verbal Reasoning
Premium Inequality Prime number Integer
LOG INVESTIGATION 1. INTRODUCTION The following assessment aims to investigate logarithms and several different expressions. The following sequences (from now on referred to as P roblem1 ) is in the form of an = logmn mk ‚ where n represents the term number and an represents the given answer. 1. a1 = log2 8‚ a2 = log4 8‚ a3 = log8 8‚ a4 = log16 8‚ a5 = log32 8‚ ... 2. a1 = log3 81‚ a2 = log9 81‚ a3 = log27 81‚ a4 = log81 81‚ ... 3. a1 = log5 25‚ a2 = log25 25‚ a3 = log125 25‚ a4 = log625
Premium Calculator Natural number Integer
marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted. SECTION – A (Question numbers 1 to 10 are of one mark each.) 1. Euclid’s Division Lemma states that for any two positive integers a and b‚ there exist unique integres q and r such that a = bq + r‚ where r must satisfy : (a) 1 < r < b (b) 0 < r < b (c) 0 < r < b (d) 0 < r < b Sol. (c) 0 < r < b 2. In the figure‚ the graph of a polynomial p(x) is shown. The number of zeroes of
Premium Harshad number Integer Natural number
will be your response? Chapter 5 Evaluation 5-1B 15. Prove that ?x ?y= ?y-x‚ for all integers x and y. 18. Find all integers x‚ if there exist any‚ such that the following are true: Evaluation 5-2 B 12. Prove that the distributive property of multiplication over addition‚ a (b+c) =ab+ac are true for all of the given values of a‚ b‚ and c: 13. Calculate the following: 17. Find the property of integers being illustrated in each of the following: Evaluation 5-3B 3. Without utilizing a calculator
Premium Natural number Plagiarism Mathematics