math middle school 8

Question: Answer: ..

Question: For the post of 5 teachers, there are 23 applicants. 2 posts are reserved for S.C. candidates and there are 7 S.C. candidates among applicants. In how many ways can the selection be made? Answer: There are 23 applicants. Among this, 7 are S.C. candidates. We have to select 2 S..

Question: Find n, if P(n-1,3): P(n+1,3):: 5 : 12. Answer: n = 8 (as n cannot be a fraction..

4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..

i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..

Question: A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry Part II, unless Part I is also borrowed. In how many ways can he choose the three books to be borrowed? Answer: There are two ways of se..

1. 2 and 3 are two digits and with these digits, the numbers 32 and 23 are formed. Although both numbers viz., 32 and 23 consist of the digits 2 and 3, the order of digits is different. Each of the above arrangements is called a 'permutation'. Thus, the number of arrangements or permutations of tw..

Question: Given five different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking atleast one green and one blue dye? Answer: The least number of dyes that a combination can have is 2. (one blue and one green). Maximum ..

Question: At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer, in how many ways can they be allotted to the different wards? Answer: Let the three wards be labelled as A, B and C respectively. Let us select 4 men for ward A. ..

= (32.16.8.4.2)(33.31.30.18.17.15.14.13.12.11.10....3.1) = (2 5 .2 4 .2 3 .2 2 .2 1 )(33.31.30.....3.1) which is divisible by 2 1 5 . vi) (n! + 1) is not divisible by any natural number between 2 and ..