class 10 mathematics

Question: Find n if P(n,4) = 20P(n,2) Answer: ..

Question: Twelve students are participating in a competition. In how many ways can the first 3 prizes be won? Answer: Number of students participating in the competition = 12 The number of ways in which the first three prizes can be won = P (12,3) = 12 x 11 x 10 = 1320 Hence, ..

Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..

i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..

The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one of the n ..

Question: From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, including atleast 4 boys and 4 girls. 2 girls who won prizes last year should be included. In how many ways the selection can be made? Answer: There are 12 boys ..

= (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 ..

Number of ways of filling hundred's place = 2 Number of ways of filling ten's place = 2 Number of ways of filling unit's place = 2 By the fundamental principle of counting, the total number of numbers = 2 x 2 x 2 =..

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same comm..

Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..