In a conference 10 speakers are present. If `S_1` wants to speak before `S_2a n dS_2` wants to speak after `S_3,` then find the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number.

Avarage lifetime of a hydrogen atom excited to n =2 state 10^(-6)s find the number of revolutions made by the electron on the avarage before it jump to the ground state

Among 10 persons, A, B, C are to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is a. 10 !//24 b. 9!//6 c. 10 !//6 d. none of these

Statement 1: Number of ways in which Indian team (11 players) can bat, if Yuvraj wants to bat before Dhoni and Pathan wants to bat after Dhoni is 11!/3!. Statement 2: Yuvraj, Dhoni, and Pathan can be arranged in batting order in 3! ways.

Sixteen players S_(1) , S_(2) , S_(3) ,…, S_(16) play in a tournament. Number of ways in which they can be grouped into eight pairs so that S_(1) and S_(2) are in different groups, is equal to

Consider two A.P. s: S_1:2,7,12 ,17 , 500t e r m s a n dS_1:1,8,15 ,22 , 300t e r m s Find the number of common term. Also find the last common term.

If the number of ways in which the letters of the word ABBCABBC can be arranged such that the word ABBC does not appear is any word is N , then the value of (N^(1//2)-10) is_________.

Column I, Column II The number of five-digit numbers having the product of digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many was the person can select either an Indian or a Chinese food? (ii) There are 3 typesof toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train? (iii) How many of two-digit numbers can be formed using 1,2,3,4,5 without repetiton of digits? (iv) There persons enter in to a conference hall in which there are 10 seats, In how many ways they can take their place? (v) In how many ways 5 persons can be seated in a row?

A track consists of two circular pars ABC and CDE of equal radius 100 m and joined smoothly as shown in figure.Each part subtends a right angle at its centre. A cycle weighing 100 kg together with rider travels at a constant speed of 18 km/h on the track. A. Find the normal contact force by the road on the cycle when it is at B and at D. b.Find the force of friction exerted by the track on the tyres when the cycle is at B,C and D. c. Find the normal force between the road and the cycle just before and just after the cycle crosses C. d. What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g=10 m/s^2