A class has three teachers, Mr. P , Ms. Q, and Mrs. R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is `k !(18),` then value of`k` is ________.

A class has tree teachers, Mr. X , Ms. Y and Mrs. Z and six students A , B , C , D , E , F Number of ways in which they can be seated in a line of 9 chairs,if between any two teachers there are exactly two students is

A team of four students is to be selected from a total of 12 students. The total number of ways in which the team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to a. 220 b. 182 c. 226 d. none of these

The probabilities that three students Subhas, Monisha and Satabdi can solve a problem independently are p, q and r respectively. The chance that exactly two of the three students solve the problem is -

Number of integral values of k for which the equation 4 cos^(-1)(-|x|)=k has exactly two solutions, is: (a) 4 (b) 5 (c) 6 (d) 7

Statement 1: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

A certain coin is tossed with probability of showing head being 'p' . Let 'q' denotes the probability that when the coin is tossed four times the number of heads obtained is even. Then (a) there is no value of p , if q=(1)/(4) (b) there is exactly two value of p , if q=(3)/(4) (c) there are exactly three value of p , if q=(3)/(5) (d) there are exactly four value of p , if q=(4)/(5)

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

Number of ways in which 7 people can occupy 6 seats, 3 seats on each side in a first class railway compartment if two specified persons are to be always included and occupy adjacent seats on the same side is (5!)dotk ,t h e nk has the value equal to ___________.

Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is .^6C_2 . Statement 2: Number of positive integral solutions of x+y+z+w=7i s^6C_3dot

Column I, Column II The number of five-digit numbers having the product o 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)