Statement 1: When number of ways of arranging 21 objects of which `r` objects are identical of one type and remaining are identical of second type is maximum, then maximum value of `^13 C_ri s78.` Statement 2: `^2n+1C_r` is maximum when `r=ndot`

Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20)dot Statement 2: ^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot

Statement 1: Number of ways of selecting 10 objects from 42 objects of which 21 objects are identical and remaining objects are distinct is 2^(20)dot Statement 2: ^42 C_0+^(42)C_1+^(42)C_2++^(42)C_(21)=2^(41)dot

Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 2^(2n-1)+((2n) !)/(2(n !)^2)

Statement-1 : The expression n!(100 - n)! is maximum when n = 50 . Statement-2 : .^(2n)C_(r) is maximum when r = n .

Statement 1 a+b+c=18(a,b,cgt0) , then the maximum value of abc is 216. Statement 2 Maximum value occurs when a=b=c .

Show that The maximum value of sinx. cosx in R is 1/2

Statement -1: The expression n!(20-n)! is minimum when n=10 . because Statement -2: .^(2p)C_(r) is maximum when r=p .

Statement 1: If p ,q ,ltr , the number of different selections of p+q things taking r at a time, where p thingks are identical and q other things are identical, is p+q-r+1. Statement 2: If p ,q ,>r , the number of different selections of p+q things taking r at a time, where p thingks are identical and q other things are identical, is r-1.

Let n be a positive integer and k be a whole number, klt=2ndot Statement 1: The maximum value of ^2n C_ki s^(2n)C_ndot Statement 2: (^(2n)C_(k+1))/(^(2n)C_k) >1,fork=n+1,n+2, ,2n .

If a, b, c in R^(+) such that a+b+c=27 , then the maximum value of a^(2)b^(3)c^(4) is equal to