Find the number of ways in which 3 distinct numbers can be selected from the set `{3^(1),3^(2),3^(3),..,3^(100),3^(101)}` so that they form a G.P.

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^(1),3^(2),3^(3),3^(100),3^(101)} so that they form a G.P.is 2500. Statement 2: if a,b,c are in A.P.then 3^(a),3^(b),3^(c) are in G.P.

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P.

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P.

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^(1),3^(2),3^(3),...,3^(10)} so that they form a G.P. then the value of N/5 is

Statement 1: The number of ways in which three distinct numbers can be selected from the set {3^1,3^2,3^3, ,3^(100),3^(101)} so that they form a G.P. is 2500. Statement 2: if a ,b ,c are in A.P., then 3^a ,3^b ,3^c are in G.P. (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.

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^1,3^2,3^3, ,3^(10)} so that they form a G.P. then the value of N//5 is ______.

If N is the number of ways in which 3 distinct numbers canbe selected from the set {3^1,3^2,3^3, ,3^(10)} so that they form a G.P. then the value of N//5 is ______.

The number of ways in which three distinct numbered in an increasing A.P. can be selected from the set {1,2,3……24} is