Statement-1: The total number of ways in which three distinct numbers in AP, can be selected from the set {1,2,3, . .,21}, is equal to 100. Statement-

Question

Statement-1: The total number of ways in which three distinct numbers in AP, can be selected from the set {1,2,3, . .,21}, is equal to 100. Statement-

Statement-1: The total number of ways in which three distinct numbers in AP, can be selected from the set {1,2,3, . .,21}, is equal to 100.
Statement-2: If a,b,c are inn AP, then a+c=2b.
A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
`because a+c=2b`
i.e., sum of two numbers is even, the both numbers are even or odd. In {1,2,3,4, . . ,21},11 numbers are odd and 10 numbers are even.
then, total number of ways=`.^(11)C_(2)+.^(10)C_(2)=55+45=100`
hence, both statements are true but statement-2 is not a correct explanation for statement-1.