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Statement-1: The total number of ways in...

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

Text Solution

Verified by Experts

The correct Answer is:
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.
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