Progressions-12 (IIT-JEE 2009)

If the sum of first n terms of A.P is cn², then the sum of squares of these n terms is:

(a)n(4n²-1)c²/6          (b) n(4n²+1)c²/3        (c) n(4n²-1)c²/3        (d) n(4n²+1)c²/6

Solution follows here:

Progressions -11 (CAT-2006)

Consider the series S = {1,2,3,…1000}, how many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

(1) 3                (2) 4                (3) 6                (4) 7                (5) 8                           

Solution follows here:

Progressions-10 (CAT-2007)

Consider the set S = {2, 3, 4, ...., 2n + 1}, where n  is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

                        (1) 0

                        (2) 1

                        (3) n/2

                        (4) n+1/2n

                        (5) 2008

Solution follows here:

Puzzle -26

		H
		G
A	B	O	C	D
		E
		F

A,B,C,D,E,F,G,H,O are distinct single digit non-zero positive integers placed as shown in the above diagram. Given that, sum of numbers placed north of ‘O’ = sum of numbers placed south of ‘O’ = sum of numbers placed east of ‘O’ = sum of numbers placed west of ‘O’. Then find all the possible values of ’O’?

(1)1,2,3                       (2)1,3,5                       (3)1,5,9                       (4)2,4,6                       (5)1,3,9

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