NET JRF PART - A : Questions and Solutions : NET JUNE-2013

NET JRF PART - A : Questions and Solutions:

NET JUNE-2013

1.) How many rectangles (which are not squares) are there in the following figure? 

(a) 56 

(b) 70 

(c) 86 

(d) 100 

Ans. : (b) 70 .

Solution:

For n × n , total number of possible rectangles :

Hence for 4 × 4 ,

= [ 4 × ( 4 + 1 )/2 ]²

= [ 4 × 5/2 ]²

= [ 2 × 5 ]²

= 10² = 100 .

For 4 × 4 , total number of possible rectangles = 100 .

For n × n , total number of squares :

Hence for 4 × 4 ,

= 4 × ( 4 + 1 ) ( 2 × 4 + 1 )/6 

= 4 × 5 × ( 8 + 1 )/6 

= 4 × 5 × 9/6 = 30 .

For 4 × 4 , total number of squares = 30 .

Hence, number of rectangles ( not squares ) = 100 - 30 = 70 .