Question ID - 48808 | SaraNextGen Top Answer
Consider a 
chessboard. Then match the following columns
Column-I
Column- II
(A)
Number of rectangles
(p)
(B)
Number of squares
(q)
441
(C)
Number of ways three squares can be selected if they are not in same row or column
(r)
91
(D)
In how many ways eleven ‘+’ sign can be arranged in the squares if no row remains empty
(s)
2400
CODES :
A
B
C
D
a)
r
s
p
q
b)
q
r
s
p
c)
p
q
r
s
d)
s
p
q
r
Consider a chessboard. Then match the following columns
Column-I
Column- II
(A)
Number of rectangles
(p)
(B)
Number of squares
(q)
441
(C)
Number of ways three squares can be selected if they are not in same row or column
(r)
91
(D)
In how many ways eleven ‘+’ sign can be arranged in the squares if no row remains empty
(s)
2400
CODES :
A
B
C
D
a)
r
s
p
q
b)
q
r
s
p
c)
p
q
r
s
d)
s
p
q
r
|
|
(b) 1. Number of rectangles is equal to number of ways we can select two vertical lines and two horizontal lines. Total number of ways is
If the square is of 1 sq. units like If the square is of 4 sq. units like shaded region of the squares Similarly we have Hence, total number of squares is
The first square can be selected in 36 ways. If one such square Hence, number of ways of selections is d. Given number of ways is equivalent to selecting 11 squares form 36 squares if no row remains empty Suppose Then we must have The number of positive integral solutions of the above equation is |
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, then we have such 
squares.
, then we have such 5 squares in the belt formed by rows 1 and 2. Similarly we have 4 more belts 
and 56. Hence, there are 
such squares.
squares of increasing sizes
.png)
is selected, we are left with 25 squares; second square cannot be selected from row 1 and column 
. If second square is 
, we are left with 16 squares, from which third square can be selected, e.g., 
. But in this one-by-one type of selection order of selection is also consider. Hence, actual number of ways is 
be the number of squares selected from the 
and 
row
(where
)
Answer Link
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