Number of Rectangles in nxn Squares

Q.

How many rectangles does a $4\times 4$ square has?

1. $1^3+2^3+3^3+4^3$

2. $1^3+2^3+3^3$

3. $1^3+2^3+3^3+4^3+5^3$

4. $1^3+2^3+3^3+4^3+5^3+6^3$

Q. How many rectangles does a $3\times 3$ square has?

1. $6^2$
2. ${10}^2$
3. $7^2$
4. $8^2$

Q. How many rectangles does a $4\times 4$ square has?

1. $1^3+2^3+3^3+4^3$
2. $1^3+2^3+3^3$
3. $1^3+2^3+3^3+4^3+5^3$
4. $1^3+2^3+3^3+4^3+5^3+6^3$

Q.

Can a determinant be calculated for a $5\times 4$ matrix?

Q. How many rectangles does a $3\times 3$ square has?

1. $6^2$
2. ${10}^2$
3. $7^2$
4. $8^2$

Q. Matrix $A$ has $m$ rows and$(n+5)$ columns, matrix $B$ has $m$ rows and $(11-n)$ column. If both $AB$ ans $AB$ exist, then

1. $AB$ and $BA$ are square matrix
2. $AB$ and$BA$ are of orders $8\times 8$ and $3\times 13$ respectively
3. $AB=BA$
4. $Noneoftheabove$

Q. Number of rectangles in the grid shown which are not squares is

1. $160$
2. $162$
3. $170$
4. $185$

Q.

How many rectangles does a $3\times 3$ square has?

1. $6^2$

2. ${10}^2$

3. $7^2$

4. $8^2$

Q. How many rectangles does a $4\times 4$ square has?

1. $1^3+2^3+3^3+4^3$
2. $1^3+2^3+3^3$
3. $1^3+2^3+3^3+4^3+5^3$
4. $1^3+2^3+3^3+4^3+5^3+6^3$