Forming Rectangles Using Dot Grids

Q. Solve:
$\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

Q.

If we wish to create rectangles with 30 dots, what can be the possible values for the number of dots along the width and length of the rectangle?

1. 15, 2

2. 6, 5

3. 10, 5

4. 3, 10

Q.

If the product $AB$ equals 72, what are the missing entries $x,y,z$ in the table?

1. $x=36,y=24,z=18$

2. $x=18,y=24,z=36$

3. $x=18,y=36,z=24$

4. $x=24,y=36,z=18$

Q. The maximum possible number of identical rectangular blocks are placed inside a rectangular carton. The rectangular blocks each have a length of $7$, a width of $5$, a height of $4$ and the rectangular carton has inside dimensions that are a length of $16$, a width of $15$ and a height of $14$. Calculate the total surface area of the rectangular blocks that are inside the rectangular carton.

1. $1,348$
2. $1,992$
3. $2,656$
4. $3,360$
5. $3,984$

Q.

If we wish to create different rectangles with 36 dots, find the missing entries in the following table:

1. $x=6,y=12$

2. $x=36,y=1$

3. $x=12,y=6$

4. $x=12,y=36$

Q. 4 + $\frac{3}{100}$ = ____

1. $0.43$
2. $4.03$
3. $43$
4. $4.3$

Q. If $3\frac{1}{x}\times 3\frac{3}{4}=12\frac{1}{2}$, then the value of $x$ is

1. $\frac{1}{3}$
2. $1$
3. $3$
4. $2$

Q. The length of a rectangle is $\frac{6}{5}$th of its breadth. If its perimeter is $132$ m, its area will be ...............

1. $640$ $m^2$
2. $1080$ $m^2$
3. $1620$ $m^2$
4. $2160$ $m^2$

Q. Identify the numbers which are divisible by 5.

1. 56732
2. 3489340
3. 6347945
4. 436429
5. 1024
6. 5325
7. 7230
8. 6780

Q.
Select the number representing the given rectangular dot structure.

1. 18
2. 21
3. 15

Q.

Which options represent a rearrangement of dots of the below figure?

1. 

2. 

3. 

4. 

Q. The variable type and the correct relation between Running time ($a$) and Maintainance cost ($z$) is-

Running time ($a$)	3	7	11	15
Maintainance cost ($z$)	9	17	25	33

1. $z$—Independent, $a$—Dependent $z=2a+3$
2. $z$—Dependent, $a$—Independent and $z=2a+3$
3. $z$—Dependent, $a$—Independent and $z=3a+2$
4. $z$—Independent, $a$—Dependent and $z=3a+2$

Q. Solve:
$1\frac{1}{3}+3\frac{2}{3}$

Q. Here is a key board of a harmonium:
Find the ratio of white keys on the keyboard.

Q.

Find the HCF of 12 and 28.

1. 4

2. 3

3. 5

4. 2

Q. LCM of the numbers 40, 48 and 90 is _______ .

1. 720