Explanation

Simply Connected: A region is simply connected if every closed curve within it can be continuously shrunk to a point without leaving the region.

Multi-Connected: A region is multi-connected if it is not simply connected.

This meaning it has "holes" or other topological features that prevent some closed curves from being shrunk to a point within the region.

Explanation

Using the order of operations (PEMDAS), we get:

Evaluate the expression inside the parentheses:

• 2 × 5 = 10
• 13 - 10 = 3

Now, multiply 12 by the result:

• 12 × 3 = 36

So, the correct answer is 36.

Explanation

For one digit number 1 to 9

→1 × 9 = 9

For two digit number 10 to 99

→ 2 × 90 = 180

For three digit number 100 to 300

→3 × 201 = 603

Hence, total number of required digits

= 9 + 180 + 603 = 792

Explanation

Let’s analyze each option under the assumption that a and b are integers:

a⁷ → Square of an integer → Always an integer

b* → Ambiguous; if it means b raised to some power (like a^b or b^a), then:

If b = 2 and a = -1, then b^a = 2⁻¹ = 0.5, not an integer

So, this is not necessarily an integer

a * b → Product of two integers → Always an integer

2a – 5b → Linear combination of integers → Always an integer

Explanation

1/10 = 0.1

Explanation

The sum of 72 + 21 + 8 + 66 + 37 equals 204.

Explanation

To evaluate this expression, we can simplify the fraction:

12.1 ÷ 19.8 = 0.61 (approximately)

11/18 = 0.61 (approximately)

Explanation

1:4 is the correct answer

Volume ratio=x^3/y^3 =1/8 that implies x/y=2 so for surface area ration x^2/y^2=1/4

Explanation

We are told:

• Circumference of a circle = a

• Area of the circle = b

• And a = b

We know the formulas:

• Circumference:

  $$a = 2pi r$$
  

• Area:

  $$b=\pi r^2$$r=0orr=

Since $a = b$, set the formulas equal:

$$2pi r = pi r^2$$

Divide both sides by $pi$:

$$2r = r^2$$

Rearrange:

$$r^2 - 2r = 0 Rightarrow r(r - 2) = 0$$

So the solutions are:

r=0 or r=2

Explanation