1. Perimeter of a regular pentagon A is 6 times the perimeter of the regular pentagon B. If the perimeter of pentagon B is 35cm, then the side length of pentagon A is:

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**Correct answer is option - 5**

**Explanation: **Let the side length of pentagon A = a, then the perimeter of the regular pentagon A = 5a (since all the sides are equal to each other in a regular pentagon).

Now the perimeter of pentagon B = 35cm.

Given: 5a = 6 * (35). Now solving for ‘a’ we get: 5a = 210.

This gives: a = 210/5 = 42cm.

2. If 2x = y = 4z, then what is the average of x, y, and z in terms of ‘y’?

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**Correct answer is option - 3**

**Explanation: **Average is finding the mean of the values x, y and z.

The average of x, y, and z is (x + y + z)/3. However, we should write ‘x’ and ‘z’ in terms of ‘y’.

First given, 2x = y ==> x = y/2 and given 4z = y ==> z = y/4.

Substituting the above values we get, average = (x + y + z)/3 = (y/2 + y + y/4)/3

This implies: (2y + 4y + y)/ (4 * 3) = 7y/12.

3. In the function, y = f(x), ‘y’ is inversely proportional to ‘x’. When x = 8, if y is 72, then what is the value of ‘y’ when x is 72?

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**Correct answer is option - 2**

**Explanation: **Since ‘x’ and ‘y’ are inversely proportional to each other, we can say x_{1} * y_{1} = x_{2} * y_{2}.

Let x_{1} = 8, y_{1} = 72 and x_{2} = 72 and y_{2} =?

This gives: 8 * 72 = 72 * y_{2} ==> y_{2} = 8.

4. The equivalent expression of ‘i’ is:

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**Correct answer is option - 4**

**Explanation: **Multiply and divide the given expression by ‘i’.

This gives: i * (i/i) ==> (i * i)/ i = i^{2}/ i.

In complex numbers, i^{2} = -1.

Hence we get -1/i as the answer!

5. If √(3p + 18) = p, then what is the value of p?

I) 6

II) -3

III) 6 or -3

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**Correct answer is option - 1**

**Explanation:**

If we square the equation on both sides, then we get: (3p + 18) = p^{2}.

Get all the terms on one side ==> p^{2} – 3p – 18 = 0.

We can factor this quadratic equation as: (p – 6) (p + 3) = 0.

This gives: p = 6, p = -3.

However let’s check these values back into the equation.

When p = 6, then √ (18 +18) = √36 = 6 and p is also 6. Yes, valid solution!

When p = -3, then √ (-9 + 18) = √9 = 3, but p = -3. Not a valid solution, also known as an extraneous solution!

6. If 4(t + 6) – 2(t – 6) = 10, then the value of ‘t’ is:

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**Correct answer is option - 1**

**Explanation: **Distribute the number present outside to the numbers present inside the parenthesis.

This gives: 4t + 24 – 2t + 12 = 10.

4t – 2t + 24 + 12 = 10 which implies 2t + 36 = 10 ==> 2t = 10 – 36 = -26.

Therefore, t = -26/2 = -13.

7. What is the vertex of the graph of the function, f(x) = x^{2} – 4x – 32?

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**Correct answer is option - 3**

**Explanation: **The graph of a quadratic function is a parabola and if it’s in the form of f(x) = ax^{2}+ bx+ c, then the vertex of the graph is given by, x = -b/2a.

In the given quadratic function, f(x) = x^{2} – 4x – 32, the value of a = 1, b = -4 and c = -32.

This gives the vertex, x = -b/2a ==> x = - (-4)/ 2(1) = 4/2 ==> x = 2.

Plug-in x = 2 in the given function, we get: f(2) = 2^{2} – 4(2) – 32 = 4 – 8 – 32 = -36.

Therefore the vertex of the parabola is (2, -36).