1. Which of the following gives the factored expression of x^{2}–20x + 100?

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**Correct answer is option - 2**

**Explanation: **We can factor the given expression and we get: x^{2} – 10x – 10x + 100.

Now we take the common factors from the first two terms and the last two terms.

This gives: x(x – 10) – 10(x – 10) ==> (x – 10) (x – 10) = (x – 10)^{2}.

2. What is the value of (36)^{-3/2}?

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**Correct answer is option - 5**

**Explanation: **The number 36 can also be written as: 36 = 6^{2}.

So for the given expression we get: (36)^{-3/2} = (6^{2})^{-3/2} ==> (6)^{2 * -3/2}.

Therefore we get: (6)^{-3} ==> 1/ 6^{3} ==> 1/216.

3. What is the value of –i^{69}?

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**Correct answer is option - 1**

**Explanation: **In complex numbers, i^{2} = -1 ==> i^{4} = 1.

Therefore we can write the expression close to 69 in terms of the number divisible by ‘4’.

This gives: 64 which is exactly divisible by ‘4’.

So – i^{64 + 5} ==> - i^{64} * i^{5} ==> - (-i^{4})^{16} * i^{5} ==> - (1) * i^{4} * i ==> - (1) (1) i = - i.

4. The center of a circle is (-1, 4) and the radius of the circle is 5. Which of the following is the point where the circle intersects the X-axis?

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**Correct answer is option - 4**

**Explanation**:

Given the circle and the radius and hence the equation of the circle can be written as: (x + 1)^{2} + (y – 4)^{2} = 5^{2} which gives: (x + 1)^{2} + (y – 4)^{2} = 25.

To find the point where the circle intersects the X-axis, we can plug-in y = 0 in the above equation.

This implies: (x + 1)^{2} + (0 – 4)^{2} = 25 ==> (x + 1)^{2} + (-4)^{2} = 25 ==> (x + 1)^{2} + 16 = 25.

This gives: (x + 1)^{2} = 25 – 16 ==> (x + 1)^{2} = 9 ==> x + 1 = √9 ==>x + 1 = ± 3.

Hence we get: x + 1 =3 ==> x = 2 and x + 1 = -3 ==> x = -4.

Therefore the points are (2, 0) (not given in the options) and hence the answer is (-4, 0).

5. What is the value of ‘x’ if log_{2}(32) – x = 5?

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**Correct answer is option - 1**

**Explanation: **To simplify log_{2}(32), we can write ‘32’ also in terms of ‘2’ as: 32 = 2^{5}.

This gives: log_{2}(2^{5}) and according to the logarithm rule, we have: log_{a}(a^{m}) = m * log_{a}(a).

Hence we get: 5 * log_{2}(2) = 5 * 1 since log_{2}(2) = 1.

Therefore the given equation is: 5 – x = 5 ==> x = 5 – 5 ==> x = 0.

6. If the line x + 4y – 7 = 0 intersects the line y = 3, then the intersection point on a coordinate plane is?

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**Correct answer is option - 5**

**Explanation: **Since both the lines are intersecting at a certain point, we can get the intersection point by solving both the lines.

Given one of the lines is y = 3, hence substituting this into the first equation we get: x + 4(3) – 7 = 0.

This gives: x + 12 – 7 = 0 ==> x + 5 = 0 ==> x = -5.

Hence the intersection point is (-5, 3).