1. Which of the following gives the solution to |7x – 9| = 5?

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**Correct answer is option - 4**

**Explanation: **Absolute value equation always splits in two ways: (7x – 9) = 5 and (7x - 9) = -5.

When (7x – 9) = 5, it gives: 7x = 5 + 9 ==> 7x = 14 ==> x = 14/7 ==> x = 2.

Similarly, when (7x – 9) = -5, it gives: 7x = -5 + 9 ==> 7x = 4 ==> x = 4/7.

Hence the values of ‘x’ are x = 2 and x = 4/7.

2. The minimum point on the graph of the function, f(x) = 2x^{2} – 8x + 9 is?

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**Correct answer is option - 3**

**Explanation:**The given function is a quadratic function in the form of f(x) = ax^{2} + bx + c where a = 2, b = -8 and c = 9 and its graph is a parabola.Since a = 2 > 0, hence the parabola opens upward.

The minimum point on the graph is the vertex where the x-coordinate = -b/ 2a.

Hence the x-coordinate of the vertex = - (-8)/ (2 * 2) ==> x = 8/4 ==> x = 2.

Therefore, f(2) = 2(2)^{2} – 8(2) + 9 = 8 – 16 + 9 ==> f(2) = 1

Hence the minimum point on the graph is = (2, 1).

3. Which of the following is equivalent to 4log_{4}(x – 4) – 2log_{4}(y)?

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**Correct answer is option - 2**

**Explanation: **According to the logarithm rule: m * log_{b}(a) = log_{b}(a)^{m}.

Applying the above rule we get: log_{4}(x – 4)^{4} – log_{4}(y)^{2}.

Now according to the logarithm rule: log_{b}(a) – log_{b}(b) = log_{b}(a/b).

This gives: log_{4}(x – 4)^{4} – log_{4}(y)^{2} = log_{4}[(x – 4)^{4}/ y^{2}] is the answer!

4. If f(x) = 4x + 3, then the inverse of this function is?

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**Correct answer is option - 3**

**Explanation: **In order to find the inverse of a function, we should first switch the ‘x’ and ‘y’ places in the given function, y = 4x + 3.

This gives: x = 4y + 3. Now solve for y.

This implies: (x – 3) = 4y ==> y = (x – 3)/ 4.

Hence the inverse function, f^{-1}(x) = (x – 3)/ 4.

5. A circular field has an area of 288π. How much fencing is required in order to cover the entire field?

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**Correct answer is option - 1**

**Explanation: **Area of a circle, A = π * (radius)^{2} ==> Area, A = 288π.

This implies: π (r)^{2} = 288π ==> radius, r = √288 ==> r = √ (144 * 2) = 12√2.

The fencing required is the circumference of the circle = 2 * π * radius.

Therefore the fencing required around the circular field = 2 * π * 12√2 = 24√2 π.

6. The slope of the line parallel to the line 4x + 5y – 9 = 0 is?

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**Correct answer is option - 4**

**Explanation:**The given equation can be rearranged as 5y = -4x + 9 ==> y = (-4/5)x + (9/5).

This is in the form of y = mx + b where ‘m’ is the slope of the line.

Hence slope of the given line, m = -4/5.

If two lines are parallel to each other, then slopes are equal to each other.

Hence slope of the parallel line is also = -4/5.

7. The equation of a circle in the coordinate plane is given by: (x + 6)^{2} + (y – 5)^{2} = 12. What is the circumference of this circle?

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**Correct answer is option - 5**

**Explanation:**The equation of a circle in a coordinate plane is given by: (x – h)^{2} + (y – k)^{2} = r^{2} where (h, k) is the center of the circle and ‘r’ is the radius of the circle.

Hence from the given equation, we get the radius, r^{2} = 12 ==> r = √12 = √ (4 * 3) = 2√3.

The circumference of the circle = 2 * π * r ==> Circumference = 2 * π * 2√3 = 4√3 π.