1. If a, p, q, and r are non-zero integers such that a/q = 5p/3r. The value of ‘r’ is?

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**Correct answer is option - 5**

**Explanation:**Cross-multiply the denominator to the opposite side numerator.

This gives: a/q= 5p/3r which implies 3r * a = 5p * q.

So, r = 5pq/3a.

2. A single dice is thrown. The probability of getting the number 6 is?

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**Correct answer is option - 4**

**Explanation:**The total number of outcomes when a dice is thrown is = 6.

The chance of getting the number ‘6’ is one out of 6 other numbers.

Therefore, the probability of getting the number 6 is 1/6.

3. In a triangle ABC, if tan(C) = 6/8, then the length of the side AC is?

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**Correct answer is option - 1**

**Explanation:**tan(θ) = opposite side/ adjacent side where ‘θ’ is the given angle.

In triangle ABC, tan(C) = 6/8 implies the opposite side, AB = 6 and the adjacent side BC= 8.

Therefore, the length of the side AC = hypotenuse can be calculated using the Pythagorean Theorem.

AC^{2} = 6^{2} + 8^{2} = 36 + 64 = 100.

Side length, AC = √100 = 10.

4. Which of the following is the x-intercept of the graph of y = x^{2} + x -12?

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**Correct answer is option - 4**

**Explanation: **To find the x-intercept of the graph of a function, substitute y = 0.

This gives: x^{2} + x – 12 = 0. Factoring the quadratic equation gives (x + 4) (x – 3) = 0.

This implies: x + 4 = 0 and x – 3 = 0 ==> x = -4 and x = 3.

Since -4 is not in the options, the answer is x = 3.

5. If the equation of a parabola is y = x^{2} – 4x + 6, then what is the x-coordinate of the highest point on the graph of the parabola?

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**Correct answer is option - 3**

**Explanation: **The vertex is the highest point on the graph of this parabola since it opens upward as a> 0.

The x-coordinate of the vertex, x = -b/2a

x = - (-4)/2 ==> x = 2

6. Given two points on the X-Y plane, A (5, -3) and B (2, 3). What is the length of the line segment AB?

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**Correct answer is option - 2**

**Explanation:**Distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is √ [(x_{2} – x_{1})^{2} + (y_{2} – y_{1)}^{2}].

This gives distance between A (5, -3) and B (2, 3) is √ [(2 – 5)^{2} + (3 – (-3))^{ 2}]

So, length AB = √9 + 36 = √45 = 3√5.

7. Which of the following is the x-intercept of the graph of y = x^{2} + x -12?

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**Correct answer is option - 4**

**Explanation:**

To find the x-intercept of the graph of a function, substitute y = 0.

This gives: x^{2} + x – 12 = 0. Factoring the quadratic equation gives (x + 4) (x – 3) = 0.

This implies: x + 4 = 0 and x – 3 = 0 ==> x = -4 and x = 3.

Since -4 is not in the options, the answer is x = 3.