1. If x² - y² = 16, and x - y = 8, then y =

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**Correct answer is option - 5**

**Explanation:**The given expression can be expanded as: x^{2} – y^{2} = (x + y)(x – y) and given x – y = 8. This implies that x + y = 2 since 2 * 8 = 16. Solving the system of linear equations gives, x= 5 and y = -3.

2. If b^{2} = 15, then what is b^{4}?

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**Correct answer is option - 2**

**Explanation:** Since b^{2} = 15, hence b^{4} can also be written as (b^{2})^{2} = 15^{2} = 225.

3. What is the length of the line segment in the X-Y coordinate plane with the end points (-3, 3) and (4, -1).

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**Correct answer is option - 1**

**Explanation:** The length of a line segment can be calculated by the formula, distance or length = √(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}. By substituting the ‘x’ and ‘y’ values in the distance formula, we get √(4 – (-3)^{2} + (-1 – 3)^{2} = √7^{2} + 4^{2} = √49 + 16 = √65.

4. If the radius of the circle with center O is 10 and the measure of angle POQ is 120°, what is the best approximation to the length of arc PQ?

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**Correct answer is option - 4**

**Explanation:** To find the length of the arc PQ, we can use the formula:

Length of the arc = (θ π r)/ 180° where ‘θ’ is in degrees.

Given radius, r = 10 and angle, θ = 120°.

Therefore, length of the arc (taking π = 3.14)= (120° * 3.14 * 10)/ (180°) = 21 (approximately).

5. Given, f(x) = (2x + 1)/(x -1) where ‘x’ is any integer except x = 1. From the given options, which gives the greatest function value?

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**Correct answer is option - 5**

**Explanation:** To find the function value, simply plug-in the given ‘x’ value in the function.

f(-1) means x = -1. This gives f(-1) = 2(-1) + 1/ (-1 - 1) = 1/2

f(0) means x = 0. This gives f(0) = 2(0) + 1/(0 – 1) = -1

f(-2) means x = -2. This gives f(-2) = 2(-2) +1/ (-2 – 1) = 1

f(3) means x = 3. This gives f(3) = 2(3) + 1/(3 – 1) = 7/2

f(2) means x = 2. This gives f(2) = 2(2) + 1/(2 – 1) =** 5**is the greatest among all the above numbers!

6. If two sides of the triangle have lengths 7 and 9, the perimeter of the triangle could be which of the following:

I) 16

II) 22

III) 35

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**Correct answer is option - 2**

**Explanation: **16 cannot be the answer since sum of the given two sides 9 + 7 is already 16.

Also, 35 cannot be the answer since if the perimeter is 35, that means the third side of the triangle = 35 - (7 + 9) = 35 – 16 = 19.

According to the Triangle Inequality theorem, sum of any two sides of a triangle should be greater than the third side. Therefore the third side cannot be equal to 19.

Hence, if the perimeter is 22, then third side = 22 – (9 + 7) = 22 – 16 = ‘6’ can be the third side!

7. Which of the following is the equation of a line passing through the origin and parallel to the line 3x – y = 4?

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**Correct answer is option - 2**

**Explanation:**

The equation can be re-written in the slope-interceptform of y = mx + bas y = 3x – 4.

Comparing the two equations, we get slope, m = 3.

Parallel lines always have same slopes. Hence slope, m = 3 and origin point = (0, 0).

The lines passes through origin, hence 0 = 3(0) + b which gives b = 0

Therefore, we can rearrange to get y = 3x + 0 which can be also written as 3x – y = 0