1. If the discriminant of a quadratic equation is -9, then the number of real roots the equation has are:

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**Correct answer is option - 1**

**Explanation: **If the discriminant of a quadratic equation is a negative number, then the equation does not have real roots or solutions. It has imaginary roots (also known as complex roots).

Therefore the number of real roots = 0.

2. If f(x) = 3x + k and f(-3) = 2, then the value of ‘k’ is:

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**Correct answer is option - 4**

**Explanation: **Given f(x) = 3x + k and f(-3) = 2 implies f(-3) = 3(-3) + k = 2.

This gives: -9 + k = 2 ==> k = 2 + 9 = 11.

Hence k = 11.

3. If (a + i) (2 + i) = 3 + 4i, then what is the value of ‘a’?

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**Correct answer is option - 3**

**Explanation: **(a + i) (2 + i) = (2a + ai + 2i + i^{2}) = 3 + 4i. In complex numbers, i^{2} = -1.

Group the real numbers and imaginary numbers together.

This gives: 2a + ai + 2i – 1 = 3 + 4i ==> (2a – 1) + (a + 2)i = 3 + 4i.

Here the real number parts can be equated or the imaginary number parts can be equated.

This gives 2a – 1 = 3 ==> 2a = 4 ==> a = 2.

4. The slope of a line parallel to the line 4x – y + 8 is:

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**Correct answer is option - 3**

**Explanation: **The given line can be rearranged as: y = 4x + 8.

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

This implies that the slope, m = 4.

Parallel lines have equal slopes and hence slope of the parallel line is also = 4.

5. ** **If Josh can paint a house in 5 hours and Jake can paint a house of exactly same size in 7 hours, then how many hours will it take to paint the house if both work together?

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**Correct answer is option - 5**

**Explanation: **Josh can paint a house in 5hours which implies that in 1 hour Josh can paint 1/5^{th} of the house.

Similarly, Jake can paint a house in 7 hours which implies that in 1 hour Jake can paint 1/7^{th} of the house.

Now if both work together, let the time taken be ‘x’ hours: Then, 1/5 + 1/7 = 1/x.

Hence 1/x = (7 + 5)/ 35 = 12/35 ==> x = 35/12 = 2.92 hours.

6. The simplified expression to the expression (√3 + 1)/ (√3 – 1) is:

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**Correct answer is option - 1**

**Explanation: **In order to simplify the given expression, we should first rationalize the denominator by multiplying and dividing the given expression by its conjugate which is (√3 + 1).

This gives: (√3 + 1)(√3 + 1)/ (√3 – 1)(√3 – 1) = (√3 + 1)^{2}/ [ (√3)^{2} – 1^{2}].

Expanding the numerator, we get: (3 + 2√3 + 1)/ (3 – 1).

This implies: (4 + 2√3)/ 2 = 2 + √3.

7. If Mike runs a distance of 160m in a time period of 40 seconds, then the speed with which he is running is:

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**Correct answer is option - 4**

**Explanation:**

Speed is given by the formula: Speed = (Distance travelled)/ (Time)

Distance travelled by Mike = 160m and time taken = 40 seconds

Therefore speed of Mike = (160m)/ (40secs) = 4m/sec.