1. If the value of 15 less than twice a number is 15, then the number is:

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**Correct answer is option - 4**

**Explanation: **Let the number be = x.

Twice the number means ==> 2x

15 less than twice the number ==> 2x – 15

Given the value of this expression is again equal to 15 ==>2x – 15 = 15.

Solving for ‘x’, add 15 on both sides ==> 2x – 15 + 15 = 15 + 15.

This gives: 2x = 30 ==> x = 30/2 = 15. Hence the value of x is 15.

2. If √(4x + 9) = 3, then the value of x is:

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**Correct answer is option - 1**

**Explanation: **Squaring the given equation on both sides gives: [√(4x + 9)]^{2} = 3^{2} ==> 4x + 9 = 9.

Solving for ‘x’, subtract 9 on both sides: 4x + 9 - 9 = 9 – 9.

This gives: 4x = 0 ==> x = 0/4 = 0.

But before we confirm it is important to check if it is an extraneous solution.

Plug-in x = 0 in the expression: √ (4*0 + 9) = √(0 + 9) = √9 = 3. The answer is verified!

Hence the value of x = 0.

3. If p^{2} – q^{2} = 5 and (p – q) = 5, then the value of (p + q) is:

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**Correct answer is option - 1**

**Explanation:**According to the ‘Difference of Squares’ formula: a^{2} – b^{2} = (a + b) (a – b).

Similarly, p^{2} – q^{2} = 5 ==> (p + q) (p – q) = 5.

If given (p – q) = 5, then (p + q) * 5 = 5 ==> (p + q) = 5/5 = 1.

Hence the value of (p + q) = 1.

4. Given the parallelogram ABCD as shown in the figure below. If the measure of the angle ABC is (3x – 11) and the measure of the angle ADC is (2x + 13), then the measure of angle ABC is:

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**Correct answer is option - 2**

**Explanation: **In a parallelogram, the opposite angles are congruent to each other.

This implies that the measure of angle ABC = angle ADC, and similarly angle BAD = angle BCD.

Therefore we can say that: 3x – 11 = 2x + 13 ==> 3x – 2x = 13 + 11.

This gives: x = 24.

Hence the measure of the angle ABC = 3x – 11 = (3*24 – 11) = 61°

5. Which of the following is the factor of the polynomial, 3x^{2} – 4x – 7?

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**Correct answer is option - 3**

**Explanation: **The given polynomial, 3x^{2} – 4x – 7 can be also written as 3x^{2} + 3x – 7x – 7.

Grouping and taking the common factor out from the first two terms and the last two terms, we get: 3x (x + 1) – 7 (x + 1).

This gives: (x + 1) (3x – 7)

Since (x + 1) is not in the options, hence (3x – 7) is the answer!

6. If the value of sin(θ) = 0.8, then what is the value of the expression sin(θ) + cos(θ) in the first quadrant?

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**Correct answer is option - 5**

**Explanation: **According to the trigonometric identity: sin^{2}(θ) + cos^{2}(θ) = 1.

Since sin(θ) = 0.8, using the above identity we get: (0.8)^{2} + cos^{2}(θ) = 1.

This gives: cos^{2}(θ) = 1 – 0.64 = 0.36. This implies cos(θ) = √0.36 = 0.6.

In the first quadrant both sin(θ) and cos(θ) are positive, therefore the above answers verify it.

Hence the value of sin(θ) + cos(θ) = 0.8 + 0.6 = 1.4

7. The equivalent expression for the given expression, √-(-15)^{2} is?

(Note: i = √-1).

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**Correct answer is option - 4**

**Explanation: **15^{2} = 225, and hence the given expression can also be written as: √-(225).

This gives: √ [(-1) * (225)] = √-1 * √225 = i * 15.

Hence the answer is 15i.