1. If S = (4PQ)/ (MN^{2}), then which of the following is an expression of ‘Q’ in terms of P, Q, M and N?

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**Correct answer is option - 5**

**Explanation: **In order to write the expression of ‘Q’, we should get rid of everything beside Q and take them to the other side.

Cross-multiplying MN^{2} to the other side gives: MN^{2}S = 4PQ.

Dividing 4P on both sides gives: Q = (MN^{2}S)/ (4P)

2. The equation of a line is given as 2x -ky + 6 = 0. If the slope of the given line is 1/2, then the value of ‘k’ is?

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**Correct answer is option - 5**

**Explanation: **The given equation, 2x – ky + 6 = 0 can also be rearranged as ky = 2x + 6.

This gives: y = (2/k) x + (6/k).

Now this is in the form of y = mx + b, where ‘m’ is the slope of the equation and given m = 1/2.

Equating the slopes, we get 2/k = m = 1/2 ==> k = 4.

3. A line segment has its endpoint at A and B where A = (-2, 4). If the coordinates of the midpoint of the line AB is (6, -3), then the point B is?

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**Correct answer is option - 3**

**Explanation:**

The midpoint of a line joining points (x_{1}, y_{1}) and (x_{2}, y_{2}) is [(x_{1} + x_{2})/ 2, (y_{1} + y_{2})/ 2].

Let the point B = (x, y).

Then [(-2 + x)/ 2, (4 + y)/ 2] = (6, -3).

Here we can equate the respective ‘x’ coordinates and the ‘y’ coordinates.

This gives: (-2 + x)/ 2 = 6 which implies -2 + x = 12 ==> x = 12 + 2 ==> x = 14.

Similarly, (4 + y)/ 2 = -3 which implies 4 + y = -6 ==> y = -6 – 4 ==> y = -10.

Hence we get: (x, y) = (14, -10).

4. If (3x – 7)^{2} = px^{2} – 42x + q, then the value of (q – p) is?

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**Correct answer is option - 3**

**Explanation:**

We can expand (3x – 7)^{2} using the formula: (a – b)^{2} = a^{2} - 2ab + b^{2}.

Here a = 3x and b = 7. Hence we get: (3x – 7)^{2} = (3x)^{2} – (2 * 3x * 7) + (7)^{2}.

This gives: (3x – 7)^{2} = 9x^{2} – 42x + 49 which is given as px^{2} – 42x + q^{2}.

Therefore, p = 9 and q = 49 which implies q – p = 49 – 9 = 40.

5. If the circumference of a circle is 18, then the area of the circle is?

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**Correct answer is option - 4**

**Explanation:**

Circumference of the circle = 2 * π * radius = 18

This gives radius of the circle, r = 18/ (2 * π) ==> radius, r = 9/ π.

Area of the circle, A = π * (radius)^{2} ==> Area = π * (9/ π)^{2}

Area of the circle, A = π * 81/ π^{2} ==> Area = 81/ π.

6. If (v/ w) = 2/5 and ‘w’ is 75% of 60, then what is the value of ‘v’?

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**Correct answer is option - 4**

**Explanation:**

Given ‘w’ is 75% of 60 ==> w = (75/100) * 60 ==> w = (3/ 4) * 60.

This gives the value of ‘w’ = 45.

Since (v / w) = 2/5, hence v = 2w/5 ==> v = (2 * 45)/ 5 ==> the value of ‘v’ is 18.

7. The measure of the angles is shown in the figure below. If the measure of the angle PQT is 147°, then what is the measure of the angle PQS?

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**Correct answer is option - 4**

**Explanation:**

In the given figure angle PQT is split into three parts by 3 different rays. Since the total angle given is 147°, hence the sum of the three angles adds up to 147°.

This gives: 4a + 2a + a = 147° which implies 7a = 147°.

This gives a = 147°/7 ==> a = 21°.

Therefore the measure of the angle PQS = 4a + 2a = 6a ==> 6 * 21° = 126°.