1. If (x + y)^{2} = p, (x – y)^{2} = q, then what is (x^{2} + y^{2}) only in terms of ‘p’ and ‘q’?

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**Correct answer is option - 3**

**Explanation: **Expanding (x + y)^{2}, we get: (x + y)^{2} = x^{2} + 2xy + y^{2} = p.

Similarly expanding (x – y)^{2} = x^{2} – 2xy + y^{2} = q.

Now adding ‘p’ and ‘q’ together we get: 2x^{2} + 2y^{2} = p + q (as 2xy gets cancelled).

This implies: 2(x^{2} + y^{2}) = p + q ==> x^{2} + y^{2} = (p + q)/ 2.

2. If f(x) = 4x – 6, then what is the value of f(-2) – f(2)?

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**Correct answer is option - 2**

**Explanation: **Given f(x) = 4x – 6 which means that f(-2) = 4(-2) – 6 = -8 – 6 = -14.

Similarly f(2) = 4(2) – 6 ==>8 – 6 = 2

Now, f(-2) – f(2) = -14 – 2 = -16.

3. Given two points (-1, 3) and (2, k) and the slope of the line passing these through two points is -2/3. What is the value of k?

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**Correct answer is option - 2**

**Explanation: **Slope of any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given be, m = (y_{2} – y_{1})/ (x_{2} – x_{1}).

Therefore the slope of the two given points is: m = (k – 3)/ (2 – (-1)) = -2/3

This implies: (k – 3)/ 3 = -2/3 ==> cross-multiplying we get: 3(k – 3) = -2 * 3.

This gives: 3k – 9 = -6 ==> 3k = 9 – 6 ==> 3k = 3 ==> k = 1.

4. ** **If an object is travelling with a speed of 30m/sec, then how much distance would it cover in a time interval of 1.5minutes?

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**Correct answer is option - 3**

**Explanation: **

The formula to answer this question is: Distance = Speed * time.

However all the units must be consistent and given speed = 30m/sec, but time is 1.5 minutes.

Therefore we first have to convert time from minutes to seconds è 1.5mins * (60 seconds)/ (1 minute) = 90 seconds.

So the distance covered by the object = 30m/sec * 90 seconds = 2700m.

5. If the width of a rectangle is 12m and the length of its diagonal is 20m, then what is the area of the rectangle in ‘m^{2}’?

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**Correct answer is option - 5**

**Explanation: **A diagonal divides any rectangle into two equal parts and hence it divides the rectangle in two right angled triangles.

The diagonal is the hypotenuse of the right triangle and we can use the Pythagorean Theorem to find the length of the rectangle.

So, (length)^{2} + (12)^{2} = (20)^{2} ==> (length)^{2} + 144 = 400 ==> length = √(400 – 144) = √256 = 16m

Hence we get area of the rectangle = length * width = 16 * 12 = 192m^{2}.

6. In triangle ABC, the measure of the exterior angle ABD is 4x – 26, and the measure of the angles A and C are x + 11 and x + 13 respectively as shown in the figure below. What is the value of x?

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**Correct answer is option - 1**

**Explanation: **In any given triangle, the exterior angle is always equal to the sum of the interior opposite angles.

This means: measure of angle ABD = measure of angles A and angle C.

Thisimplies: 4x – 26 = x + 11 + x + 13. This gives: 4x – 26 = 2x + 24.

Solving for ‘x’ we get: 4x – 2x = 24 + 26 ==> 2x = 50 ==> x = 25.