1. Which of the following functions is an even function?

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**Correct answer is option - 3**

**Explanation: **An even function is a function which obeys the rule: f(x) = f(-x).

So for option (a), f(-x) = -2(-x) + 3 ==> 2x + 3. This function is not the same as the original f(x).

Similarly all the other options except option (d) do not give the same f(-x) as f(x).

However in option (d), f(-x) = 2(-x)^{2} + 3 ==> f(-x) = 2x^{2} + 3 = f(x).

Hence f(x) = 2x^{2} + 3 is an even function.

2. The bases of a trapezoid are 6m and 8m. The altitude of the trapezoid is 10m. The area of the trapezoid in m^{2} is?

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**Correct answer is option - 4**

**Explanation: **Area of a trapezoid = 1/2 * (b_{1} + b_{2}) * h where b_{1}, b_{2} are the bases of the trapezoid and ‘h’ is the altitude.

In the given question let b_{1} = 6m and b_{2} = 8m and the height h = 10m.

Hence the area of the trapezoid, A = 1/2 * (6 + 8) * 10 ==> A = 1/2 * 14m * 10m = 70m^{2}

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

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**Correct answer is option - 1**

**Explanation: **f(-2) = 6(-2) – 4 ==> f(2) = -12 – 4 = -16.

f(2) = 6(2) – 4 ==> f(2) = 12 – 4 = 8.

This gives: f(-2) – f(2) = -16 – 8 = -24.

4. If f(x) = (x + 3)/ (x^{2} – x – 30), then the value of ‘x’ can be any real number except?

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**Correct answer is option - 4**

**Explanation: **In a rational function, if the denominator is equal to 0, then the function becomes undefined.

In the denominator we have (x^{2} – x – 30) and this function can be factored as (x – 6) (x + 5).

Now if we set the denominator to 0, we have (x – 6) (x + 5) = 0.

This gives: (x – 6) = 0 ==> x = 6 and (x + 5) = 0 ==> x = -5.

Hence ‘x’ can be any real number except -5 and 6 as these two values make the denominator 0.

5. If the equation of a circle is given by (x – 4)^{2} + (y + 3)^{2} = 49, then the area of the circle is?

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**Correct answer is option - 1**

**Explanation **The general equation of a circle is (x – h)^{2} + (y – k)^{2} = r^{2}, where (h, k) is the center of the circle and ‘r’ is the radius of the circle. From the given equation we can hence say that r^{2} = 49. Therefore the area of the circle, A = π * (radius)^{2} ==> Area, A = π * 49 = 49π.

6. If f(x) = 2x + 1 and g(x) = 3 – x, then the value of fog(1) is?

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**Correct answer is option - 5**

**Explanation: **fog(x) is the representation of composition of two function, f(x) and g(x).

So, fog(x) = f(g(x)) ==> f(3 – x).

If f(x) = 2x + 1, then f(3 – x) = 2 (3 – x) + 1 ==> 6 – 2x + 1 ==> fog(x) = 7 – 2x.

fog(1) = 7 – 2(1) = 7 – 2 ==> fog(1) = 5.

7. Which of the following is equivalent to the logarithmic expression, log(2x^{3})?

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**Correct answer is option - 2**

**Explanation: **According to logarithm rule we have: log(ab) = log(a) + log(b)

Therefore we get: log(2x^{3}) = log(2) + log(x^{3}).

Applying the logarithm rule: log(a^{m}) = m * log(a).

Hence we have: log(2x^{3}) = log(2) + 3log(x).