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) = 2x² + 3 = f(x).
Hence f(x) = 2x² + 3 is an even function.

Correct answer is option - 4
Explanation: Area of a trapezoid = 1/2 * (b₁ + b₂) * h where b₁, b₂ are the bases of the trapezoid and ‘h’ is the altitude.
In the given question let b₁ = 6m and b₂ = 8m and the height h = 10m.
Hence the area of the trapezoid, A = 1/2 * (6 + 8) * 10 ==> A = 1/2 * 14m * 10m = 70m²

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.
 

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 (x² – 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.
 

Correct answer is option - 1
Explanation The general equation of a circle is (x – h)² + (y – k)² = r², 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 r² = 49. Therefore the area of the circle, A = π * (radius)² ==> Area, A = π * 49 = 49π.
 

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.

Correct answer is option - 2
Explanation: According to logarithm rule we have: log(ab) = log(a) + log(b)
Therefore we get: log(2x³) = log(2) + log(x³).
Applying the logarithm rule: log(a^m) = m * log(a).
Hence we have: log(2x³) = log(2) + 3log(x).