Correct answer is option - 1
Explanation:
We can cross- multiply the numbers to the other side of the equation sign.
This gives: 12 * 7 = 4 * k which implies 84 = 4k.
Dividing 4 on both sides gives k = 84/4 = 21.
 

Correct answer is option - 4
Explanation:
First distribute the numbers on the outside to numbers inside the parenthesis.
8x – 8 – 20x – 40 = 12 which gives -12x – 48 = 12.
This implies: -12x = 60 and hence x = 60/-12 = -5.
 

Correct answer is option - 3
Explanation:
The original price of the bag = $40.
The 20% discount on the bag gives $40 – ($40 * 0.2) = $32.
Additional 10% discount on the reduced price of bag = $32 – ($32 * 0.1) = $28.80.
 

Correct answer is option - 4
Explanation: 3602 can be written as 3600 + 2. This gives: i³⁶⁰² = i^{(300 + 2)} = i³⁶⁰⁰ * i²
This implies: (i⁴)⁹⁰⁰ * i² and i⁴ = (i²)² = (-1)² = 1
Therefore we get: (1)⁹⁰⁰ * -1 = -1.

Correct answer is option - 5
Explanation: According to the formula, (a –b)² = a² – 2ab + b².
Therefore, (p – 7)² = p² -14p + 7²
Hence, p² – 14p + 49 implies c = 49.

Correct answer is option - 4
Explanation: Since it’s a square, all the side lengths are equal.
Let the side PQ = QR = s
Here, triangle PQR is a right triangle and hence we can use the Pythagorean Theorem.
This gives: s² + s² = 6² which implies 2s² = 36.
Therefore s² = 18 which gives s = √18 = 3√2.

Correct answer is option - 2
Explanation: The above given quadratic equation can be factored as (x – 12)(x + 3)= 0.
This gives (x – 12) = 0 and (x + 3) = 0.
Hence x = 12 and x = -3.
Therefore the sum of the two solutions is 12 + (– 3) = 9.