PCM Test Quiz: 8th Grade!

Explanation
In the given quadrilateral ABCD, BM and DN are perpendiculars drawn to AC. Since BM = DN and BR = 8cm, we can conclude that MR = 8cm as well. Also, since BM and DN are perpendiculars, we can infer that the quadrilateral is a rectangle. In a rectangle, the diagonals are equal in length. Therefore, BD = 2(BR) = 2(8cm) = 16cm.

Explanation
If p and q are two co-prime numbers, it means that they do not have any common factors other than 1. Therefore, the highest common factor (H.C.F.) of p and q would be 1, as there is no other factor that divides both p and q.

Explanation
The correct answer is 1 : 2. This is because when a square is drawn on its diagonal, it is divided into two congruent right-angled triangles. The area of each triangle is half the area of the square. Therefore, the ratio of the area of the square to the area of the square drawn on its diagonal is 1 : 2.

Explanation
The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the sides of the square are equal in length, so we can call them "x". Using the Pythagorean theorem, we can set up the equation x^2 + x^2 = d^2, where d is the length of the diagonal. Simplifying this equation gives us 2x^2 = d^2. Since we know the area of the square is 72 sq. units, we can solve for x by setting x^2 = 72 and finding that x = 6. Plugging this value back into our equation, we get 2(6)^2 = d^2, which simplifies to 72 = d^2. Taking the square root of both sides gives us d = 12. Therefore, the length of the diagonal is 12 units.

Explanation
When a body starts from a point and returns back to the same point, its displacement is zero since the initial and final positions are the same. Therefore, the average velocity, which is calculated by dividing the displacement by the time taken, will also be zero. However, the average speed, which is calculated by dividing the total distance traveled by the time taken, will not be zero as it considers only the magnitude of the distance traveled, not the direction. Therefore, the correct answer is that the average velocity is zero but not the average speed.

Explanation
When a body moves with a constant velocity, it means that its speed and direction remain unchanged over time. In other words, there is no change in its velocity. Acceleration, on the other hand, is the rate at which velocity changes. Since the body is moving with a constant velocity, there is no change in velocity, and therefore the acceleration is zero.

Explanation
Kinetic energy is not a vector quantity because it does not have a specific direction associated with it. Vector quantities have both magnitude and direction, whereas kinetic energy only has magnitude. Velocity, acceleration, and force are all vector quantities because they have both magnitude and direction.

Explanation
The number of electrons present in an atom is denoted by the atomic number. The atomic number represents the number of protons in the nucleus of an atom, which is equal to the number of electrons orbiting around the nucleus in a neutral atom. It is a fundamental characteristic of an element and determines its place in the periodic table. The atomic number is crucial in understanding the chemical properties and behavior of an atom.

Explanation
Nucleons are particles found in the nucleus of an atom. They include protons and neutrons, which are responsible for the mass of an atom. Electrons, on the other hand, are found outside the nucleus and have a much smaller mass compared to nucleons. Therefore, the correct answer is "Protons and neutrons."

Explanation
The qualitative meaning of a formula refers to the information it provides about the name and composition of a compound. It not only tells about the name of the compound but also represents one molecule of the compound. Therefore, the correct answer is both a and b.