Correct Answer: B. Courtship behaviors involve displays and rituals performed by both males and females to attract a mate

Explanation

The statement that best describes courtship behaviors in animals is that they involve displays and rituals performed by both males and females to attract a mate. Courtship behaviors play a crucial role in mate selection and reproductive success in many animal species. They involve a variety of displays, rituals, vocalizations, dances, or other behaviors that serve to communicate sexual receptivity, readiness, and attractiveness.

Correct Answer: d) Peninsula

Correct Answer: A. M2Y3

Correct Answer: D. joy

Correct Answer: C. labour intensive

Explanation

Position vector of A is (8i - 10j)

Position vector of B is (2i + 6j)

Position vector of C is (-10i + 4j).

Let position vector of N be (ai + bj).

ABCN is a parallelogram.

\(\therefore \overrightarrow{AB} = \overrightarrow{NC}\).

\(\begin{bmatrix} (2 - 8)i \\ (6 + 10)j \end{bmatrix} = \begin{bmatrix} (-10 - a)i \\ (4 - b)j \end{bmatrix}\)

Equating components,

\(2 - 8 = -10 - a \implies a = -4\)

\(6 + 10 = 4 - b \implies b = -12\)

The position vector of N is (-4i - 12j).

(b) \(\overrightarrow{AN} \cdot \overrightarrow{AB}\)

\(\overrightarrow{AN} = \bar{A} - \bar{N} \)

= \((8i - 10j) - (-4i - 12j)\)

= \(12i + 2j\)

\(\overrightarrow{AB} = \bar{A} - \bar{B}\)

= \((8i - 10j) - (2i + 6j)\)

= \(6i - 16j\)

\(\therefore \overrightarrow{AN} \cdot \overrightarrow{AB} = (12i + 2j) \cdot (6i - 16j)\)

= \(72 - 32 = 40\)

(c) Let \(\theta\) be the acute angle between \(\overrightarrow{AN}\) and \(\overrightarrow{AB}\).

\(\overrightarrow{AN} \cdot \overrightarrow{AB} = |AN||AB| \cos \theta\)

\(|AN| = |12i + 2j| = \sqrt{12^{2} + 2^{2}} = \sqrt{144 + 4} = \sqrt{148}\)

\(|AB| = |6i - 16j| = \sqrt{6^{2} + (-16)^{2}} = \sqrt{36 + 256} = \sqrt{292}\)

\(\therefore 40 = (\sqrt{148})(\sqrt{292}) \cos \theta\)

\(\cos \theta = \frac{40}{(\sqrt{148})(\sqrt{292})}\)

\(\cos \theta = \frac{40}{207.88} = 0.1924\)

\(\theta = \cos^{-1} (0.1924) = 78.907°\)

\(\approxeq 78.9°\)

Correct Answer: D. beauty and purity

Correct Answer: C. resident of a country travel within it

Explanation

(a)(i) X-rays can produce photographs of fractures in bones; it can pass through fractures but cannot penetrate bones.

(ii) Uses of x-ray other than in medicine:

—detection of cracks in metallic products

—detection of alternations in art works

—detection of fake gems

—examination of bags and luggage

—identification of chemical elements and their isotopes.

(b) The energy transformations: Electrical energy

—> Heat energy

—> Kinetic energy

—> Electromagnetic energy

—> X-rays and Heat energy.

(c)(i) Dangers of over exposure to x-rays are:

— Cell mutation, i.e. change in cell genetic codes.

— Leukaemia: the destruction of living cells, tissues and organs.

— Skins harm, causes skin burn and tanning.

(ii) A person working on x-rays should take the following precautions:

— wear lead protective coats

— wear dosimeter

— wear protective goggles

— go for routine regular medical check-up.

(d)(i) K.E. = eV = 1.6x10\(^{-19}\) x 33 x 10\(^3\)

= 5.28 x 10\(^{-15}\)J

V = \(\sqrt{\frac{2K.E}{m}} = \sqrt{\frac{2 \times 5.28 \times 10^{-15}}{9.1 \times 10^{-31}}}\)

Correct Answer: B. temperature