Explain the following along with their applications. a) Artificial Intelligence b) Machine Learning

Define vector product. Describe vector product of two vectors with at least two examples. Mention the properties of vector product.

The vector product, also known as the cross product, is a binary operation on two vectors in three-dimensional space that results in a vector that is perpendicular to both input vectors.

The vector product of two vectors A and B, denoted as A x B, is given by:

A x B = |A| |B| sin(θ) n

where |A| and |B| are the magnitudes of vectors A and B respectively, θ is the angle between the two vectors, and n is a unit vector perpendicular to both A and B according to the right-hand rule.

Examples:

1. If A = 2i + 3j - k and B = i - 2j + 3k, then A x B = 9i - j - 7k
2. If C = 3i + 5j + 2k and D = i - 4j + 6k, then C x D = -8i - 8j - 23k

Properties of Vector Product:

• Non-commutative: A x B ≠ B x A
• Distributive: A x (B + C) = A x B + A x C
• Associative with Scalar Multiplication: α(A x B) = (αA) x B = A x (αB)
• Follows the Right-hand Rule: The direction of the resulting vector is determined by the right-hand rule, based on the direction of the two input vectors.

(a) What is an electromagnet? Describe the construction and working of an electromagnet with the help of a labelled diagram.

(b) Explain why an electromagnet is called a temporary magnet.

(c) Explain why the core of an electromagnet should be made of soft iron and not of steel.

(d) State the factors on which the strength of an electromagnet depends. How does it depend on these factors?

(e) Write some of the important uses of electromagnets.

Redox reactions play a pivotal role in chemistry and biology. The values of standard redox potential ($E_{\ominus}$) of two half cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniell cell in which zinc goes into solution and copper gets deposited. Given below are a set of half cell reactions (acidic medium) along with their $E_{\ominus}$ (V with respect to normal hydrogen electrode) values. Using this data, obtain correct explanations for the following questions. $$ \begin{array}{lr} \mathrm{I}{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{I}^{-} ; & E^{\ominus}=0.54 \ \mathrm{Cl}{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cl}^{-} ; & E^{\ominus}=1.36 \ \mathrm{Mn}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+} ; & E^{\ominus}=1.50 \ \mathrm{Fe}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+} ; & E^{\ominus}=0.77 \ \mathrm{O}{2}+4 \mathrm{H}^{+}+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}{2} \mathrm{O} ; & E^{\ominus}=1.23 \end{array} $$

Among the following, identify the correct statement: A Chloride ion is oxidized by $\mathrm{O}_{2}$. B $\mathrm{Fe}^{2+}$ is oxidized by iodine. C Iodide ion is oxidized by chlorine. D $\mathrm{Mn}^{2+}$ is oxidized by chlorine.

Attitudes Towards and Awareness of Waste Management : A Survey The problem of household garbage (domestic waste) is common in most Indian cities. The concern for a clean environment is increasing, but we do not know to what extent citizens know how to dispose of the garbage that collects in their household. Along with some of your classmates, conduct a survey in your own colony to find out what people do about household garbage. Each student may visit two houses in their colony, and ask the heads of the household the following questions. Their answers must be written down.

Which of the following statements are true with regard to Biofuels?

1. They are derived from living matter.
2. The National Policy on Biofuels aims to achieve 20% blending of bio-fuels, both for bio-diesel and bio-ethanol by 2017.
3. Aquatic weeds are a rich source of biofuels.

Option a) 2 and 3 only

Option b) 1 only

Option c) 1 and 3 only

Option d) All of the above