1. choose the sentence that is correct.

a. la bicicleta es de el niño.
b. la bicicleta es del niña.
c. la bicicleta es de la niña.

2. choose the sentence that is correct.

a. la comida es de el señor.
b. la comida es del señor.
c. la comida es del señora.

3. choose the possessive adjective that can be modified to match gender and number.

a. vuestro
b. mis
c. mi
d. su

4. choose the possessive adjective that can be used formally with usted.

a. mi
b. nuestro
c. su
d. tu

The first two questions are a good example of the usage of the article in Spanish grammar.

The article is a word that clearly indicates the gender and the number of the noun. Its function is to modify the noun it introduces.

There are two types of articles, Variable Articles and Invariable Articles:

Variable Articles:  

-Defined Articles:

Singular Masculine: el

Singular Feminine: la

Plural Masculine: los

Plural Feminine: las

-Indefinite Articles:

Singular Masculine: un/uno

Singular Feminine: una

Plural Masculine: unos

Plural Feminine: unas

Invariable Articles:  

Neutral: Lo

Contractions: al (a+el) and del (de+el)

Koniwing this, let’s answer questions 1 and 2:

This is a sentence written in present with the 3rd person in singular. In this case we are talking about a bike, but not any bike is “the girl’s bike”. Therefore the Defined Article for the Singular Feminine la must be used.

In eglish the sentence is: The bicycle is the girl's

The other options are incorrect because:

-La bicicleta es de el niño: This sentence must be written with the contraction del (de+el) according to the rule explained above as La bicicleta es del niño (The bicycle is the boy's).

-La bicicleta es del niña: This sentence is with the incorrect usage of the article. It must be written as La bicicleta es de la niña, in order to match in gender and the number of the noun niña (girl).

This is a sentence written in present with the 3rd person in singular. In this case we are talking about somebody’s food, hence we must use the contraction del (de+el).

The other options are incorrect because:

-La comida es de el señor is gramatically incorrect. This sentence does not follow the rule of the article del (de+el).

-La comida es del señora is grammatically incorrect. Instead of del it must be used de la.

La comida es de la señora

Now, the following two questions are examples of the usage of the possessive adjectives.

The possessive adjectives indicate belonging (that someone or something belongs to the noun in the sentence).  

In Spanish, there are two kinds of possessive adjectives:

-Atonic possessive adjective: they are written before the noun they modify

1st person singular Yo (I): mi/mis (when the noun is plural)

2nd person singular Tú (you): tu/tus (when the noun is plural)  

2nd person singular (formal) Usted (you): su/sus (when the noun is plural)  

3rd person singular Él/Ella/eso/esa (he/she/it): su

1st person plural Nosotros (we):nuestro/nuestra or nuestros/nuestras (when the noun is plural)  

2nd person plural Ustedes (you) (In latinAmerica): su/sus (when the noun is plural)

2nd person plural Vosotros (you) (In Spain): vuestro/vuestra or vuestros/vuestras (when the noun is plural)

3rd person plural Ellos/Ellas (They): su/sus (when the noun is plural)

-Tonic possessive adjectives: they are written after the noun they modify

1st person singular Yo (I): mío/mía or míos/mías (when the noun is plural)

2nd person singular Tú (you): tuyo/tuya or tuyos/tuyas (when the noun is plural)  

2nd person singular (formal) Usted (you): suyo/suya or suyos/suyas (when the noun is plural)  

3rd person singular Él/Ella/eso/esa (he/she/it): suyo/suya

1st person plural Nosotros (we):nuestro/nuestra or nuestros/nuestras (when the noun is plural)  

2nd person plural Ustedes (you) (In latinAmerica): suyos/suyas

2nd person plural Vosotros (you) (In Spain): vuestro/vuestra or vuestros/vuestras (when the noun is plural)

3rd person plural Ellos/Ellas (They): suyos/suyas

Knowing this, let's answer the other questions:

In this case the option that can be modified to match gender and number is the tonic possessive adjective vuestro for the 2nd person plural Vosotros (you).  

The options mis, mi and su work with both genders.  Therefore cannot be modified and are incorrect for this case.

Usted is the formal way to use Tú in Spanish language. It is used with people in formal situations: strangers, with elderly people, with people with a degree, such as Dr., teacher, Miss, Mr, Mrs.

Now the correct atonic possesive adjective for Usted is su, as shown in the list and prior explanation.

The other options are incorrect because do not match with usted:

mi is the atonic possessive adjective for Yo (I)

nuestro is the possessive adjective for nosotros (we)

tu is the atonic possessive adjective for tú (you)

guatemala is the correct answer