किताबों की अलमारी बड़ी है।

Because किताब is in the plural oblique form here.

• किताबें = plural direct form
• किताबों = plural oblique form

In Hindi, a noun usually changes to the oblique form when it comes before a postposition such as का / की / के, में, से, etc.

Here, किताबों comes before की, so it must be oblique:

• किताबें = books
• किताबों की अलमारी = book cupboard / bookcase / cupboard for books

So this is a very common pattern:

• लड़के = boys
• लड़कों का स्कूल = the boys’ school

की is a form of the Hindi genitive marker, often meaning of or showing possession/relationship.

So:

• किताबों की अलमारी literally means the cupboard of books
• In natural English, this is usually bookcase, bookshelf, or cupboard for books

It does not always mean strict ownership. It can also show association, type, or purpose.

For example:

• चाय का कप = tea cup / cup of tea
• कपड़ों की दुकान = clothes shop
• किताबों की अलमारी = book cupboard / bookcase

Because का / की / के agree with the noun that comes after them, not with the noun before them.

Here the noun after की is अलमारी, and अलमारी is:

• feminine
• singular

So the correct form is की.

Quick rule:

• का → masculine singular
• की → feminine singular
• के → masculine plural or certain plural contexts

Examples:

• लड़के का कमरा = the boy’s room
• लड़की की किताब = the girl’s book
• लड़कों के कमरे = the boys’ rooms

So in your sentence:

• अलमारी is feminine singular
• therefore: किताबों की अलमारी

Yes, अलमारी is a feminine noun.

One clue is that many Hindi nouns ending in -ी are feminine, though this is not a perfect rule. In this sentence, you can also tell from agreement:

• की matches a feminine noun
• बड़ी is the feminine form of big

So the sentence itself shows that अलमारी is feminine.

Because बड़ा is an adjective that changes form to agree with the noun it describes.

Since अलमारी is feminine singular, बड़ा becomes बड़ी.

Forms of big:

• बड़ा = masculine singular
• बड़ी = feminine singular
• बड़े = masculine plural / masculine oblique singular in some contexts

So:

• बड़ा कमरा = a big room
• बड़ी अलमारी = a big cupboard
• बड़े कमरे = big rooms

In your sentence, बड़ी agrees with अलमारी.

Because the main noun being described is अलमारी, and it is singular.

The sentence is saying:

• The bookcase is big
• not The bookcases are big

So:

• अलमारी बड़ी है = The cupboard is big.
• अलमारियाँ बड़ी हैं = The cupboards are big.

Even though किताबों is plural, it is not the main noun of the sentence. The main noun is अलमारी.

The main noun is अलमारी.

A helpful way to see the structure is:

• किताबों की अलमारी = the book cupboard / bookcase
• बड़ी है = is big

So the whole subject-like noun phrase is किताबों की अलमारी, but the head noun inside that phrase is अलमारी. That is why:

• की agrees with अलमारी
• बड़ी agrees with अलमारी
• है is singular because अलमारी is singular

The structure is:

[noun phrase] + [adjective] + [copula]

So:

• किताबों की अलमारी = the bookcase
• बड़ी = big
• है = is

Literally:

• Bookcase big is

This is normal Hindi word order. Hindi often places:

• the noun first,
• then the description,
• and the verb है at the end.

So this pattern is very common:

• घर बड़ा है। = The house is big.
• किताब अच्छी है। = The book is good.
• अलमारी बड़ी है। = The cupboard is big.

Yes, but the meaning and structure are a little different.

• बड़ी अलमारी = a big cupboard / the big cupboard

  • Here the adjective comes before the noun.
  • This is an attributive adjective.

• अलमारी बड़ी है = the cupboard is big

  • Here the adjective is part of the predicate.
  • This is a predicative adjective.

So:

• किताबों की बड़ी अलमारी = the big bookcase
• किताबों की अलमारी बड़ी है = the bookcase is big

Not necessarily. In Hindi, this kind of X + का/की/के + Y structure often shows a broad relationship, not just ownership.

So किताबों की अलमारी can mean:

• a cupboard containing books
• a cupboard meant for books
• a bookcase / bookshelf

This is similar to how English uses noun combinations:

• coffee cup
• school bus
• book shelf

Hindi often expresses those relationships with का / की / के.

Hindi usually does not use articles like English a, an, and the.

So अलमारी can mean:

• a cupboard
• the cupboard

The exact meaning depends on context.

That is why किताबों की अलमारी बड़ी है could be understood as:

• The bookcase is big
• or A bookcase for books is big

In most real situations, context tells you which one is meant.