Which Article of the Indian Constitution prohibits providing of any religious instruction in the educational institutions maintained by the State?

Correct — B. Article 28 bars religious instruction in any educational institution wholly maintained out of State funds.

The article then graduates the rule. An institution administered by the State but established under an endowment or trust that requires religious instruction is exempt, and in a State-recognised or State-aided institution no one may be made to attend religious instruction without consent.

No other article touches religious instruction at all, so option (b).

Why the others are wrong

• (a)
  Article 29 — Article 29 protects the language, script and culture of any section of citizens and bars denial of admission to State-aided institutions on grounds of religion, race, caste or language. It says nothing about religious instruction.
• (c)
  Article 30 — Article 30 gives religious and linguistic minorities the right to establish and administer educational institutions of their choice. It is a right to run institutions, not a restriction on what State-funded ones may teach.
• (d)
  Article 31 — Article 31, the old right to property, was repealed by the 44th Amendment in 1978, and the right now sits in Article 300A. It never dealt with education.

Articles 25 to 28 make up the Right to Freedom of Religion, and Article 28 is where the State's own secularism is enforced inside a classroom.

Read the article as a ladder. In an institution wholly maintained out of State funds there is a flat ban on religious instruction. In a State-administered institution founded under a trust requiring such instruction, the ban lifts.
In a merely recognised or aided institution, instruction may be given but attendance is voluntary.

Articles 29 and 30 next door are cultural and minority rights, which is why they crowd the options.

Key facts

• Article 28(1) prohibits religious instruction in educational institutions wholly maintained out of State funds.
• Article 28(3) makes attendance at religious instruction in State-recognised or State-aided institutions voluntary, with the guardian's consent required for a minor.
• Articles 25 to 28 together form the Right to Freedom of Religion.
• Article 31 was repealed by the 44th Amendment, 1978, and the right to property now sits in Article 300A.

Common traps

• Confusing Article 28, which restricts State-funded institutions, with Article 30, which empowers minority ones.
• Missing the words 'wholly maintained', which are what separate the flat ban from the voluntary-attendance rule.

No directly related past PYQ was found.