JEE Advanced Paper 2 free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper JEE Advanced Paper 2 set, then download the 4-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
The number of distinct arrangements of all the letters of the word CARDIGAN in which the vowels appear in the order in which they occur in the word (as a subsequence) is
A 5376
B 6720
C 7056
D 20160
[Permutations and combinations]
Correct answer: B — 6720
- Choose which 3 of the 8 places hold vowels: C(8, 3) = 56.
- The vowels fill those places in the fixed order, so there is one way for them.
- Arrange the consonants in the other places: 120 ways.
- Why the other options are wrong:
- A (5376): This is only about 0.8 of the correct value (6720); it does not follow from the steps above.
- C (7056): This is about 1.1 times the correct value (6720); it does not follow from the steps above.
- D (20160): Counted all arrangements of the letters, ignoring the condition.
Place the unrestricted letters first, then fit the restricted ones into gaps or fixed order.
Your sample is downloading. Liked it? JEE Advanced Paper 2 Paper 1 is the full paper: 48 questions and 180 marks in 3 hours (Mathematics, Physics and Chemistry, 16 each): 4 single-correct (+3, −1), 4 multiple-correct (+4 with partial marks, −2) and 8 numerical-value (+4) questions per subject, no calculator, with a worked solution for every question.
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Questions about this sample
What is in the JEE Advanced Paper 2 free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 4-page PDF; this page shows question 1 with its answer.
How many full JEE Advanced Paper 2 papers are there?
20 original papers for students in India preparing for JEE Advanced (Paper 2) for entry to the IITs. Each is 48 questions and 180 marks in 3 hours (Mathematics, Physics and Chemistry, 16 each): 4 single-correct (+3, −1), 4 multiple-correct (+4 with partial marks, −2) and 8 numerical-value (+4) questions per subject, no calculator, with a worked solution for every question. Papers start at A$11.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.