Permutations & Combinations · JEE Main previous year questions

2024 12 questions

1. Q282024 · 9 Apr 2024 · Shift 2· Numerical answer

   The number of integers, between 100 and 1000 having the sum of their digits equal to 14 , is __________.

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   Answer: 70

2. Q252024 · 8 Apr 2024 · Shift 1· Numerical answer

   The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to ________.

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   Answer: 36

3. Q162024 · 8 Apr 2024 · Shift 2

   The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

   1. A.179
   2. B.177
   3. C.175
   4. D.181
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   Answer: A

4. Q162024 · 6 Apr 2024 · Shift 2

   If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315^{\text{th}}$ position in this arrangement is :

   1. A.NRAPUG
   2. B.NRAGUP
   3. C.NRAPGU
   4. D.NRAGPU
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   Answer: C

5. Q182024 · 5 Apr 2024 · Shift 2

   60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50^{\text{th}}$ word is:

   1. A.OBBJH
   2. B.HBBJO
   3. C.OBBHJ
   4. D.JBBOH
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   Answer: A

6. Q42024 · 4 Apr 2024 · Shift 1

   There are 5 points ${\mathrm{P}}_1,{\mathrm{P}}_2,{\mathrm{P}}_3,{\mathrm{P}}_4,{\mathrm{P}}_5$ on the side $AB$, excluding $A$ and $B$, of a triangle $ABC$. Similarly there are 6 points ${\mathrm{P}}_6,{\mathrm{P}}_7,\dots ,{\mathrm{P}}_{11}$ on the side $\mathrm{BC}$ and 7 points ${\mathrm{P}}_{12},{\mathrm{P}}_{13},\dots ,{\mathrm{P}}_{18}$ on the side $\mathrm{CA}$ of the triangle. The number of triangles, that can be formed using the points ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots ,{\mathrm{P}}_{18}$ as vertices, is:

   1. A.751
   2. B.776
   3. C.796
   4. D.771
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   Answer: A

7. Q302024 · 4 Apr 2024 · Shift 2· Numerical answer

   There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ________.

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   Answer: 5626

8. Q52024 · 1 Feb 2024 · Shift 1

   If $\mathrm{n}$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $\mathrm{n}$ is equal to :

   1. A.47
   2. B.53
   3. C.51
   4. D.43
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   Answer: C

9. Q282024 · 31 Jan 2024 · Shift 1· Numerical answer

   The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to __________.

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   Answer: 3734

10. Q12024 · 31 Jan 2024 · Shift 2

    The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

    1. A.130
    2. B.136
    3. C.142
    4. D.406
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    Answer: B

11. Q272024 · 29 Jan 2024 · Shift 1· Numerical answer

    All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is _________.

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    Answer: 553

12. Q12024 · 29 Jan 2024 · Shift 2

    Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

    1. A.18
    2. B.16
    3. C.12
    4. D.15
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    Answer: D