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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2008

MCQ (Single Correct Answer)
In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of different ways the child can buy the six ice-cream is $${}^{10}{C_5}$$.
Statement - 2: The number of different ways the child can buy the six ice-cream is equal to the number of different ways of arranging 6 A and 4 B's in a row.
A
Statement - 1 is false, Statement - 2 is true
B
Statement - 1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1
C
Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for Statement - 1
D
Statement - 1 is true, Statement - 2 is false

Explanation

Note : n items can be distribute among p persons are $${}^{n + p - 1}{C_{p - 1}}$$ ways.

Here n = 6 ice-cream

p = 5 types of ice-cream

Each ice-cream belongs to one of the 5 ice-cream type. So chosen 6 ice-crean can be divide into 5 types of ice-cream.

$$ \therefore $$ The number of different ways the child can buy the six ice-cream is = $${}^{6 + 5 - 1}{C_{5 - 1}}$$ = $${}^{10}{C_4}$$

$$ \therefore $$ Statement - 1 is false.

Number of different ways of arranging 6 A and 4 B's in a row

= $${{10!} \over {6!4!}} = {}^{10}{C_4}$$

$$ \therefore $$ Statement - 2 is true.
2

AIEEE 2007

MCQ (Single Correct Answer)
The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $$A \cup B \cup C = S,\,A \cap B = B \cap C = A \cap C = \phi $$. The number of ways to partition S is
A
$${{12!} \over {{{(4!)}^3}}}\,\,$$
B
$${{12!} \over {{{(4!)}^4}}}\,\,$$
C
$${{12!} \over {3!\,\,{{(4!)}^3}}}$$
D
$${{12!} \over {3!\,\,{{(4!)}^4}}}$$

Explanation

The total number of ways is

$${}^{12}{C_4} \times {}^{12 - 4}{C_4} \times {}^{12 - 4 - 4}{C_4} = {}^{12}{C_4} \times {}^8{C_4} \times {}^4{C_4} = {{12!} \over {{{(4!)}^3}}}$$

3

AIEEE 2006

MCQ (Single Correct Answer)
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
A
5040
B
6210
C
385
D
1110

Explanation

A voter can give vote to either 1 candidate or 2 candidates or 3 candidates or 4 candidates.

Case 1 : When he give vote to only 1 candidate then no ways = $${}^{10}{C_1}$$

Case 2 : When he give vote to 2 candidates then no ways = $${}^{10}{C_2}$$

Case 3 : When he give vote to 3 candidates then no ways = $${}^{10}{C_3}$$

Case 4 : When he give vote to 4 candidates then no ways = $${}^{10}{C_4}$$
So, total no of ways he can give votes
= $${}^{10}{C_1} + {}^{10}{C_2} + {}^{10}{C_3} + {}^{10}{C_4}$$
= 385

Note : Here we use addition rule as he can vote any one of those four rules. Whenever there is "or" choices, we use addition rule.
4

AIEEE 2005

MCQ (Single Correct Answer)
If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
A
601
B
600
C
603
D
602

Explanation

Questions Asked from Permutations and Combinations

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
JEE Main 2021 (Online) 1st September Evening Shift (1)
JEE Main 2021 (Online) 25th July Evening Shift (1)
JEE Main 2021 (Online) 18th March Morning Shift (1)
JEE Main 2021 (Online) 17th March Evening Shift (1)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Evening Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (1)
JEE Main 2021 (Online) 26th February Morning Shift (1)
JEE Main 2021 (Online) 25th February Morning Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Morning Slot (1)
JEE Main 2020 (Online) 5th September Evening Slot (1)
JEE Main 2020 (Online) 3rd September Morning Slot (1)
JEE Main 2020 (Online) 2nd September Evening Slot (1)
JEE Main 2020 (Online) 9th January Morning Slot (1)
JEE Main 2020 (Online) 8th January Morning Slot (1)
JEE Main 2020 (Online) 7th January Evening Slot (1)
JEE Main 2020 (Online) 7th January Morning Slot (1)
JEE Main 2019 (Online) 12th April Evening Slot (1)
JEE Main 2019 (Online) 12th April Morning Slot (1)
JEE Main 2019 (Online) 10th April Evening Slot (1)
JEE Main 2019 (Online) 10th April Morning Slot (1)
JEE Main 2019 (Online) 9th April Morning Slot (1)
JEE Main 2019 (Online) 8th April Evening Slot (1)
JEE Main 2019 (Online) 8th April Morning Slot (1)
JEE Main 2019 (Online) 12th January Evening Slot (1)
JEE Main 2019 (Online) 12th January Morning Slot (1)
JEE Main 2019 (Online) 11th January Evening Slot (1)
JEE Main 2019 (Online) 10th January Evening Slot (1)
JEE Main 2019 (Online) 9th January Evening Slot (2)
JEE Main 2019 (Online) 9th January Morning Slot (1)
JEE Main 2018 (Online) 16th April Morning Slot (1)
JEE Main 2018 (Offline) (1)
JEE Main 2018 (Online) 15th April Evening Slot (1)
JEE Main 2018 (Online) 15th April Morning Slot (1)
JEE Main 2017 (Online) 9th April Morning Slot (1)
JEE Main 2017 (Online) 8th April Morning Slot (1)
JEE Main 2017 (Offline) (1)
JEE Main 2016 (Online) 10th April Morning Slot (2)
JEE Main 2016 (Online) 9th April Morning Slot (2)
JEE Main 2016 (Offline) (1)
JEE Main 2015 (Offline) (1)
JEE Main 2013 (Offline) (2)
AIEEE 2012 (1)
AIEEE 2011 (2)
AIEEE 2010 (1)
AIEEE 2009 (1)
AIEEE 2008 (2)
AIEEE 2007 (1)
AIEEE 2006 (1)
AIEEE 2005 (1)
AIEEE 2004 (2)
AIEEE 2003 (3)
AIEEE 2002 (4)

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