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NIMCET Previous Year Questions (PYQs)

NIMCET Permutations And Combinations PYQ


NIMCET PYQ 2019
In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


Let the total number of experts be Unexpected text node: 'N'.
Unexpected text node: 'E' is the set of experts who voted for miss Unexpected text node: 'A'.
Unexpected text node: 'F' is the set of experts who voted for miss Unexpected text node: 'B'.
Since Unexpected text node: '6' did not vote for either, n(EF)=N6.
n(E)=N2,n(F)=23N and n(EF)=10
.
So, N6=N2+23N10
Solving the above equation gives 

NIMCET PYQ 2019
If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in  English Dictionary, then the position of the word QUEEN is





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


Letters of the word QUEEN are E,E,N,Q,U

Words beginning with E (4!) = 24

Words beginning with N (4!/2!)=12

Words beginning with QE (3!) =  6

Words beginning with QN (3!/2!)= 3

Total words = 24+12+6+9=45

QUEEN is the next word and has rank 46th.


NIMCET PYQ 2019
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is






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NIMCET PYQ 2024
There are 9 bottle labelled 1, 2, 3, ... , 9 and 9 boxes labelled 1, 2, 3,....9. The number of ways one can put these bottles in the boxes so that each box gets one bottle and exactly 5 bottles go in their
corresponding numbered boxes is 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
The value of nr=1nPrr! is:





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
Lines L1,L2,..,L10are distinct among which the lines L2,L4,L6,L8,L10 are parallel to each other and the lines L1,L3,L5,L7,L9 pass through a given point C. The number of point of intersection of pairs of lines from the complete set L1,L2,L3,...,L10 is 





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2021
If n!2!(n2)! and n!4!(n4)! are in the ratio 2:1, then the value of n is 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2021
A polygon has 44 diagonals, the number of sides are 





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2018
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is






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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


First off all select 5 boxes out 6 boxes in which 5 big ball can fit then arrange these ball in these 5 boxes and then put remaining 4 ball in any remaining box. 
So Ans is [(6C5)5!](4!) = 6!4! = 17280

NIMCET PYQ 2018
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2018
How many natural numbers smaller than  can be formed using the digits 1 and 2 only?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
If n is an integer between 0 to 21, then find a value of n for which the value of n!(21n)! is  minimum





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NIMCET PYQ 2017
m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small cages and p large animal (n < p < m). The large animals are so large that they do not fit in small cage. However, small animals can be put in any cage. The number of putting the animals into cage is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2017
Let A and B two sets containing four and two elements respectively. The number of subsets of the A × B, each having at least three elements is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

n(A) = 4
n(B) = 2
Then the number of subsets in A*B is 2= 256

NIMCET PYQ 2020
If , then the values of n and r are:





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2021
There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2020
How many words can be formed starting with letter D taking all letters from the word DELHI so that the letters are not repeated:





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


(10-3)C6= 7C6 = 7

NIMCET PYQ 2020
There is a young boy’s birthday party in which 3 friends have attended. The mother has arranged 10 games where a prize is awarded for a winning game. The prizes are identical. If each of the 4 children receives at least one prize, then how many distributions of prizes are possible?





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NIMCET PYQ 2023
In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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