JEE MATH APEX

Permutations and Combinations-JEE-Main-PYQ’s

Mathematics Questions

Let S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
(A) 56x = 9y
(B) 21x = 4y
(C) 45x = 7y
(D) 29x = 5y
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The letters of the word “UDAYPUR” are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word “UDAYPUR” is
(A) 1579
(B) 1578
(C) 1580
(D) 1581
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The largest value of n, for which 40^n divides 60!, is
(A) 14
(B) 13
(C) 11
(D) 12
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The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
(A) 384
(B) 403
(C) 429
(D) 455
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The largest n \in \mathbb{N}, for which 7^n divides 101!, is :
(A) 18
(B) 15
(C) 19
(D) 16
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The number of strictly increasing functions f from the set \{1, 2, 3, 4, 5, 6\} to the set \{1, 2, 3, \dots, 9\} such that f(i) \neq i for 1 \le i \le 6, is equal to :
(A) 21
(B) 28
(C) 27
(D) 22
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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:
(A) 179
(B) 177
(C) 175
(D) 181
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Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f: A \rightarrow \mathbb{Z} be the function f(x)=\left[\log _{2}\left(x^{2}+\left[\frac{x^{3}}{5}\right]\right)\right]. The number of one-to-one functions from A to the range of f is
(A) 20
(B) 120
(C) 25
(D) 24
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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 :
(A) NRAPUG
(B) NRAGUP
(C) NRAPGU
(D) NRAGPU
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Let 0 \leq r \leq n. If { }^{n+1} C_{r+1}:{ }^{n} C_{r}:{ }^{n-1} C_{r-1}=55: 35: 21, then 2 n+5 r is equal to :
(A) 62
(B) 60
(C) 55
(D) 50
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