Permutations & Combinations · JEE Main previous year questions

2021 11 questions

1. Q212021 · 26 Aug 2021 · Shift 2· Numerical answer

   The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is _____________.

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   Answer: 7744

2. Q22021 · 27 Jul 2021 · Shift 2

   A possible value of 'x', for which the ninth term in the expansion of ${\left\{3^{{\log }_3\sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right){\log }_3(5^{x-1}+1)}\right\}}^{10}$ in the increasing powers of $3^{\left(-\frac{1}{8}\right){\log }_3(5^{x-1}+1)}$ is equal to 180, is :

   1. A.0
   2. B.$-1$
   3. C.2
   4. D.1
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   Answer: D

3. Q252021 · 25 Jul 2021 · Shift 1· Numerical answer

   There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100 k, then k is equal to _____________.

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   Answer: 238

4. Q222021 · 22 Jul 2021 · Shift 2· Numerical answer

   If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.

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   Answer: 96

5. Q272021 · 20 Jul 2021 · Shift 1· Numerical answer

   There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is ______________.

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   Answer: 777

6. Q142021 · 18 Mar 2021 · Shift 1

   The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :

   1. A.26664
   2. B.122664
   3. C.122234
   4. D.22264
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   Answer: A

7. Q212021 · 18 Mar 2021 · Shift 1· Numerical answer

   The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :

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   Answer: 300

8. Q52021 · 26 Feb 2021 · Shift 1

   The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :

   1. A.35
   2. B.42
   3. C.82
   4. D.77
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   Answer: D

9. Q132021 · 26 Feb 2021 · Shift 1

   The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is 2000 after $\frac{k}{{\log }_e\left(\frac{6}{5}\right)}$ hours, then ${\left(\frac{k}{{\log }_{e}2}\right)}^2$ is equal to :

   1. A.16
   2. B.8
   3. C.2
   4. D.4
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   Answer: D

10. Q212021 · 26 Feb 2021 · Shift 2· Numerical answer

    The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.

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    Answer: 1000

11. Q222021 · 25 Feb 2021 · Shift 2· Numerical answer

    The total number of two digit numbers 'n', such that $3^n+7^n$ is a multiple of 10, is ______ .

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    Answer: 45