Permutations & Combinations · JEE Main previous year questions

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2022 14 questions

Q232022 · 29 Jul 2022 · Shift 2· Numerical answer
The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is ________.
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Answer: 6
Q222022 · 28 Jul 2022 · Shift 2· Numerical answer
A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $b + 3 g$ is equal to _________.
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Answer: 17
Q232022 · 27 Jul 2022 · Shift 2· Numerical answer
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $tan^{- 1} \frac{3}{4}$ . Water is poured in it at a constant rate of $6$ cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is $4$ meters, is ____.
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Answer: 5
Q222022 · 26 Jul 2022 · Shift 1· Numerical answer
The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.
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Answer: 180
Q212022 · 30 Jun 2022 · Shift 1· Numerical answer
The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is ____________.
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Answer: 360
Q32022 · 28 Jun 2022 · Shift 2
The number of ways to distribute 30 identical candies among four children $C_{1}, C_{2}, C_{3}$ and $C_{4}$ so that $C_{2}$ receives at least 4 and at most 7 candies, $C_{3}$ receives at least 2 and at most 6 candies, is equal to :
1. A. $205$
2. B. $615$
3. C. $510$
4. D. $430$
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Answer: D
Q232022 · 27 Jun 2022 · Shift 1· Numerical answer
The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _____________.
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Answer: 56
Q222022 · 26 Jun 2022 · Shift 1· Numerical answer
There are ten boys $B_{1}, B_{2}, ......., B_{10}$ and five girls $G_{1}, G_{2}, ......., G_{5}$ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both $B_{1}$ and $B_{2}$ together should not be the members of a group, is ____.
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Answer: 1120
Q252022 · 26 Jun 2022 · Shift 2· Numerical answer
The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.
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Answer: 150
Q282022 · 26 Jun 2022 · Shift 2· Numerical answer
If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.
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Answer: 33
Q212022 · 25 Jun 2022 · Shift 1· Numerical answer
The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is _____________.
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Answer: 63
Q82022 · 25 Jun 2022 · Shift 2
Water is being filled at the rate of $1 cm^{3} / sec$ in a right circular conical vessel (vertex downwards) of height $35 cm$ and diameter $14 cm$ . When the height of the water level is $10 cm$ , the rate (in $cm^{2} / sec$ ) at which the wet conical surface area of the vessel increases is
1. A. $5$
2. B. $\frac{21}{5}$
3. C. $\frac{26}{5}$
4. D. $\frac{26}{10}$
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Answer: C
Q272022 · 25 Jun 2022 · Shift 2· Numerical answer
The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.
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Answer: 243
Q232022 · 24 Jun 2022 · Shift 2· Numerical answer
The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____________.
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Answer: 576