1
Numerical

JEE Main 2021 (Online) 1st September Evening Shift

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is ___________.
Your Input ________

Answer

Correct Answer is 77

Explanation

First find all possible words and then subtract words from each case that have both R together.

FARMER (6)

A, E, F, M, R, R

A
E
F A E
F A M
F A R E
F A R M E R


2
Numerical

JEE Main 2021 (Online) 31st August Morning Shift

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________.
Your Input ________

Answer

Correct Answer is 576

Explanation

Total possible words = 6! = 720

When 4 consonants are together (V, W, L, S)
such cases = 3! ⋅ 4! = 144

All consonants should not be together

= Total $$-$$ All consonants together,

= 6! $$-$$ 3! 4! = 576
3
Numerical

JEE Main 2021 (Online) 27th August Morning Shift

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is ____________.
Your Input ________

Answer

Correct Answer is 100

Explanation

5 a b b a 5


For divisible by 55 it shall be divisible by 11 and 5 both, for divisibility by 5 unit digit shall be 0 or 5 but as the number is six digit palindrome unit digit is 5.

A number is divisible by 11 if the difference between sum of the digits in the odd places and the sum of the digits in the even places is a multiple of 11 or zero.

Sum of the digits in the even place = a + b + 5

Sum of the digits in the odd places = a + b + 5

Difference between the two sums = (a + b + 5 ) - (a + b + 5) = 0

0 is divisible by 11.

Hence, 5abba5 is divisible by 11.

So, required number = 10 $$\times$$ 10 = 100
4
Numerical

JEE Main 2021 (Online) 26th August Morning Shift

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______________.
Your Input ________

Answer

Correct Answer is 52

Explanation

(i) When '0' is at unit place



Number of numbers = 20

(ii) When 4 or 6 are at unit place



Number of numbers = 32

Total three digit even number = 20 + 32 = 52

Questions Asked from Permutations and Combinations

On those following papers in Numerical
Number in Brackets after Paper Name Indicates No of Questions
JEE Main 2021 (Online) 1st September Evening Shift (1)
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JEE Main 2021 (Online) 31st August Morning Shift (1)
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JEE Main 2021 (Online) 27th August Morning Shift (1)
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JEE Main 2021 (Online) 26th August Morning Shift (2)
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JEE Main 2021 (Online) 27th July Evening Shift (1)
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JEE Main 2021 (Online) 25th July Morning Shift (1)
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JEE Main 2021 (Online) 22th July Evening Shift (1)
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JEE Main 2021 (Online) 20th July Morning Shift (1)
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JEE Main 2021 (Online) 18th March Evening Shift (1)
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JEE Main 2021 (Online) 18th March Morning Shift (2)
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JEE Main 2021 (Online) 25th February Morning Shift (1)
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JEE Main 2021 (Online) 24th February Evening Shift (2)
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JEE Main 2020 (Online) 6th September Evening Slot (1)
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JEE Main 2020 (Online) 5th September Morning Slot (2)
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JEE Main 2020 (Online) 4th September Evening Slot (1)
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JEE Main 2020 (Online) 3rd September Evening Slot (1)
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JEE Main 2020 (Online) 2nd September Morning Slot (1)
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JEE Main 2020 (Online) 8th January Evening Slot (1)
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JEE Main 2020 (Online) 8th January Morning Slot (1)
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