KVPY 2020-21 SA Exam Previous Papers

Question : 61 of 80

Marks: +1, -0

PART-II : MATHEMATICS

Let A denote the set of all 4-digit natural numbers with no digit being 0. Let B ⊂ A consist of all numbers x such that no permutation of the digits of x gives a number that is divisible by 4. Then the probability of drawing a number from B with all even digits is

$625/1641$
$16/641$
$16/1641$
$1000/1641$

Validate

Solution:

For number not divisible by 4 and not having zero can be formed as
Number of ways to form
All digits odd

=5^{4}

3 digits odd

+

even

(4

or 8

)=5^{3} \.2 \.4

2 digits odd

+2

even

(4

or 8

)=0

1 digit odd

+3

even

=0

All even

=2^{4}

(Only 2 or 6 can be used)
Probability

={2^{4}}/{5^{4}+5^{3} .8+2^{4}}={16}/{1641}

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