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The number of even proper divisors of 10...

The number of even proper divisors of `1008`

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`because1008=2^(4)xx3^(2)xx7^(1)`
`therefore` Required number of evenn proper divisors
`=`Total number of selections of atleast one 2 and any number of 3's or 7's.
`=4xx(2+1)xx(1+1)-1=23`.
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
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  6. The letters of the word COCHIN are permuted and all the permutation...

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  7. The set S""=""{1,""2,""3,"" ,""12) is to be partitioned into three...

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  8. Consider all possible permutations of the letters of the word ENDEANOE...

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  9. How many different words can be formed by jumbling the letters in the ...

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  10. In a shop, there are five types of ice-creams available. A child buys ...

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  11. The number of seven digit integers, with sum of the digits equal to 10...

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  14. Statement-1: The number of ways of distributing 10 identical balls in ...

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  15. There are 10 points in a plane, out of these 6 are collinear. The numb...

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  16. The total number of ways in which 5 balls of differert colours can be ...

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  17. Let n denote the number of all n-digit positive integers formed by the...

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  18. Let a(n) denote the number of all n-digit numbers formed by the digits...

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  19. Assuming the balls to be identical except for difference in colours, t...

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  20. Let Tn be the number of all possible triangles formed by joining ve...

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  21. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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