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Let 'a' be an integer. If there are 10 i...

Let `'a'` be an integer. If there are `10` inegers satisfying the `((x-a)^(2)(x-2a))/((x-3a)(x-4a))le0` then

A

`a` is prime number

B

`e^(a) lt pi^(a)`

C

`a^(2) - 2` is prime number

D

number of possible values of `a` is `2`

Text Solution

Verified by Experts

The correct Answer is:
C, D
If `a gt 0`

`x in [(2a, 3a) cup (4a, a^(2))]`
`:. (a^(2) - 4a) + (3a - 2a) = 10`
`a^(2) - 3a - 10 = 0`
`(a - 5) (a + 2) = 0 rArr a = 5`
if `a lt 0`

`x epsilon (4a, 3a) cap [2a, a^(2)]`
`:. (a^(2) - 2a + 1) + (3a - 4a - 1) = 10`
`rArr a^(2) - 3a - 10 = 0`
`(a - 5) (a + 2) = 0 rArr a = -2`
`:. a in {-2, 5}`
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