# State which of th

(i) Given: 35 {x | x has exactly four positive factors}

To check: 35 belongs to given set or not

The possible positive factors of 35 are 1, 5, 7, 35

Since, 35 has exactly four positive factors

The given statement is true.

(ii) Given: 128 {y | the sum of all the positive factors of y is 2y}

To check: 128 belongs to given set or not

The possible positive factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128

The sum of them

= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128

= 255

2y = 2 * 128 = 256

Since, the sum of all the positive factors of y is not equal to 2y

The given statement is false.

(iii) Given: 3 {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}

To check: 128 belongs to given set or not

x4 – 5x3 + 2x2 – 112x + 6 = 0

On putting x = 3 in LHS:

(3)4 – 5(3)3 + 2(3)2 – 112(3) + 6

= 81 – 135 + 18 – 336 + 6

= –366

So, 3 does not belong to given set

The given statement is true.

(iv) Given: 496 {y | the sum of all the positive factors of y is 2y}

To check: 128 belongs to given set or not

The possible positive factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496

The sum of them

= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 + 496

= 996

2y = 2 * 496 = 992

Since, the sum of all the positive factors of y is equal to 2y

496 belongs to given set

The given statement is false.

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