Q. 44.3( 22 Votes )

State which of th

Answer :

(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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