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If X = {8^(n) - 7 n - 1 | n in N} an...

If `X = {8^(n) - 7 n - 1 | n in N}` and `y = {49n - 49 | n in N}`. Then,

A

`X subY`

B

`Y sub X`

C

`X=Y`

D

none of these

Text Solution

Verified by Experts

we have ,
`8^(n)- 7n-1=(1+7)^(n)-7n-1`
`=(""^(n)C_(0)+""^(n)C_(1)xx7+""^(n)C_(2)xx7^(2)+. . .+""^(n)C_(n)xx7^(n))-(7n+1)`
`=7^(2)(""^(n)C_(2)+""^(n)C_(3)xx7+. . . +""^(n)C_(n)xx7^(n-2))`
`therefore ` X contains some multiples of 49 .
Clearly , Y contains all multiples of 49 including 0.
`therefore X sub Y.`
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OBJECTIVE RD SHARMA ENGLISH-SETS-Chapter Test
  1. If X = {8^(n) - 7 n - 1 | n in N} and y = {49n - 49 | n in N}. ...

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  2. Which of the following cannot be the number of elements in the power s...

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  3. If A={1,2,3,4}, then the number of subsets of set A containing element...

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  4. If A={1,2,3,4}, then the number of substets of A that contain the elem...

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  5. If n(u)=100,n(A)=50,n(B)=20 and n(A nnB)=10, then n{(AuuB)^©}

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  6. Let Z denoted the set of integers, then {x inZ:|x-3|lt4}nn{x inZ:|x-...

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  7. If A(n) is the set of first n prime numbers, then underset(n=2)overset...

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  8. If A(n) is the set of first n prime numbers, then underset(n=2)overset...

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  9. Let A(1),A(2),A(3),…, A(100) be 100 seta and such that n(A(1))=i+1and ...

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  10. If A and B are two sets such that n(A)=7, n(B)=6and (A nnB)ne phi Then...

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  11. If A and B are two sets such that n(A)7, n(B),=6 and n(AnnB) ne phi Th...

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  12. If A(1),A(2),..., A(100) are sets such that n(A(i))=i+2,A(1)subA(2)sub...

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  13. If A,B and C are three non=empty sets such that A and B are disjoint a...

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  14. If A={n:(n^(3)+5n^(2)+2)/(n)"is an integer"},then the number of elemen...

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  15. If {p in N: "p is a prime" and p=(7n^(2)+3n+3)/(n)"for some n" in N}' ...

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  16. A, B and C are three non-empty sets. If A sub B and B subC then which ...

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  17. If A=[1,2,3,4,5,6] then how many subsets of A contain the element 2, 3...

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  18. If S is the set of squares and R is the set of rectangles, then (SuuR)...

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  19. If P is the set of all parallelogrma, and T is the set of all trapeziu...

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  20. If n (AnnB)=10, n (BnnC) =20 and n(AnnC)=30, then the greatest possibl...

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  21. If n (annB)=5, n(AnnC)=7 and n(AnnBnnC)=3, then the minimum possible v...

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