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If  X=\left \{ 4^{n}-3n-1\; :\; n\; \epsilon \; N \right \}\; and\;\; Y= \; \left \{9(n-1):n\; \epsilon \; N \right \},where\; N is the set of natural numbers,then

X\cup Y  is equal to :

Option: 1

X\;

 

Option: 2

Y\;

 

 

Option: 3

N\;

 

 

Option: 4

Y-X

 

Let us 1st simplify set X

X=(1+3)^n-3n-1

X=^nC_0+\;^nC_1\cdot3+\;^nC_2\cdot3^2\ldots \ldots+ \;^nC_n\cdot 3^n-3n-1X=1+\;3n+\;^nC_2\cdot3^2\ldots \ldots+ \; 3^n-3n-1

X=3^2\cdot\left (^nC_2+\;^nC_3\cdot3\ldots \ldots+ \; 3^{n-2} \right )

X=9\cdot\left (^nC_2+\;^nC_3\cdot3\ldots \ldots+ \; 3^{n-2} \right )

For n=1; X=0

For n=2; X=9

For n=3; X=54

:

:

And

Y=9\left ( n-1 \right )

For n=1; Y=0

For n=2; Y=9

For n=3; Y=18

:

For n=7; Y=54

:

Hence we can say

X\cup Y=Y

View Full Answer(1)
Posted by

Rishi

Calculate the acceleration of block m_1 of the following diagram. Assume all surfaces are frictionless . Here m1 = 100kg and m2 = 50kg

 

Option: 1

0.33m/s2


Option: 2

0.66m/s2


Option: 3

1m/s2


Option: 4

1.32m/s2


0.66m/s2

View Full Answer(5)
Posted by

Guru G

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Mercury in water changes to soluble

Option: 1

Dimethyl mercury


Option: 2

diethyl mercury


Option: 3

Hg_2Cl_2


Option: 4

None of these


2

View Full Answer(2)
Posted by

Karumudi.santhoshreddy

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