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For a real number x, [x] denotes greates...

For a real number `x, [x]` denotes greatest integer function, then find value of `[1/2]+[1/2+1/100]+[1/2+2/100]+....+[1/2+99/100]`

A

49

B

50

C

48

D

51

Text Solution

Verified by Experts

The correct Answer is:
B
We know that for any ` x in R and n in N`
`[x]+[x+(1)/(n)]+[x+(2)/(n)]+…..+[x+(n-1)/(n)]=[nx]`
Here, `x=(1)/(2) and n=100.`
` :. [(1)/(2)]+[(1)/(2)+(1)/(100)]+[(1)/(2)+(2)/(100)]+….+[(1)/(2)+(99)/(100)]=[100xx(1)/(2)]=50`
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OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Chapter Test
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  9. If N denotes the set of all positive integers and if f : N -> N is def...

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  13. If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

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  15. The domain of definition of the real function f(x)=sqrt(log(12)x^(2)) ...

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  18. The period of the function sin""((pix)/(2))+cos((pix)/(2)), is

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  20. If x in R , then f(x)=cos^(-1)((1-x^(2))/(1+x^(2))) is equal to

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  21. The equivalent definition of the function f(x)=lim(n to oo)(x^(n)-x^(-...

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