The number of ways in which n prizes can be distributed among n-Turito

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General

Easy

Maths-

The number of ways in which n prizes can be distributed among n students when each student is eligible to get any number of prizes is-

Maths-General

nⁿ
n!
nⁿ - n
None of these

Answer:The correct answer is: nⁿ

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A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

W equals increment U equals U subscript f end subscript minus U subscript i end subscript equals U subscript infinity end subscript minus U subscript P end subscript

equals negative U subscript P end subscript equals negative m V subscript P end subscript

equals negative V subscript P end subscript open parentheses a s blank m equals 1 close parentheses

Potential at point

P

will be obtained by in integration as given below. Let

d M

be the mass of small rings as shown

d M equals fraction numerator M over denominator pi left parenthesis 4 R right parenthesis to the power of 2 end exponent minus pi left parenthesis 3 R right parenthesis to the power of 2 end exponent end fraction open parentheses 2 pi r close parentheses d r

equals fraction numerator 2 M r d r over denominator 7 R to the power of 2 end exponent end fraction

d V subscript P end subscript equals negative fraction numerator G. d M over denominator square root of 16 R to the power of 2 end exponent plus r to the power of 2 end exponent end root end fraction

equals negative fraction numerator 2 G M over denominator 7 R to the power of 2 end exponent end fraction not stretchy integral subscript 3 R end subscript superscript 4 R end superscript fraction numerator r over denominator square root of 16 R to the power of 2 end exponent plus r to the power of 2 end exponent end root end fraction bullet d r

equals negative fraction numerator 2 G M over denominator 7 R end fraction open parentheses 4 square root of 2 minus 5 close parentheses

therefore W equals plus fraction numerator 2 G M over denominator 7 R end fraction left parenthesis 4 square root of 2 minus 5 right parenthesis

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physics-General

W equals increment U equals U subscript f end subscript minus U subscript i end subscript equals U subscript infinity end subscript minus U subscript P end subscript

equals negative U subscript P end subscript equals negative m V subscript P end subscript

equals negative V subscript P end subscript open parentheses a s blank m equals 1 close parentheses

Potential at point

P

will be obtained by in integration as given below. Let

d M

be the mass of small rings as shown

d M equals fraction numerator M over denominator pi left parenthesis 4 R right parenthesis to the power of 2 end exponent minus pi left parenthesis 3 R right parenthesis to the power of 2 end exponent end fraction open parentheses 2 pi r close parentheses d r

equals fraction numerator 2 M r d r over denominator 7 R to the power of 2 end exponent end fraction

d V subscript P end subscript equals negative fraction numerator G. d M over denominator square root of 16 R to the power of 2 end exponent plus r to the power of 2 end exponent end root end fraction

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equals negative fraction numerator 2 G M over denominator 7 R end fraction open parentheses 4 square root of 2 minus 5 close parentheses

therefore W equals plus fraction numerator 2 G M over denominator 7 R end fraction left parenthesis 4 square root of 2 minus 5 right parenthesis

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