Maths-
General
Easy

Question

Find the value of a+b in the given figure

  1. 90 to the power of ring operator end exponent    
  2. 75 to the power of ring operator end exponent    
  3. 180 to the power of ring operator end exponent    
  4. 360 to the power of ring operator end exponent    

The correct answer is: 180 to the power of ring operator end exponent

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In the figure, the potentiometer wire AB of length L and resistance 9r is joined to the cell D of emf e and internal resistance r. The cell C's emf is fraction numerator epsilon over denominator 2 end fraction and is internal resistance is 2r. The galvanometer G will show no deflection when the length AJ is

In the figure, the potentiometer wire AB of length L and resistance 9r is joined to the cell D of emf e and internal resistance r. The cell C's emf is fraction numerator epsilon over denominator 2 end fraction and is internal resistance is 2r. The galvanometer G will show no deflection when the length AJ is

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Here R =blank fraction numerator V to the power of 2 end exponent over denominator P end fraction Total power supplied
equals fraction numerator V to the power of 2 end exponent over denominator fraction numerator 3 over denominator 2 R end fraction end fraction equals open parentheses fraction numerator 2 over denominator 3 end fraction close parentheses open parentheses fraction numerator V to the power of 2 end exponent over denominator R end fraction close parentheses equals fraction numerator 2 over denominator 3 end fraction cross times 60 equals 40 W

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Here R =blank fraction numerator V to the power of 2 end exponent over denominator P end fraction Total power supplied
equals fraction numerator V to the power of 2 end exponent over denominator fraction numerator 3 over denominator 2 R end fraction end fraction equals open parentheses fraction numerator 2 over denominator 3 end fraction close parentheses open parentheses fraction numerator V to the power of 2 end exponent over denominator R end fraction close parentheses equals fraction numerator 2 over denominator 3 end fraction cross times 60 equals 40 W
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For natural numbers m,n if left parenthesis 1 minus y right parenthesis to the power of text m  end text end exponent left parenthesis 1 plus y right parenthesis to the power of n equals 1 plus a comma y plus a squared y squared plus horizontal ellipsis horizontal ellipsis and a subscript 1 end subscript equals a subscript 2 end subscript equals 10 then (m,n) is

left parenthesis 1 minus y right parenthesis to the power of m end exponent left parenthesis 1 plus y right parenthesis to the power of n end exponent equals 1 plus a y plus a subscript 2 end subscript y to the power of 2 end exponent plus horizontal ellipsis.
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rightwards double arrow a subscript 1 end subscript equals n subscript c subscript 1 end subscript end subscript minus m subscript c subscript 1 end subscript end subscript semicolon a subscript 2 end subscript equals m subscript c subscript 2 end subscript end subscript minus m subscript c subscript 1 end subscript end subscript n subscript c subscript 1 end subscript end subscript plus n subscript c subscript 2 end subscript end subscript
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left parenthesis 1 minus y right parenthesis to the power of m end exponent left parenthesis 1 plus y right parenthesis to the power of n end exponent equals 1 plus a y plus a subscript 2 end subscript y to the power of 2 end exponent plus horizontal ellipsis.
rightwards double arrow open parentheses 1 minus m subscript c subscript 1 end subscript end subscript y plus m subscript c subscript 2 end subscript end subscript y to the power of 2 end exponent minus horizontal ellipsis horizontal ellipsis. close parentheses open parentheses 1 plus n subscript c subscript 1 end subscript end subscript y plus n subscript c subscript 2 end subscript end subscript y to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis. close parentheses equals 1 plus a comma y plus a subscript 2 end subscript y to the power of 2 end exponent plus horizontal ellipsis horizontal ellipsis..
rightwards double arrow a subscript 1 end subscript equals n subscript c subscript 1 end subscript end subscript minus m subscript c subscript 1 end subscript end subscript semicolon a subscript 2 end subscript equals m subscript c subscript 2 end subscript end subscript minus m subscript c subscript 1 end subscript end subscript n subscript c subscript 1 end subscript end subscript plus n subscript c subscript 2 end subscript end subscript
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