Chemistry-
General
Easy

Question

The bond between carbon atom (A) and carbon atom (B) in compound involves the hybridization

  1. s p to the power of 2 end exponent and s p to the power of 2 end exponent    
  2. s p to the power of 3 end exponent and sp    
  3. sp and s p to the power of 2 end exponent    
  4. sp and sp    

The correct answer is: sp and s p to the power of 2 end exponent

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There is a rectangular sheet of dimension left parenthesis 2 m minus 1 right parenthesis ×left parenthesis 2 n minus 1 right parenthesis, (where m greater than 0 comma n greater than 0 right parenthesis. It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length

Along horizontal side one unit can be taken in (2m–1) ways and 3 unit side can be taken in 2 m minus 3 ways.
\ The number of ways of selecting a side horizontally is
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Similarly the number of ways along vertical side is left parenthesis 2 n minus 1 plus 2 n minus 3 plus.... plus 5 plus 3 plus 1 right parenthesis.

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Along horizontal side one unit can be taken in (2m–1) ways and 3 unit side can be taken in 2 m minus 3 ways.
\ The number of ways of selecting a side horizontally is
left parenthesis 2 m minus 1 plus 2 m minus 3 plus 2 m minus 5 plus.... plus 3 plus 1 right parenthesis
Similarly the number of ways along vertical side is left parenthesis 2 n minus 1 plus 2 n minus 3 plus.... plus 5 plus 3 plus 1 right parenthesis.

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equals left square bracket 1 plus 3 plus 5 plus..... plus left parenthesis 2 m minus 1 right parenthesis right square bracket cross times left square bracket 1 plus 3 plus 5 plus.... plus left parenthesis 2 n minus 1 right parenthesis right square bracket
equals fraction numerator m left parenthesis 1 plus 2 m minus 1 right parenthesis over denominator 2 end fraction cross times fraction numerator n left parenthesis 1 plus 2 n minus 1 right parenthesis over denominator 2 end fraction equals m to the power of 2 end exponent n to the power of 2 end exponent.
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