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NBHM Ph.D. 2016
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Nbhm ph.d 2016

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Nbhm ph.d 2016

  • 1. NBHM Ph.D. 2016 ( )( ) ( )( ) . / ( ) ( ) ( ) ( ) * + ( ) ( ) , - ( ) , - ( ) ( ) ( ) ̂ ( ) ( ) ̂ ( ) ̂ ( ) ( ) 2 ( ) ( ) ( ) * + ( ) ( )
  • 2. ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 1 * + | ( ) | , - , , ∫ ( ) ( ) * ( )+ ( ) ( ) ( ) ∑ ( ) ( ) ( ) | | ∫ ( ) ∫ . / ( ) ( ) ( ) ( ) ( ) ( ) , - ( ) { ( ) ( ) , - ( ) ( ) ∫ * + ( ) ( )
  • 3. ( ) ∫ ( ) ∫ ( ) ( ) ( ) ( ) ( ) * + * + ( ) ( ) ( ) ( ) ( ) | | | ( )| | | * + ( ) ( ) { , - , - , - { | ∫ | ( )| } ( ) ( ) , - ( ) ( ) , - ( ) { , - ( ) * + ( ) * +
  • 4. ( ) * + ( ) ( ) ( ) , - ( ) ⋃ ( ) ( ) ( ) ( ) ( ) * ( )| + ( ) ( ) ( ) {( ) | } *( )+ ( ) *( ) | + *( ) | + ( ) *( ) | + *( ) | + ( ) ⋃*( ) | + ( ) ( ) ( ) ( ) ( ) ( ) * ( )| ( ) + ( ) , - ( ) { , -| ∫ ( ) ( ) , -} (- -) ( ) ( )
  • 5. ( ) *( ) | ( )+ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) *( ) | + ( ) *( ) | + ( ) *( ) | + ( ) *( ) | + Section 4: Calculus and Differential Equations ∫ 0 1 , - , - ∬ ( ) ∫ ∫ ( ) ( ) ( ) ∫ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 1 ( ) ( )
  • 6. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Section 5: Miscellaneous ( ) . / ∑ . / ( ) ( ) ( ) ( ) { ∫ ( ) Which of the following numbers are rational? ( ) ( ) ( )