Important Questions of લક્ષ-સાતત્ય અને વિકલન for JEE Mathematics | Zigya

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Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

101. bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold 1 bold space bold minus bold space bold cos bold space bold x bold space bold હ ો ય bold space bold ત ો bold space bold lim with bold x bold rightwards arrow bold infinity below bold space open curly brackets bold e to the power of square root of bold f open parentheses bold 1 over bold x close parentheses square root of bold f open parentheses bold 1 over bold x close parentheses end root square root of bold f open parentheses bold 1 over bold x close parentheses end root bold. bold. bold. end root end exponent close curly brackets to the power of blank to the power of fraction numerator bold 1 over denominator bold cos to the power of bold minus bold 1 end exponent open curly brackets bold 1 bold minus bold f open parentheses bold 1 over bold x to the power of bold 2 close parentheses close curly brackets end fraction end exponent end exponent bold equals bold space bold. bold. bold. bold.
  • square root of bold e
  • square root of square root of bold e end root
  • e

  • 1


102. bold જ ો bold space square root of bold r bold space bold equals bold space bold ae bold space to the power of bold theta bold space bold cot bold space bold alpha end exponent bold space bold ત ો bold space fraction numerator bold d to the power of bold 2 bold r over denominator bold dθ to the power of bold 2 end fraction bold space bold minus bold space bold 4 bold space bold r bold space bold cot to the power of bold 2 bold space bold alpha bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space bold left parenthesis bold a bold comma bold space bold alpha bold space bold element of bold space bold R bold right parenthesis
  • 0

  • 1

  • bold 1 over bold r
  • r


103.

જો f(x + y + z) = f(x) f(y) f(z), ∀x, y ∈ R, f(4) = 4, f(0) = 2 તો f'(4), f(4), f(0) એ ....

  • આપેલ તમામ સત્ય છે.

  • સમાંતર શ્રેણીમાં છે. 

  • સમગુણોત્તર શ્રેણીમાં છે. 

  • સ્વરિત શ્રેણીમાં છે. 


104. bold જ ો bold space bold y bold space bold equals bold space bold sin bold space bold x bold times bold space bold sin bold space bold 2 bold x bold space bold times bold space bold sin bold space bold 3 bold x bold space bold. bold. bold. bold. bold space bold comma bold space bold sin bold space bold nx bold comma bold space bold ત ો bold space bold dy over bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space
  • bold sum from bold k bold equals bold 1 to bold n of bold space bold k bold space bold cot bold space bold kx
  • bold sum from bold k bold equals bold 1 to bold n of bold space bold k bold space bold tan bold space bold kx
  • bold y bold space bold sum from bold k bold equals bold 1 to bold n of bold space bold k bold space bold cot bold space bold kx bold space bold right square bracket
  • bold y bold space bold sum from bold k bold equals bold 1 to bold n of bold space bold k bold space bold tan bold space bold kx bold space

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105. bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold vertical line bold x bold vertical line over denominator bold vertical line bold x bold vertical line bold space bold plus bold space bold 2016 end fraction એ કેટલા બિંદુએ વિકલનીય નથી ? 
  • 0

  • 1

  • 2

  • અનંત


106.
ધારો કે, bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell bold xnsin bold x over bold 1 end cell cell bold x bold space bold # bold space bold 0 end cell row bold 0 cell bold x bold space bold equals bold 0 end cell end table closeજો f(x) એ x = 0 આગળ સતત હોય, પરંતુ વિકલનીય ન હોય તો 
  • n = 0

  • n∈(0,1]

  • n∈[1, ∞)

  • n∈(-∞, 0)


107.

જો xy = e - ey તો open parentheses fraction numerator bold d to the power of bold 2 bold y over denominator bold dx to the power of bold 2 end fraction close parentheses subscript bold x bold equals bold 0 end subscript bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.

  • e2

  • bold 1 over bold e
  • bold 1 over bold e to the power of bold 3
  • bold 1 over bold e to the power of bold 2

108. bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold sin to the power of bold 2 bold space bold x over denominator bold 1 bold plus bold cot bold space bold x bold space end fraction bold space bold plus bold space fraction numerator bold cos to the power of bold 2 bold space bold x over denominator bold 1 bold plus bold tan bold space bold x bold space end fraction bold space bold ત ો bold space bold f bold apostrophe bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space
  • sin 2x 

  • -sin 2x

  • cos 2x

  • -cos 2x 


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109. bold જ ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open parentheses bold sum from bold k bold equals bold 0 to bold n of bold a to the power of bold k bold space bold vertical line bold x bold minus bold 1 bold vertical line to the power of bold k close parentheses bold space bold જ ્ ય ાં bold space bold a subscript bold k bold greater than bold 0 bold comma bold space bold ત ો bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold એ bold space
  • R પર વિકલનીય છે.

  • R પર સતત છે. પરંતુ x = 1 આગળ વિકલનીય નથી.

  • x = 1 આગળ સતત નથી. 

  • R પર સતત છે, પરંતુ x = 0 આગળ વિકલનીય નથી. 


110. Error converting from MathML to accessible text.
  • 0

  • 1

  • fraction numerator square root of bold 3 over denominator bold 5 end fraction bold space
  • bold 3 over bold 5

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