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Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

31.

y = xⁿ (a cos (log x) + b sin (log x)). જો y એ x²y₂ + (1 - 2n) xy, + ay = 0 નું સમાધાન કરે તો A = .......

n
1 - n²
1 + n²
$bold 1 bold plus bold 1 over bold n$

32. જો f(x) = $bold x over bold 2 bold minus bold 2$ તો અંતરાલ $bold left square bracket bold 0 bold comma bold space bold pi bold right square bracket$ પર

tan (f(x)) અને f^-1(x) બંને સતત થશે.
tan (f(x)) અને f^-1(x) બંને અસતત થશે.
tan (f(x)) અને $fraction numerator bold 1 over denominator bold f bold left parenthesis bold c bold right parenthesis end fraction$ બંને સતત થશે.
tan (f(x)) અને $fraction numerator bold 1 over denominator bold f bold left parenthesis bold c bold right parenthesis end fraction$ બંને અસતત થશે.

33. જો x = f(t), y = g(t), y = g(t) તો $fraction numerator bold d to the power of bold 2 bold y over denominator bold dx to the power of bold 2 end fraction$ = ........

$bold space fraction numerator bold f bold apostrophe bold g bold " bold space bold minus bold space bold g bold apostrophe bold f bold " over denominator bold left parenthesis bold f bold apostrophe bold right parenthesis to the power of bold 3 end fraction bold space$
$fraction numerator bold f bold " over denominator bold g bold " end fraction bold space$
$fraction numerator begin display style bold f bold apostrophe bold g bold " bold space bold minus bold space bold g bold apostrophe bold f bold " end style over denominator begin display style bold left parenthesis bold f bold apostrophe bold right parenthesis to the power of bold 2 end style end fraction$
$fraction numerator bold g bold " over denominator bold f bold " end fraction$

bold space fraction numerator bold f bold apostrophe bold g bold " bold space bold minus bold space bold g bold apostrophe bold f bold " over denominator bold left parenthesis bold f bold apostrophe bold right parenthesis to the power of bold 3 end fraction bold space

Tips: -

bold dy over bold dx bold space bold equals bold space fraction numerator bold g bold apostrophe bold left parenthesis bold t bold right parenthesis over denominator bold f bold apostrophe bold left parenthesis bold t bold right parenthesis end fraction bold space fraction numerator bold d to the power of bold 2 bold y over denominator bold dx to the power of bold 2 end fraction bold space bold equals bold space bold d over bold dx bold space open parentheses bold dy over bold dx close parentheses bold equals bold space bold d over bold dt bold space open parentheses bold dy over bold dx close parentheses bold space bold. bold space bold dt over bold dx bold space bold equals bold space fraction numerator bold g bold " bold left parenthesis bold t bold right parenthesis bold f bold apostrophe bold left parenthesis bold t bold right parenthesis bold space bold minus bold space bold g bold apostrophe bold left parenthesis bold t bold right parenthesis bold space bold f bold " bold left parenthesis bold t bold right parenthesis over denominator bold left square bracket bold f bold apostrophe bold left parenthesis bold t bold right parenthesis bold right square bracket to the power of bold 2 end fraction bold space fraction numerator bold 1 over denominator bold f bold apostrophe bold left parenthesis bold t bold right parenthesis end fraction bold space bold equals bold space fraction numerator bold f bold apostrophe bold g bold " bold space bold minus bold space bold g bold apostrophe bold t bold " over denominator bold left parenthesis bold f bold apostrophe bold right parenthesis to the power of bold 3 end fraction

34.

f(x) = $fraction numerator bold 1 over denominator bold 1 bold minus bold x end fraction$ g(x) = f³ⁿ(x) જ્યાં fⁿ(x) = fofof ..... of (n વખત). વિધેય g(x) કેટલા બિંદુએ અસતત થશે ?

2ન
3n
2
2n + 1

35.

bold જ ો bold space bold space bold f bold left parenthesis bold x bold right parenthesis bold space open curly brackets table row cell bold left parenthesis bold 1 bold plus bold vertical line bold sin bold space bold x bold vertical line to the power of fraction numerator bold a over denominator bold vertical line bold sin bold space bold x bold vertical line end fraction end exponent end cell cell fraction numerator bold minus bold pi over denominator bold 6 end fraction bold less than bold x bold less than bold 0 end cell row bold b cell bold x bold space bold equals bold space bold 0 bold space end cell row cell bold e to the power of bold tan bold 2 bold x bold µ bold tan bold 3 bold x end exponent end cell cell bold 0 bold space bold less than bold space bold x bold space bold less than bold space bold pi over bold 6 end cell end table close bold space bold એ bold space open parentheses fraction numerator bold minus bold pi over denominator bold 6 end fraction bold comma bold pi over bold 6 close parentheses bold space bold પર bold space bold સતત bold space bold હ ો ય bold space bold ત ો bold comma bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space

$bold a bold space bold equals bold space bold 2 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 2 bold space bold space$
$bold space bold a bold space bold equals bold space bold 1 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 1 over bold 3 end exponent bold space$
$bold a bold space bold equals bold space bold e to the power of bold 1 over bold 2 end exponent bold comma bold space bold b bold space bold equals bold e bold space to the power of bold 2 over bold 3 end exponent bold space bold space$
$bold space bold a bold space bold equals bold space bold 2 over bold 3 bold comma bold space bold b bold space bold equals bold space bold e to the power of bold 2 over bold 3 end exponent$

36.

f અને g વિકલનીય વિધેય છે. g'(a) = 2. g(a) = b તથા fog = I તો f'(b) = ........

1
2
$bold 2 over bold 3$
$bold 1 over bold 2$

37.

bold જ ો bold space bold y bold space bold equals bold space fraction numerator bold ax to the power of bold 2 over denominator bold left parenthesis bold x bold space bold minus bold space bold a bold right parenthesis bold space bold left parenthesis bold x bold space bold minus bold space bold b bold right parenthesis bold space bold left parenthesis bold x bold space bold minus bold space bold c bold right parenthesis bold space end fraction bold space bold plus bold space fraction numerator bold bx over denominator bold left parenthesis bold x bold space bold minus bold space bold b bold 0 bold space bold left parenthesis bold x bold space bold minus bold space bold c bold right parenthesis bold space end fraction bold space bold plus bold space fraction numerator bold c over denominator bold x bold space bold minus bold space bold c end fraction bold space bold plus bold space bold 1 bold space bold ત ો bold space bold y over bold y bold space bold equals bold space bold. bold. bold. bold. bold.

$Error converting from MathML to accessible text.$
$bold 1 over bold 2 open parentheses fraction numerator bold a over denominator bold a bold minus bold x end fraction bold plus fraction numerator bold b over denominator bold b bold minus bold x end fraction bold plus fraction numerator bold c over denominator bold c bold minus bold x end fraction close parentheses bold space$
$Error converting from MathML to accessible text.$
$bold 1 over bold x$

38.

$bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold tan bold left square bracket bold e to the power of bold 2 bold right square bracket bold space bold minus bold space bold tan bold left square bracket bold minus bold e bold right square bracket bold x to the power of bold 3 over denominator bold sin to the power of bold 3 bold x end fraction bold comma bold space$ x # 0. જો f એ x = 0 આગળ સતત હોય તો f(0) = .....

39. f(x) = $fraction numerator bold 1 over denominator bold log bold space bold vertical line bold x bold vertical line end fraction$ એ કેટલાં બિંદુઓએ અસતત થશે ?

40.

જો વિધેય f એ R પર સતત છે તથા $bold f open parentheses fraction numerator bold 1 over denominator bold 4 bold n end fraction close parentheses bold space bold equals bold space bold left parenthesis bold sin bold space bold e to the power of bold n bold right parenthesis bold space bold e to the power of bold minus bold n to the power of bold 2 end exponent bold space bold plus bold space fraction numerator bold n to the power of bold 2 over denominator bold n to the power of bold 2 bold space bold plus bold space bold 1 end fraction bold space bold ત ો bold space bold f bold left parenthesis bold 0 bold right parenthesis bold space bold space$ ની કિંમત .....

0
-1
1
$bold 1 over bold 2$

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Gujarati JEE Mathematics : લક્ષ-સાતત્ય અને વિકલન

Multiple Choice Questions

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