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Gujarati JEE Mathematics : ગણ, સંબંધ અને વિધેય

Multiple Choice Questions

41.

bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold x to the power of bold 2 bold space bold plus bold space bold x bold space bold plus bold space bold 2 over denominator bold x to the power of bold 2 bold space bold plus bold space bold x bold space bold plus bold space bold 1 end fraction bold comma bold space bold x bold space bold element of bold space bold R

નો વિસ્તાર ....... હોય.

(1, ∞)
$left parenthesis 1 comma 7 over 3 right square bracket$
$left parenthesis 1 comma 7 over 5 right square bracket$
$left parenthesis 1 comma space 1 over 7 right parenthesis$

42. $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold sin to the power of bold minus bold 1 end exponent bold left parenthesis bold x bold minus bold 3 bold right parenthesis over denominator square root of bold 9 bold minus bold x to the power of bold 2 end root end fraction$ નો મહત્તમ પ્રદેશ ....... હોય.

[3, 2]
[2, 1]
[2, 3)
[1, 2]

43. જો S = {(1, 3), (4, 2), (2, 3), (3, 1)} એ ગણ A = {1, 2, 3, 4} પરનો સંબંધ દર્શાવે તો S એ .........

સંમિત સંબંધ નથી
સ્વવાચક સંબંધ છે.
પરંપરિત સંબંધ છે.
કોઈ સંબંધ નથી.

44. જો g (f(x) = |sin x| તથા f(g(x) = (sin $square root of bold x$ )² હોય, તો ......

$straight f left parenthesis straight x right parenthesis space equals space sin squared straight x comma space straight g left parenthesis straight x right parenthesis space equals space square root of straight x$
$straight f left parenthesis straight x right parenthesis space equals space sin space straight x comma space straight g left parenthesis straight x right parenthesis space equals space vertical line straight x vertical line$
$bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold x to the power of bold 2 bold comma bold space bold g bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold sin bold space square root of bold x$
f અને g નિશ્વિત ન કરી શકાય.

45. વિધેય f(x) = log $open parentheses bold x bold plus square root of bold x to the power of bold 2 bold space bold plus bold space bold 1 end root close parentheses$ એ .........

અયુગ્મ વિધેય છે.
યુગ્મ કે અયુગ્મ વિધેય નથી.
યુગ્મ વિધેય છે.
આવર્તી વિધેય છે.

46. f(x) sin x + cos x; g(x) = x²-1 હોય, તો g(f(x)) એ x ∈ ....... માટે પ્રતિવિધેય ધરાવે.

$left square bracket 0 comma space straight pi right square bracket$
$open square brackets negative straight pi over 4 comma straight pi over 4 close square brackets$
$open square brackets negative straight pi over 2 comma pi over 2 close square brackets$
$open square brackets 0 comma pi over 4 close square brackets$

47. f : [1, ∞] → [1, ∞) f(x) = 2^x(x-1) હોય, તો f^-1(x) = ........

1 + $square root of 4 space log subscript 2 space straight x end root$
$1 half plus 1 half square root of 1 plus 4 log subscript 2 x end root$
$square root of 1 plus 4 log subscript 2 straight g end root$
અસ્તિત્વ ધરાવતું નથી

48. sin^-1 $open square brackets bold log subscript bold 3 open parentheses bold x over bold 3 close parentheses close square brackets$ નો મહત્તમ પ્રદેશ ............ છે.

[1, 9]
(1, 9)
[9, 1]
[-1, 9]

[1, 9]

Tips: -

sin^-1 : [-1, 1] → $open square brackets fraction numerator bold minus bold pi over denominator bold 2 end fraction bold comma bold pi over bold 2 close square brackets$ વ્યાખ્યાયિત વિધેય છે.

$bold therefore bold space bold log subscript bold 3 bold space open parentheses begin inline style bold x over bold 3 end style close parentheses bold space bold element of bold space bold left square bracket bold minus bold 1 bold comma bold space bold 1 bold right square bracket$ જરૂરી છે.
$bold therefore bold space bold minus bold space bold 1 bold space bold less than bold space bold log subscript bold 3 bold space open parentheses bold x over bold 3 close parentheses bold space bold less or equal than bold space bold 1 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 1 bold right parenthesis$

$bold therefore bold space bold 1 over bold 3 bold space bold less or equal than bold space bold x over bold 3 bold space bold less or equal than bold space bold 3$ (log₃ વધતું વિધેય છે.)

આમ, x ∈ [1, 9]

∴ sin^-1 $open square brackets bold log subscript bold 3 open parentheses bold x over bold 3 close parentheses close square brackets$ નો પ્રદેશ [1, 9] મળે.

49. f: N→Z, દ્વારા, વ્યાખ્યાયિત વિધેય $bold f bold left parenthesis bold n bold right parenthesis bold space bold equals bold space open curly brackets table attributes columnalign left end attributes row cell fraction numerator bold n bold minus bold 1 over denominator bold 2 end fraction end cell row cell fraction numerator bold minus bold n over denominator bold 2 end fraction end cell end table close$

એક-એક નથી તથા વ્યાપ્ત વિધેય પણ નથી.
એક-એક વિધેય છે પરંતુ વ્યાપ્ત વિધેય નથી.
વ્યાપ્ત વિધેય છે પરંતુ એક-એક વિધેય નથી.
એક-એક તથા વ્યાપ્ત વિધેય છે.

50. f: [0, ∞) → [0, ∞) દ્વારા વ્યાખ્યાયિત વિધેય f(x) = $fraction numerator bold x over denominator bold 1 bold plus bold x end fraction$ હોય, તો f એ ......... .

એક-એક તથા વ્યાપ્ત વિધેય છે.
એક-એક વિધેય નથી પરંતુ વ્યાપ્ત વિધેય છે.
એક-એક નથી તથા વ્યાપ્ત વિધેય પણ નથી
એક-એક વિધેય છે પરંતુ વ્યાપ્ત વિધેય નથી

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Gujarati JEE Mathematics : ગણ, સંબંધ અને વિધેય

Multiple Choice Questions

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