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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

71.

જો α, β અને γ એ સમીકરણ x³ + px + q = 0 નાં બીજ હોય, તો નું મૂલ્ય .......... છે.

3pq
p² = 2q
p + q
p - q

72. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold x to the power of bold 5 end cell cell bold sin to the power of bold 2 bold x end cell cell bold 3 to the power of bold x to the power of bold 4 end cell row cell bold tan to the power of bold 3 bold x end cell bold 1 cell bold sec to the power of bold 2 bold x end cell row cell bold minus bold sin to the power of bold 5 bold x end cell cell bold x to the power of bold 6 end cell bold 5 end table close vertical bar bold space bold ત ો bold space table row bold pi row bold integral row cell bold minus bold pi end cell end table bold f bold left parenthesis bold x bold right parenthesis bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.$

0
1
2
-2

73.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold x cell bold e to the power of bold x to the power of bold 4 end cell bold cosx row cell bold cosec bold space bold x end cell bold 3 bold secx row bold cotx cell bold x to the power of bold 2 end cell bold 7 end table close vertical bar bold space bold ત ો bold space table row cell bold pi over bold 2 end cell row bold integral row cell fraction numerator bold minus bold pi over denominator bold 2 end fraction end cell end table bold f bold left parenthesis bold x bold right parenthesis bold space bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.$

0
34
$bold 1 bold equals bold minus bold pi over bold 2$
$bold 5 bold e to the power of bold pi$

74.

bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold x bold 1 bold 1 row bold 1 bold x bold 1 row bold 1 bold 1 bold x end table close vertical bar bold space bold ત ો bold space table row bold 1 row bold integral row bold 0 end table bold f bold left parenthesis bold x bold right parenthesis bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

$fraction numerator bold minus bold 3 over denominator bold 4 end fraction$
$bold 1 over bold 4$
$bold 2 over bold 3$
$bold 3 over bold 4$

75.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold 1 bold cosx row bold cosx bold 1 end table close vertical bar bold comma bold space bold ત ો bold space table row cell bold pi over bold 2 end cell row bold integral row cell fraction numerator bold minus bold pi over denominator bold 2 end fraction end cell end table bold f bold left parenthesis bold x bold right parenthesis bold dx bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.$

$bold pi over bold 2 bold space$
$bold pi$
$bold space bold 2 bold pi$
2

76.

open vertical bar table row cell bold left parenthesis bold b bold plus bold c bold right parenthesis to the power of bold 2 end cell cell bold a to the power of bold 2 end cell cell bold a to the power of bold 2 end cell row cell bold b to the power of bold 2 end cell cell bold left parenthesis bold c bold plus bold a bold right parenthesis to the power of bold 2 end cell cell bold b to the power of bold 2 end cell row cell bold c to the power of bold 2 end cell cell bold c to the power of bold 2 end cell cell bold left parenthesis bold a bold plus bold b bold right parenthesis to the power of bold 2 end cell end table close vertical bar bold space bold equals bold space bold k bold space bold abc bold left parenthesis bold a bold plus bold b bold plus bold c bold right parenthesis to the power of bold 3 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.

-1
1
-2
2

77.

જો y = -9 એ આપેલ સમીકરણનું એક બીજ છે, તો $open vertical bar table row bold y bold 3 bold 7 row bold 2 bold y bold 2 row bold 7 bold 6 bold y end table close vertical bar$ નાં બીજાં બીજ ........ છે.

-2 અને 7
2 અને 7
-2 અને -7
2 અને -7

78.

જો a,b,c એ સ્વરિત શ્રેણીના અનુક્રમે p માં, r માં પદ હોય તો $open vertical bar table row bold bc bold ca bold ab row bold p bold q bold r row bold 1 bold 1 bold 1 end table close vertical bar$ નું મુલ્ય ..... છે.

0
pqr
abc
એક પણ નહિ

79.

સમીકરણો (x + 1)x + 8y = 4k અને kx + (k + 3)y = 3k - 1 નો ઉકેલ મળે નહિ, તો k = ......

k ∈ R
1
2
3

Tips: -

(k + 1)x + 8y - 4k = 0

kx + (x + 3)y - 3k + 1 = 0

$bold D bold space bold equals bold space open vertical bar table row cell bold k bold equals bold 1 end cell bold 8 row bold k cell bold k bold plus bold 3 end cell end table close vertical bar$ = K² + 4K + 3 - 8K = K² - 4K + 3 = (K - 3)(K - 1) = 0⇒k = 3 અથવા k = 1

$bold D subscript bold 1 bold space bold equals bold space open vertical bar table row bold 8 cell bold minus bold 4 bold k end cell row cell bold k bold plus bold 3 end cell cell bold minus bold 3 bold k bold plus bold 1 end cell end table close vertical bar$ = -24 k+ 8 + 4k² + 12 k

= 4k² - 12k + 8 = 4(k - 2)(k - 1). k = 3 માટે D₁ # 0, k = 1 માટે D₁ = 0

k = 1 માટે ઉકેલ અનંતગણ, k = 2 માટે અનન્ય ઉકેલ.

k = 3 માટે સમીકરણો x + 2y = 3 તથા x + 2y = નો ઉકેલગણ છે. આથી k = 3

80.

open vertical bar table row bold x cell bold minus bold 6 end cell cell bold minus bold 1 end cell row bold 2 cell bold minus bold 3 bold x end cell cell bold x bold minus bold 3 end cell row cell bold minus bold 3 end cell cell bold 2 bold x end cell cell bold x bold plus bold 2 end cell end table close vertical bar bold space bold equals bold space bold 0

3 અથવા 2 અથવા 1
-3 અથવા 2 અથવા 1
-3 અથવા - 2 અથવા 1
-3 અથવા 2 અથવા -1

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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