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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

71.

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

72.

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

73. 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

74.

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

75.

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

76.

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

77.

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

k ∈ R
1
2
3

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.

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.

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

80.

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

Tips: -

$bold D bold space bold equals bold space 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 equals bold space open vertical bar table row cell bold left parenthesis bold b bold plus bold c bold plus bold a bold right parenthesis bold left parenthesis bold b bold plus bold c bold minus bold a bold right parenthesis end cell bold 0 cell bold a to the power of bold 2 end cell row bold 0 cell bold left parenthesis bold a bold plus bold c bold plus bold b bold right parenthesis bold left parenthesis bold a bold plus bold c bold minus bold b bold right parenthesis end cell cell bold b to the power of bold 2 end cell row cell bold left parenthesis bold c bold minus bold a bold minus bold b bold right parenthesis bold left parenthesis bold c bold plus bold a bold plus bold b bold right parenthesis end cell cell bold left parenthesis bold c bold minus bold a bold minus bold b bold right parenthesis bold left parenthesis bold c bold plus bold a bold plus bold b bold right parenthesis 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 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 C subscript bold 32 bold left parenthesis bold minus bold 1 bold right parenthesis bold comma bold space bold C subscript bold 31 bold left parenthesis bold minus bold 1 bold right parenthesis bold equals bold space bold left parenthesis bold a bold plus bold b bold plus bold c bold right parenthesis to the power of bold 2 bold space open vertical bar table row cell bold b bold plus bold c bold minus bold a end cell bold 0 cell bold a to the power of bold 2 end cell row bold 0 cell bold left parenthesis bold a bold plus bold c bold plus bold b end cell cell bold b to the power of bold 2 end cell row cell bold left parenthesis bold c bold minus bold a bold minus bold b bold right parenthesis end cell cell bold left parenthesis bold c bold minus bold a bold minus bold b bold right parenthesis 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 equals bold space bold left parenthesis bold a bold plus bold b bold plus bold c bold right parenthesis to the power of bold 2 bold space open vertical bar table row cell bold b bold plus bold c bold minus bold a end cell bold 0 cell bold a to the power of bold 2 end cell row bold 0 cell bold a bold plus bold c bold minus bold b end cell cell bold b to the power of bold 2 end cell row cell bold minus bold 2 bold b end cell cell bold minus bold 2 bold a end cell cell bold 2 bold ab end cell end table close vertical bar 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 space bold space bold R subscript bold 13 bold left parenthesis bold minus bold 1 bold right parenthesis bold R subscript bold 23 bold left parenthesis bold minus bold 1 bold right parenthesis bold equals bold space bold 2 bold left parenthesis bold a bold plus bold b bold plus bold c bold right parenthesis to the power of bold 2 bold space open vertical bar table row cell bold b bold plus bold c bold minus bold a end cell bold 0 cell bold a to the power of bold 2 end cell row bold 0 cell bold a bold plus bold c bold minus bold b end cell cell bold b bold left parenthesis bold a bold plus bold c bold right parenthesis end cell row cell bold minus bold b end cell cell bold minus bold a end cell bold 0 end table close vertical bar 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 R subscript bold 2 open parentheses bold 1 over bold 2 close parentheses bold comma bold space bold પછ ી bold space bold c subscript bold 23 bold left parenthesis bold b bold right parenthesis$

2(a+b+c)² {(b+c-a) ab (a+c) + a²b(a+c-b)}

=2 abc(a+b+c)³, આથી k = 2

નોંધ : જો a,b,c પૈકી શુન્ય હોય અથવા a + b + c = 0 હોય, તો k સ્વૈર રહે.

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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