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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

11. જો a, b, c ભિન્ન અને ધન સંખ્યાઓ હોય, તો $open vertical bar table row bold a bold b bold c row bold b bold c bold a row bold c bold a bold b end table close vertical bar$ નું મૂલ્ય ........ છે.

ધન
ઋણ
શૂન્ય
સંકર

12. જો l, m અને n એ કોઈ સમગુણોત્તર શ્રેણીના p, q અને r મા પદ હોય તથા l > 0, m >0, n >0 તો $open vertical bar table row cell bold log bold space bold l end cell bold p bold 1 row cell bold log bold space bold m end cell bold q bold 1 row cell bold log bold space bold n end cell bold r bold 1 end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space bold.$

13.

ધારો a, b, c કે કોઇ પણ વાસ્તવિક સંખ્યાઓ છે. બધી જ શૂન્ય ન હોય તેવી વાસ્તવિક સંખ્યાઓ x, y, z માટે x = cy + bz; y = az + cx અને z = ay + bx છે. તો a² + c² + 2abc = .......

-1
0
1
2

14. જો a + b + c = 0 હોય, તો $open vertical bar table row cell bold a bold minus bold x end cell bold c bold b row bold c cell bold b bold minus bold c end cell bold a row bold b bold a cell bold c bold minus bold x end cell end table close vertical bar bold space bold equals bold space bold 0$ નો એક ઉકેલ ....... છે.

1
2
0
a² + b² + c²

Tips: -

હવે $open vertical bar table row cell bold a bold plus bold b bold plus bold c bold minus bold x end cell bold c bold b row cell bold a bold plus bold b bold plus bold c bold minus bold x end cell cell bold b bold minus bold x end cell bold a row cell bold a bold plus bold b bold plus bold c bold minus bold x end cell bold a cell bold c bold minus bold x end cell end table close vertical bar bold space bold equals bold space bold 0 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold C subscript bold 21 bold space bold left parenthesis bold 1 bold right parenthesis bold comma bold space bold C subscript bold 31 bold space bold left parenthesis bold 1 bold right parenthesis$

$bold therefore bold space open vertical bar table row cell bold minus bold x end cell bold c bold b row cell bold minus bold x end cell cell bold b bold minus bold x end cell bold a row cell bold minus bold x end cell bold a cell bold c bold minus bold x end cell end table close vertical bar bold space bold equals bold space bold 0 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold a bold space bold plus bold space bold b bold space bold plus bold space bold c bold space bold equals bold space bold 0$ મૂકતાં

$bold therefore bold space open vertical bar table row bold 1 bold c bold b row bold 1 cell bold b bold minus bold x end cell bold a row bold 1 bold a cell bold c bold minus bold x end cell end table close vertical bar bold space bold equals bold minus bold space bold 0$

એક ઉકેલ x = 0 થાય.

15. સુરેખ સમીકરણની સંહતિ નીચે મુજબ છે:
x₁+ 2x₂ + x₃ = 3
2x₁ + 3x₂ + x₃ = 3
3x₁ + 5x₂ + 2x₃ = 1 સંહતિના ઉકેલોની સંખ્યા ....... છે.

3
એક
થી વધુ
શૂન્ય

16. ધારો કે a, b, c ∈ R - {0} તથા a + c ≠ 0 જો $open vertical bar table row bold a cell bold a bold plus bold 1 end cell cell bold a bold minus bold 1 end cell row cell bold minus bold b end cell cell bold b bold plus bold 1 end cell cell bold b bold minus bold 1 end cell row bold c cell bold c bold minus bold 1 end cell cell bold c bold plus bold 1 end cell end table close vertical bar bold space bold plus bold space open vertical bar table row cell bold a bold plus bold 1 end cell cell bold b bold plus bold 1 end cell cell bold c bold minus bold 1 end cell row cell bold a bold minus bold 1 end cell cell bold b bold minus bold 1 end cell cell bold c bold plus bold 1 end cell row cell bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold n bold plus bold 2 end exponent bold a end cell cell bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold n bold minus bold 1 end exponent bold b end cell cell bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold n bold c end cell end table close vertical bar bold space bold equals bold space bold 0$ તો n નું મૂલ્ય .....

શૂન્ય
કોઇક શૂન્યેતર યુગ્મ પૂર્ણાંક
અસંમેય સંખ્યા
કોઈક અયુગ્મ પૂર્ણાંક

17. k ની કેટલી કિંમતો માટે સમીકરણ સંહિત
(k + 1)x + 8y = 4k
kx + (k+3)y = 3k-1 ને એક પણ ઉકેલ નથી.

2
1
3
અનંત

18. જો a ≠ p, b ≠ q, c ≠ r અને $open vertical bar table row bold p bold b bold c row bold a bold q bold c row bold a bold b bold r end table close vertical bar bold space bold equals bold space bold 0$ હોય, તો $fraction numerator bold p over denominator bold p bold minus bold a end fraction bold space bold plus bold space fraction numerator bold q over denominator bold q bold minus bold b end fraction bold space bold plus bold space fraction numerator bold r over denominator bold r bold minus bold c end fraction$ નું મૂલ્ય ....... છે.

2
-1
1
0

19. નીચેની સમીકરણ સંહિતનો ઉકેલ અનન્ય હોય, તો k ની કિંમતનો ગણ ........ છે.
x - ky + z = 0
kx + 3y - kz = 0
3x + y - z = 0

R - {2, 3}
R - {-3}
R - {2}
{2, 3}

20. જો a₁, a₂, ..., a_n સમગુણોત્તર શ્રેણીમાં હોય અને a_i > 0, i ≥ 1 તો $open vertical bar table row cell bold log bold space bold a subscript bold n end cell cell bold log bold space bold a subscript bold n bold plus bold 1 end subscript end cell cell bold log bold space bold a subscript bold n bold plus bold 2 end subscript end cell row cell bold log bold space bold a subscript bold n bold plus bold 3 end subscript end cell cell bold log bold space bold a subscript bold n bold plus bold 4 end subscript end cell cell bold log bold space bold a subscript bold n bold plus bold 5 end subscript end cell row cell bold semicolon bold pg bold space bold a subscript bold n bold plus bold 6 end subscript end cell cell bold log bold space bold a subscript bold n bold plus bold 7 end subscript end cell cell bold log bold space bold a subscript bold n bold plus bold 8 end subscript end cell end table close vertical bar space equals space......... space. space$

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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