જો 1, w, w2 એ 1 નાં ઘન મુળ હોય, તો  from Mathematics નિશ્વાયક

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

1.
જો x + 2ay + az = 0; x + 3by + bz = 0, x + 4cz + cz = 0 સમીકરણો સુસંગત હોય, તો a, b, c એ ........ છે.
  • સ્વરિત શ્રેણીમાં 

  • સમાંતર શ્રેણીમાં 
  • સમગુણોત્તર શ્રેણીમાં 
  • ત્રણમાંથી એક પણ નહી

2. જો bold D bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row bold 1 cell bold 1 bold plus bold x end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold y end cell end table close vertical bar જ્યાં x ≠ 0, y ≠ 0 તો D એ ....... x, y ∈ N
  • x અને y વડે વિભાજ્ય છે.

  • x વડે વિભાજ્ય છે પરંતુ y વડે વિભાજ્ય નથી. 
  • x વડે વિભાજ્ય નથી પરંતુ y વડે વિભાજ્ય છે. 
  • x અને y પૈકી એક પણ વડે વિભાજ્ય નથી.

3.
જો a2+ b2 + c2 + 2 = 0 અને bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold 1 bold plus bold a to the power of bold 2 bold x end cell cell bold left parenthesis bold 1 bold plus bold b to the power of bold 2 bold right parenthesis bold x end cell cell bold left parenthesis bold 1 bold plus bold c to the power of bold 2 bold right parenthesis bold x end cell row cell bold left parenthesis bold 1 bold plus bold a to the power of bold 2 bold right parenthesis bold x end cell cell bold 1 bold plus bold b to the power of bold 2 bold x end cell cell bold left parenthesis bold 1 bold plus bold c to the power of bold 2 bold right parenthesis bold x end cell row cell bold left parenthesis bold 1 bold plus bold a to the power of bold 2 bold right parenthesis bold x end cell cell bold left parenthesis bold 1 bold plus bold b to the power of bold 2 bold right parenthesis bold x end cell cell bold 1 bold plus bold c to the power of bold 2 bold x end cell end table close vertical bar તો, f(x) એ  ..........ઘાતવાળી બહુપદી થાય.
  • 3
  • 2
  • 0
  • 1

4.
જો a < 0 અને ax2 + 2bx + c નો વિવેચક ઋણ હોય, તો open vertical bar table row bold a bold b cell bold ax bold plus bold b end cell row bold b bold c cell bold bx bold plus bold c end cell row cell bold ax bold plus bold b end cell cell bold bx bold plus bold c end cell bold 0 end table close vertical bar નું મૂલ્ય ......... છે.
  • ઋણ

  • (ac-b2) (ax2+2bx+c)
  • 0
  • ધન

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5. જો, w એ 1 નું ઘન મૂળ હોય, અને w ≠ 1 open vertical bar table row bold 1 cell bold 1 bold plus bold i bold plus bold w to the power of bold 2 end cell cell bold w to the power of bold 2 end cell row cell bold 1 bold minus bold i end cell cell bold minus bold 1 end cell cell bold w to the power of bold 2 bold minus bold 1 end cell row cell bold minus bold i end cell cell bold minus bold 1 bold plus bold w bold minus bold i end cell cell bold minus bold 1 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space
  • w2
  • w
  • 1
  • 0

6. a ની કઈ કિંમત માટે સમીકરણ સંહિત
ax + y + z = a - 1
x+ ay + z = a - 1
x + y + az = a - 1 ને એક પણ ઉકેલ નથી.
  • -2
  • 2 અથવા 1
  • -2 સિવાય
  • 1

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7. જો 1, w, w2 એ 1 નાં ઘન મુળ હોય, તો open vertical bar table row bold 1 cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell row cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell bold 1 row cell bold w to the power of bold 2 bold n end exponent end cell bold 1 cell bold w to the power of bold n end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.
  • w2
  • w
  • 0
  • 1

C.

0

Tips: -

w એ 1 નું ઘન મૂળ છે, તેથી w3 = 1; w3n = 1n = 1

bold D bold space bold equals bold space open vertical bar table row bold 1 cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell row cell bold w to the power of bold n end cell cell bold w to the power of bold 2 bold n end exponent end cell bold 1 row cell bold w to the power of bold 2 bold n end exponent end cell bold 1 cell bold w to the power of bold n end cell end table close vertical bar

bold space bold space bold space bold equals bold space bold 1 bold space bold left parenthesis bold w to the power of bold 3 bold n end exponent bold minus bold 1 bold right parenthesis bold minus bold w to the power of bold n bold space bold left parenthesis bold w to the power of bold 2 bold n end exponent bold minus bold w to the power of bold 2 bold n end exponent bold right parenthesis bold space bold plus bold space bold w to the power of bold 2 bold n end exponent bold space bold left parenthesis bold w to the power of bold 2 bold minus bold w to the power of bold 4 bold n end exponent bold right parenthesis

bold space bold space bold space bold equals bold space bold 1 bold space bold left parenthesis bold 0 bold right parenthesis bold space bold minus bold space bold w to the power of bold n bold space bold left parenthesis bold 0 bold right parenthesis bold space bold plus bold space bold w to the power of bold 3 bold n end exponent bold space bold left parenthesis bold 1 bold minus bold w to the power of bold 3 bold n end exponent bold right parenthesis bold space bold equals bold space bold 0 bold space

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8. જો open vertical bar table row bold a bold b cell bold ax bold plus bold by end cell row bold b bold c cell bold ax bold plus bold cy end cell row cell bold ax bold plus bold by end cell cell bold bx bold plus bold cy end cell bold 0 end table close vertical bar bold space bold equals bold space bold 0
 અને ax2 + 2bxy + cy2 ≠ 0 તો.........  
  • a, b, cસમગુણોત્તર શ્રેણીમાં છે.

  • a, b, c સમાંતર શ્રેણીમાં છે. 
  • a, b, c સ્વરિત શ્રેણીમાં છે. 
  • a, b, c એ સમગુણોત્તર, સમાંતર કે સ્વરિત શ્રેણીમાં નથી.

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9.
જો open vertical bar table row bold a cell bold a to the power of bold 2 end cell cell bold 1 bold plus bold a to the power of bold 3 end cell row bold b cell bold b to the power of bold 2 end cell cell bold 1 bold plus bold b to the power of bold 3 end cell row bold c cell bold c to the power of bold 2 end cell cell bold 1 bold plus bold c to the power of bold 3 end cell end table close vertical bar bold space bold equals bold space bold 0 અને સદિશો (1, a, a2) ; (1, b, b2) અને (1, c, c2) એ સમતલીય હોય, તો abc = ......  
  • 1
  • 2
  • 0
  • -1

10. જો s = p + q + r, તો open vertical bar table row cell bold s bold plus bold r end cell bold p bold q row bold r cell bold s bold plus bold p end cell bold q row bold r bold p cell bold s bold plus bold q end cell end table close vertical bar ની કિંમત ....... છે.
  • s3
  • 2s3
  • 2s2
  • 3s3

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