જો x + 2ay + az = 0; x + 3by + bz = 0, x + 4cz + cz = 0 સમીકરણો સુસંગત હોય, તો a, b, c એ ........ છે. from Mathematics નિશ્વાયક

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE

Subject

Mathematics
Advertisement
zigya logo

Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

1. 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.

2.
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

3. 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

4. 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

Advertisement
5. 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

6.
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

Advertisement
7.
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

A.

સ્વરિત શ્રેણીમાં 

Tips: -

ત્રણે સમીકરણ સુસંગત છે. 
bold D bold space bold equals bold space open vertical bar table row bold 1 cell bold 2 bold a end cell bold a row bold 1 cell bold 3 bold b end cell bold b row bold 1 cell bold 4 bold c end cell bold c end table close vertical bar bold space bold equals bold space bold 0

bold therefore bold space bold 3 bold bc bold space bold minus bold space bold 4 bold bc bold space bold minus bold space bold 2 bold ac bold space bold plus bold space bold 2 bold ab bold space bold plus bold space bold 4 bold ac bold space bold minus bold space bold 3 bold ab bold space bold equals bold space bold 0

bold therefore bold space bold minus bold space bold bc bold space bold plus bold space bold 2 bold ac bold space bold minus bold space bold ab bold space bold equals bold space bold 0 bold space

bold therefore bold space bold b bold space bold equals bold space fraction numerator bold 2 bold ac over denominator bold a bold plus bold c end fraction
bold therefore bold space bold a bold comma bold space bold b bold comma bold space bold c સ્વરિત શ્રેણીમાં છે.

Advertisement
8.
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

Advertisement
9. 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

10. 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.

Advertisement

Switch