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શ્રેણિક

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JEE ગણિત પ્રશ્ન બેંક ભાગ 2

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ગણિત

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જો તો નીચે bold A bold space bold equals bold space open vertical bar table row bold 0 bold 0 bold 1 row bold 0 cell bold minus bold 1 end cell bold 0 row cell bold minus bold 1 end cell bold 0 bold 0 end table close vertical bar bold space પૈકીનું કયું સત્ય છે ? 

  • A2 = I 

  • A શુન્ય શ્રેણિક છે. 

  • A-1અસ્તિત્વ નથી 

  • A (-1) I 


A.

A2 = I 

Tips: -

bold A to the power of bold 2 bold space bold equals bold space open square brackets table row bold 0 bold 0 cell bold minus bold 1 end cell row bold 0 cell bold minus bold 1 end cell bold 0 row cell bold minus bold 1 end cell bold 0 bold 0 end table close square brackets bold space open square brackets table row bold 0 bold 0 cell bold minus bold 1 end cell row bold 0 cell bold minus bold 1 end cell bold 0 row cell bold minus bold 1 end cell bold 0 bold 0 end table close square brackets

bold A to the power of bold 2 bold space bold equals bold space open square brackets table row bold 1 bold 0 bold 0 row bold 0 bold 1 bold 0 row bold 0 bold 0 bold 1 end table close square brackets bold space bold equals bold space bold I

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ધારો કે, bold A bold space bold equals bold space open square brackets table row bold 1 cell bold minus bold 1 end cell bold 1 row bold 2 bold 1 cell bold minus bold 3 end cell row bold 1 bold 1 bold 1 end table close square brackets bold space bold અન ે bold space bold 10 bold space bold B bold space bold equals bold space open square brackets table row bold 4 bold 2 bold 2 row cell bold minus bold 5 end cell bold 0 bold alpha row bold 1 cell bold minus bold 2 end cell bold 3 end table close square brackets bold commaઅને જો B એ A નો વ્યસ્ત શ્રેણિક હોય તો α = ........ 
  • -1

  • 5

  • -1

  • -2


જો bold A bold space bold equals bold space open square brackets table row bold 1 bold 0 row bold 1 bold 1 end table close square brackets bold space bold અન ે bold space bold I bold space bold equals bold space open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square bracketsતો ગણિતિય અનુમાનના સિદ્ધાંતથી નીચેના પૈકી કયું સત્ય છે ? (n ≥ 1)
  •  An = nA + (n-1)I

  • An - nA - (n-1)I 

  • An = 2n-1 A-(n-1)I 

  • An = 2n-1 = nA + (n -1)I


જો bold A bold space bold equals bold space open square brackets table row bold 1 bold 2 row bold 3 bold 4 end table close square brackets bold space bold અન ે bold space bold B bold space bold equals bold space open square brackets table row bold a bold 0 row bold 0 bold b end table close square brackets bold comma bold space bold a bold comma bold space bold b bold element of bold N bold space bold ત ો

  • અસિમિત સંખ્યામાં B મળે કે જેથી AB = BA

  • એક B મળે કે જેથી AB = BA 

  • એક કરતાં વધુ પરંતુ સિમિત સંખ્યામાં B મળે જે જેથી AB = BA

  • AB = BA થાય, તેવો B મળે નહિ 


જો bold A bold space bold equals open square brackets table row bold a bold b row bold b bold a end table close square brackets bold space bold A to the power of bold 2 bold space bold equals bold space open square brackets table row bold alpha bold beta row bold beta bold alpha end table close square brackets bold space bold ત ો bold space bold. bold. bold. bold. bold. bold. bold. bold.
  • α= 2ab, β = a2 + b2 

  • α= a2 + b2, β= ab

  • α= a2 + b2, β = a2 - b

  • α= a2 + b2, β = 2ab 


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