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CBSE

Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

61. જો $bold A bold space bold equals bold space open square brackets table row bold 0 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 0 end table close square brackets$ નો લંબ શ્રેણિક ............ થાય.

$open square brackets table row bold cosθ cell bold minus bold sinθ end cell row bold sinθ bold cosθ end table close square brackets bold space bold space$
$open square brackets table row cell bold minus bold cosθ end cell bold sinθ row bold sinθ bold cosθ end table close square brackets bold space$
$open square brackets table row bold cosθ bold sinθ row bold sinθ cell bold minus bold cosθ end cell end table close square brackets bold space$
$open square brackets table row bold cosθ bold sinθ row bold sinθ bold cosθ end table close square brackets$

open square brackets table row bold cosθ cell bold minus bold sinθ end cell row bold sinθ bold cosθ end table close square brackets bold space bold space

Tips: -

I એ 2×2 એકમ શ્રેણિક છે.

$bold I bold space bold plus bold space bold A bold space bold equals bold space open square brackets table row bold 1 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 1 end table close square brackets bold space bold space bold space bold તથ ા bold space bold space bold I bold space bold minus bold space bold A bold space bold equals bold space open square brackets table row bold 1 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 1 end table close square brackets bold space bold space bold space bold left parenthesis bold I bold space bold minus bold space bold A bold right parenthesis bold space to the power of bold minus bold 1 end exponent bold space bold equals bold space bold cosθ bold theta over bold 2 bold space bold space open square brackets table row bold 1 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 1 end table close square brackets bold space bold space bold space bold space bold લ ં બ bold space bold શ ્ ર ે ણ િ ક bold space bold left parenthesis bold I bold space bold plus bold space bold A bold right parenthesis bold space bold left parenthesis bold I bold space bold minus bold space bold A bold right parenthesis to the power of bold minus bold 1 end exponent bold space bold equals bold space bold cos to the power of bold 2 bold space bold theta over bold 2 bold space open square brackets table row bold 1 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 1 end table close square brackets bold space bold space bold space bold space open square brackets table row bold 1 cell bold minus bold tan bold theta over bold 2 end cell row cell bold tan bold theta over bold 2 end cell bold 1 end table close square brackets bold space bold space bold space bold space bold equals bold space bold cos to the power of bold 2 bold space bold theta over bold 2 bold space open square brackets table row cell bold 1 bold minus bold tan to the power of bold 2 bold theta over bold 2 end cell cell bold minus bold 2 bold tan bold theta over bold 2 end cell row cell bold 2 bold tan bold theta over bold 2 end cell cell bold minus bold tan bold theta over bold 2 end cell end table close square brackets bold equals bold space open square brackets table row cell bold cos to the power of bold 2 bold space bold theta over bold 2 bold minus bold sin to the power of bold 2 bold theta over bold 2 end cell cell bold minus bold 2 bold sin bold theta over bold 2 bold cos to the power of bold 2 bold space bold theta over bold 2 end cell row cell bold 2 bold sin to the power of bold 2 bold theta over bold 2 bold cos to the power of bold 2 bold space bold theta over bold 2 end cell cell bold cos to the power of bold 2 bold space bold theta over bold 2 bold minus bold sin to the power of bold 2 bold theta over bold 2 end cell end table close square brackets bold space bold equals bold space open square brackets table row bold cosθ cell bold minus bold sinθ end cell row bold sinθ bold cosθ end table close square brackets$

62.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 6 bold 7 row bold 8 bold 9 end table close square brackets bold space bold અન ે bold space bold space bold B to the power of bold minus bold 1 end exponent bold space bold equals bold space open square brackets table row bold 5 cell bold minus bold 2 end cell row cell bold minus bold 7 end cell bold 3 end table close square brackets bold space bold ત ો bold space bold left parenthesis bold AB bold right parenthesis to the power of bold minus bold 1 end exponent bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.

$bold space open square brackets table row cell bold 61 over bold 2 end cell cell bold minus bold 47 over bold 2 end cell row cell bold minus bold 87 over bold 2 end cell cell bold 67 over bold 2 end cell end table close square brackets bold space$
$open square brackets table row cell bold 61 over bold 2 end cell cell bold minus bold 47 over bold 2 end cell row cell bold 87 over bold 2 end cell cell bold minus bold 67 over bold 2 end cell end table close square brackets bold space$
$open square brackets table row cell bold minus bold 61 over bold 2 end cell cell bold 47 over bold 2 end cell row cell bold 87 over bold 2 end cell cell fraction numerator bold minus bold 67 over denominator bold 2 end fraction end cell end table close square brackets bold space bold space$
$open square brackets table row cell bold minus bold 61 over bold 2 end cell cell bold 47 over bold 2 end cell row cell bold 87 over bold 2 end cell cell bold 67 over bold 2 end cell end table close square brackets$

63. વિસંમિત શ્રેણિક $bold A bold space bold equals bold space open square brackets table row bold 0 cell bold minus bold 1 end cell row bold 1 bold 0 end table close square brackets$ હોય, તો લંબ શ્રેણિક ....... થાય.

I
$open square brackets table row bold 1 bold 1 row bold 1 bold 1 end table close square brackets$
$open square brackets table row bold 0 bold 1 row cell bold minus bold 1 end cell bold 0 end table close square brackets$
$open square brackets table row bold 0 cell bold minus bold 1 end cell row bold 1 bold 0 end table close square brackets$

64.

જો સંમિત શ્રેણિક X તથા વિસંમિત શ્રેણિક Y માટે X + Y = A = $open square brackets table row bold 1 bold 6 bold 7 row bold 2 bold 5 bold 9 row bold 3 bold 4 bold 8 end table close square brackets$ તો X = .......

$open square brackets table row bold 1 bold 8 bold 10 row bold 8 bold 5 bold 13 row bold 10 bold 13 bold 8 end table close square brackets bold space$
$open square brackets table row bold 1 bold 4 bold 5 row bold 4 bold 5 cell bold 13 over bold 2 end cell row bold 5 cell bold 13 over bold 2 end cell bold 8 end table close square brackets bold space$
$open square brackets table row bold 0 bold 4 bold 4 row cell bold minus bold 4 end cell bold 0 bold 6 row cell bold minus bold 4 end cell cell bold minus bold 5 end cell bold 0 end table close square brackets$
$bold space open square brackets table row bold 0 bold 2 bold 2 row cell bold minus bold 2 end cell bold 0 cell bold 5 over bold 2 end cell row cell bold minus bold 2 end cell cell bold minus bold 5 over bold 2 end cell bold 0 end table close square brackets$

65.

bold જ ો bold space bold space bold left square bracket bold 1 bold space bold x bold space bold 1 bold right square bracket bold space open square brackets table row bold 1 bold 3 bold 2 row bold 0 bold 5 bold 1 row bold 0 bold 3 bold 2 end table close square brackets bold space open square brackets table row bold 1 row bold 1 row bold x end table close square brackets bold space bold equals bold space bold left square bracket bold 0 bold right square bracket bold space bold ત ો bold space bold x bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

$fraction numerator begin display style bold minus bold 7 bold plus-or-minus square root of bold 35 end style over denominator begin display style bold 2 end style end fraction$
$fraction numerator bold minus bold 9 bold plus-or-minus square root of bold 35 over denominator bold 2 end fraction$
$fraction numerator bold minus bold 7 bold plus-or-minus square root of bold 53 over denominator bold 2 end fraction$
$fraction numerator bold minus bold 9 bold plus-or-minus square root of bold 53 over denominator bold 2 end fraction$