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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

61.

જો A એ 3×3 સામાન્ય શ્રેણિક હોય અને AA^T = A^TA અને B = A^-1A^T તો BB^T = ...........

(B^-1)^T
I + B
I
B^-1

Tips: -

BB^T = (A^-1A^T)(A^-1A^T)^T = (A^-1A^T)(A(A^-1)^T) = [A^-1(A^TA)] (A^-1)^T

BB^T = [(A^-1(AA^T)] (A^-1)^T = [(A^-1A) (A^T) (A^-1)^T = A^T(A^T)^-1 = I

62.

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

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

63.

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.

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

64.

bold જ ો bold space bold space bold left square bracket bold x bold space bold minus bold space bold 5 bold space bold minus bold space bold 1 bold right square bracket bold space open square brackets table row bold 1 bold 0 bold 2 row bold 0 bold 2 bold 1 row bold 2 bold 0 bold 3 end table close square brackets bold space open square brackets table row bold x row bold 4 row bold 1 end table close square brackets bold space bold minus bold space bold left square bracket bold 0 bold right square bracket bold comma bold space bold ત ો bold space bold x bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space

$plus-or-minus square root of 3$
$plus-or-minus 2 square root of 3$
$square root of 3$
$plus-or-minus 4 square root of 3$

65. 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
$open square brackets table row bold 1 bold 1 row bold 1 bold 1 end table close square brackets$
$open square brackets table row bold 0 bold 1 row cell bold minus bold 1 end cell bold 0 end table close square brackets$
$open square brackets table row bold 0 cell bold minus bold 1 end cell row bold 1 bold 0 end table close square brackets$

66.

bold જ ો bold space bold space bold A bold space bold equals bold space open square brackets table row cell bold 1 over bold 2 end cell bold 2 row bold 0 cell bold 2 bold x bold minus bold 3 end cell end table close square brackets bold space bold semicolon bold space bold B bold space bold equals bold space open square brackets table row bold 2 bold 4 row bold 0 cell bold minus bold 1 end cell end table close square brackets bold space bold અન ે bold space bold space bold AB bold space bold equals bold space bold I bold space bold ત ો bold space bold x bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space

0
1
-1
2

67.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold a bold 0 row bold 1 bold 1 end table close square brackets bold space bold અન ે bold space bold A to the power of bold 2 bold space bold equals bold space bold B bold space bold ત ો bold space bold A bold space bold equals bold space bold. bold. bold. bold. bold. bold space

-1
4
1
a ન મળે

68. 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.

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

69. જો A² - 3A = I તો A^-1 = ......

3I-A
A-3I
I - 3A
3A-1

70.

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 = .......

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

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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

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