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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

71.

સંવૃત્ત અંતરાલ [-4, -1] , માં x ની કેટલી કિંમતો માટે શ્રેણિક $open square brackets table row bold 3 cell bold minus bold 1 bold plus bold x end cell bold 2 row bold 3 cell bold minus bold 1 end cell cell bold x bold plus bold 2 end cell row cell bold x bold plus bold 3 end cell cell bold minus bold 1 end cell bold 2 end table close square brackets$ અસામાન્ય શ્રેણિક છે ?

0
2
3
-4

72.

open square brackets table row bold 1 bold 2 bold 3 row bold 2 bold 3 bold 4 row bold 3 bold 4 bold 5 end table close square brackets bold space open square brackets table row cell bold minus bold 1 end cell cell bold minus bold 2 end cell row cell bold minus bold 2 end cell bold 0 row bold 0 cell bold minus bold 4 end cell end table close square brackets bold space open square brackets table row cell bold minus bold 4 end cell cell bold minus bold 5 end cell cell bold minus bold 5 end cell row bold 0 bold 0 bold 1 end table close square brackets bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold.

$bold space open square brackets table row cell bold minus bold 12 end cell cell bold minus bold 15 end cell bold 4 row bold 32 bold 40 bold 28 row bold 44 bold 55 bold 40 end table close square brackets$
$bold space open square brackets table row bold 12 bold 15 bold 18 row cell bold minus bold 24 end cell cell bold minus bold 40 end cell bold 48 end table close square brackets bold space$
$open square brackets table row bold 20 bold 25 bold 16 row bold 32 bold 40 bold 28 row bold 44 bold 55 bold 40 end table close square brackets$
આમાંથી એક પણ નહિ.

73.

bold 2 bold A bold space bold plus bold space bold 3 bold B bold space bold equals bold space open square brackets table row bold 2 cell bold minus bold 1 end cell bold 4 row bold 3 bold 2 bold 5 end table close square brackets bold space bold અન ે bold space bold A bold space bold plus bold 2 bold B bold space bold equals bold space open square brackets table row bold 5 bold 0 bold 3 row bold 1 bold 6 bold 2 end table close square brackets bold space bold ત ો bold space bold B bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

$bold space open square brackets table row bold 8 bold 1 bold 2 row cell bold minus bold 1 end cell bold 10 bold 1 end table close square brackets bold space$
$open square brackets table row bold 8 bold 1 bold 2 row cell bold minus bold 1 end cell bold 10 cell bold minus bold 1 end cell end table close square brackets bold space$
$open square brackets table row bold 8 cell bold minus bold 1 end cell bold 2 row cell bold minus bold 1 end cell bold 10 cell bold minus bold 1 end cell end table close square brackets$
$open square brackets table row cell bold minus bold 8 end cell bold 1 cell bold minus bold 2 end cell row cell bold minus bold 1 end cell bold 10 cell bold minus bold 1 end cell end table close square brackets$

74.

bold A bold space bold equals bold space open square brackets table row cell bold cos fraction numerator bold 7 bold pi over denominator bold 6 end fraction end cell cell bold sin fraction numerator bold 11 bold pi over denominator bold 6 end fraction end cell row cell bold sin fraction numerator bold 11 bold pi over denominator bold 6 end fraction end cell cell bold minus bold cos fraction numerator bold 7 bold pi over denominator bold 6 end fraction end cell end table close square brackets bold space bold ત ો bold space bold A to the power of bold 2 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space

$open square brackets table row bold 0 bold 1 row bold 1 bold 0 end table close square brackets bold space$
$open square brackets table row bold 0 bold 0 row bold 1 bold 1 end table close square brackets$
$open square brackets table row bold 1 bold 1 row bold 0 bold 0 end table close square brackets bold space$
$open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets$

75.

bold જ ો bold space bold space bold A bold space bold equals bold space open square brackets table row bold i bold 0 row bold 0 bold i end table close square brackets bold space bold ત ો bold space bold A to the power of bold 12 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

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

76.

bold P bold space bold equals bold space open square brackets table row cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell cell bold 1 over bold 2 end cell row cell bold 1 over bold 2 end cell cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell end table close square brackets bold comma bold space bold A bold space bold equals bold space open square brackets table row bold 1 bold 1 row bold 0 bold 1 end table close square brackets bold space bold અન ે bold space bold Q bold space bold equals bold space bold PAP to the power of bold T bold space bold ત ો bold space bold P to the power of bold T bold space bold Q to the power of bold 205 bold space bold P bold space bold equals bold space bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold.

$open square brackets table row bold 1 bold 205 row bold 0 bold 205 end table close square brackets$
$open square brackets table row bold 1 bold 205 row bold 0 bold 1 end table close square brackets bold space$
$open square brackets table row bold 205 bold 205 row bold 0 bold 1 end table close square brackets$
આ પૈકી એક પણ નહિ.

open square brackets table row bold 1 bold 205 row bold 0 bold 1 end table close square brackets bold space

Tips: -

$bold PP to the power of bold T bold space bold equals bold space open square brackets table row cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell cell bold 1 over bold 2 end cell row cell bold 1 over bold 2 end cell cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell end table close square brackets bold space open square brackets table row cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell cell bold minus bold 1 over bold 2 end cell row cell bold 1 over bold 2 end cell cell fraction numerator square root of bold 3 over denominator bold 2 end fraction end cell end table close square brackets bold space bold equals bold space open square brackets table row cell bold 3 over bold 4 bold plus bold 1 over bold 4 end cell cell bold minus fraction numerator square root of bold 3 over denominator bold 4 end fraction bold plus fraction numerator square root of bold 3 over denominator bold 4 end fraction end cell row cell bold minus fraction numerator square root of bold 3 over denominator bold 4 end fraction bold plus fraction numerator square root of bold 3 over denominator bold 4 end fraction end cell cell bold 1 over bold 4 bold plus bold 3 blank over bold 4 end cell end table close square brackets bold space bold equals bold space open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets$

∴P^T = P^-1, વળી P^TP= PP^T

હવે P^TQ²⁰⁵P = P^T [Q×Q×.....×Q 205 વખત] P

P^T [(PAP^T) (PAP^T)× ...... × 205 વખત] P

(P^TP)A (P^TP)A (P^TP)A ..... 205 વખત = A × A × ..... 205 વખત = A²⁰⁵

$bold A to the power of bold 2 bold space bold equals bold space bold A bold space bold times bold space bold A bold space bold equals bold space open square brackets table row bold 1 bold 1 row bold 0 bold 1 end table close square brackets bold space open square brackets table row bold 1 bold 1 row bold 0 bold 1 end table close square brackets bold space bold equals bold space open square brackets table row bold 1 bold 2 row bold 0 bold 1 end table close square brackets bold comma bold space bold A bold 3 bold space bold equals bold space bold A bold 2 bold A bold space bold equals bold space open square brackets table row bold 1 bold 2 row bold 0 bold 1 end table close square brackets bold space open square brackets table row bold 1 bold 1 row bold 0 bold 1 end table close square brackets bold equals open square brackets table row bold 1 bold 3 row bold 0 bold 1 end table close square brackets bold ત ે bold space bold જ bold space bold ર ી ત ે bold space bold A to the power of bold 4 bold space bold equals open square brackets table row bold 1 bold 4 row bold 0 bold 1 end table close square brackets bold space bold space bold આથ ી bold space bold space bold A to the power of bold 205 bold space bold equals bold space open square brackets table row bold 1 bold 205 row bold 0 bold 1 end table close square brackets$

77.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold cosα bold sinα row cell bold minus bold sinα end cell bold cosα end table close square brackets bold space bold અન ે bold space bold A bold space bold plus bold space bold AT bold space bold equals bold space open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets bold space bold ત ો bold space bold space bold alpha bold space bold equals bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold 0 bold less than bold alpha bold less than bold pi over bold 2

$bold pi over bold 3$
$bold pi over bold 2$
$bold pi over bold 6$
$bold pi over bold 4$

78.

હાર સંક્ષેપન એશિલોન પદ્ધતિનો ઉપયોગ કરી શ્રેણિક $bold A bold space bold equals bold space open square brackets table row bold 41 bold 5 bold 1 row bold 79 bold 9 bold 7 row bold 29 bold 3 bold 5 end table close square brackets$ નો વ્યસ્ત શ્રેણિક મેળવતા $open square brackets table row bold 1 bold 0 bold x row bold 0 bold 1 bold 8 row bold 0 cell bold minus bold 22 end cell cell bold minus bold 176 end cell end table close square brackets space equals bold space open square brackets table row bold 0 bold y cell bold minus bold 9 over bold 26 end cell row bold 0 cell bold minus bold 1 over bold 26 end cell cell bold 7 over bold 26 end cell row bold 1 bold 0 cell bold minus bold 5 end cell end table close square brackets bold space$ A શ્રેણિક મળ્યા તો x અને y નાં મુલ્યો અનુક્રમે ....... અને ........

$bold minus bold 1 bold space bold અન ે bold space bold space bold minus bold 5 over bold 26$
$bold 1 bold space bold અન ે bold space bold 5 over bold 26$
$bold 5 over bold 26 bold space bold અન ે bold space bold 1$
$bold 1 bold space bold અન ે bold space bold minus bold 5 over bold 26$

79.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold cosθ bold sinθ row cell bold minus bold sinθ end cell bold cosθ end table close square brackets bold space bold અન ે bold space bold space bold A bold space bold plus bold space bold A to the power of bold T bold space bold equals bold space square root of bold 3 bold space bold I bold space bold ત ો bold space bold theta bold space bold equals bold space bold. bold. bold. bold. bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold theta bold element of open parentheses bold pi over bold 2 bold comma bold pi over bold 2 close parentheses

$bold pi over bold 6$
$bold pi over bold 3$
$bold minus bold pi over bold 6$
$bold minus bold pi over bold 3$

80.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 0 bold 1 row bold 1 bold 0 end table close square brackets bold space bold ત ો bold space bold A to the power of bold 8 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space

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

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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

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