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CBSE

Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

31.

bold જ ો bold space bold શ ્ ર ે ણ િ ક bold space bold space bold A subscript bold r bold space bold equals bold space open square brackets table row bold r cell bold r bold minus bold 1 end cell row cell bold r bold minus bold 1 end cell bold r end table close square brackets bold comma bold space bold r bold space bold equals bold space bold 1 bold comma bold 2 bold comma bold 3 bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold ત ો bold space bold vertical line bold A bold vertical line bold space bold plus bold space bold vertical line bold A subscript bold 2 bold vertical line bold space bold plus bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space bold plus bold space bold vertical line bold A subscript bold 101 bold vertical line bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space

100
(100)²
101
(101)²

32.

સુરેખ સમીકરણ સંહતિ x + 3y + 4z = 8, 2x + y + 2z = 5, 5x + y + z = 7, નો અનન્ય ઉકેલ ......

x = 1, y = 2, z = 1
x = -1, y = 1, z = 1
x = 1, y = 1, z = -1
x = 1, y = 1, z = 1

x = 1, y = 1, z = 1

Tips: -

x + 3y + 4z = 8

2x + y + 2z = 5

5x + y + z = 7

$open square brackets table row bold 1 bold 3 bold 4 row bold 2 bold 1 bold 2 row bold 5 bold 1 bold 1 end table close square brackets bold space open square brackets table row bold x row bold y row bold z end table close square brackets bold space bold equals bold space open square brackets table row bold 8 row bold 5 row bold 7 end table close square brackets bold space bold rightwards double arrow bold space bold AX bold space bold equals bold space bold D bold જ ્ ય ાં bold space bold A bold space bold equals bold space open square brackets table row bold 1 bold 3 bold 4 row bold 2 bold 1 bold 2 row bold 5 bold 1 bold 1 end table close square brackets bold space bold space bold space bold space bold space bold X bold space bold equals bold space open square brackets table row bold x row bold y row bold z end table close square brackets bold space bold space bold D bold space bold equals bold space open square brackets table row bold 8 row bold 5 row bold 7 end table close square brackets bold space bold vertical line bold A bold vertical line bold space bold equals bold space open square brackets table row bold 1 bold 3 bold 4 row bold 2 bold 1 bold 2 row bold 5 bold 1 bold 1 end table close square brackets bold space bold equals bold space bold 1 bold left parenthesis bold 1 bold space bold minus bold 2 bold right parenthesis bold space bold minus bold 3 bold left parenthesis bold 2 bold space bold minus bold 10 bold right parenthesis bold space bold plus bold space bold 4 bold left parenthesis bold 2 bold space bold minus bold 5 bold right parenthesis bold space bold equals bold space bold minus bold 1 bold space bold plus bold space bold 24 bold space bold minus bold space bold 12 bold space bold equals bold space bold 11 bold space bold # bold space bold 0 bold space bold A bold minus bold 1 bold space bold ન ું bold space bold અસ ્ ત િ ત ્ વ bold space bold છ ે bold. bold space bold A subscript bold 11 bold space bold equals bold space bold minus bold 1 bold comma bold space bold A subscript bold 12 bold space bold equals bold space bold 8 bold comma bold space bold A subscript bold 13 bold space bold equals bold space bold minus bold 3 bold comma bold space bold A subscript bold 21 bold space bold equals bold space bold 1 bold comma bold space bold A subscript bold 22 bold equals bold space bold minus bold 19 bold comma bold space bold A subscript bold 23 bold space bold equals bold space bold 14 bold comma bold space bold A subscript bold 31 bold space bold equals bold space bold 2 bold comma bold space bold A subscript bold 32 bold space bold equals bold space bold 6 bold comma bold space bold A subscript bold 33 bold space bold equals bold space bold minus bold 5 bold adj bold space bold A bold space bold equals bold space open square brackets table row cell bold minus bold 1 end cell bold 1 bold 2 row bold 8 cell bold minus bold 19 end cell bold 6 row cell bold minus bold 3 end cell bold 14 cell bold minus bold 5 end cell end table close square brackets bold space bold apostrophe bold space bold A to the power of bold minus bold 1 end exponent bold space bold equals bold space bold 1 over bold 11 bold space bold adj bold space bold A open square brackets table row bold x row bold y row bold z end table close square brackets bold space bold equals bold space bold 1 over bold 11 bold space open square brackets table row cell bold minus bold 1 end cell bold 1 bold 2 row bold 8 cell bold minus bold 19 end cell bold 6 row cell bold minus bold 3 end cell bold 14 cell bold minus bold 5 end cell end table close square brackets bold space open square brackets table row bold 8 row bold 5 row bold 7 end table close square brackets bold space bold equals bold space bold 1 over bold 11 bold space open square brackets table row cell bold minus bold 8 end cell cell bold plus bold 5 end cell cell bold plus bold 14 end cell row bold 64 cell bold minus bold 95 end cell cell bold plus bold 42 end cell row cell bold minus bold 24 end cell cell bold plus bold 70 end cell cell bold minus bold 35 end cell end table close square brackets bold space bold equals bold space bold 1 over bold 11 open square brackets table row bold 11 row bold 11 row bold 11 end table close square brackets bold space bold equals bold space open square brackets table row bold 1 row bold 1 row bold 1 end table close square brackets bold x bold space bold equals bold space bold 1 bold comma bold space bold y bold space bold equals bold space bold 1 bold comma bold space bold z bold space bold equals bold space bold 1 bold space$

નોંધ : દેખીતું જ (1,1,1) ઉકેલ છે, તે પ્રત્યક્ષ ચકાસણીથી મળે.

33.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 2 bold 2 row bold 2 bold 5 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 2 bold 1 row cell bold minus bold 1 end cell bold 2 end table close square brackets bold space bold ત ો bold space bold B to the power of bold minus bold 1 end exponent bold AB bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.

$open square brackets table row bold 1 bold 0 row bold 0 cell bold minus bold 6 end cell end table close square brackets$
$open square brackets table row bold 1 bold 0 row bold 0 bold 6 end table close square brackets bold space$
$open square brackets table row bold 5 bold 0 row bold 0 bold 30 end table close square brackets bold space$
$open square brackets table row cell bold minus bold 1 end cell bold 0 row bold 0 bold 6 end table close square brackets$

34.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 3 bold 3 bold 3 row bold 3 bold 3 bold 3 row bold 3 bold 3 bold 3 end table close square brackets bold space bold ત ો bold space bold space bold A to the power of bold 3 bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space

27A
81A
243A
729A

35.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 4 bold 4 row cell bold minus bold 3 end cell bold 4 end table close square brackets bold semicolon bold space bold B 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 bold space bold ત ો bold space bold left parenthesis bold left parenthesis bold B to the power of bold minus bold 1 end exponent bold A to the power of bold minus bold 1 end exponent bold right parenthesis to the power of bold minus bold 1 end exponent

$open square brackets table row bold 4 cell bold minus bold 4 end cell row bold 4 bold 3 end table close square brackets$
$bold 1 over bold 10 open square brackets table row bold 3 bold 4 row cell bold minus bold 4 end cell bold 4 end table close square brackets$
$fraction numerator begin display style bold 1 end style over denominator begin display style bold 10 end style end fraction open square brackets table row bold 4 cell bold minus bold 4 end cell row bold 4 bold 3 end table close square brackets bold space$
$open square brackets table row bold 4 cell bold minus bold 4 end cell row bold 4 bold 4 end table close square brackets$

36.

bold A bold space bold equals bold space open square brackets table row bold sinθ bold cosθ row cell bold minus bold cosθ end cell bold sinθ end table close square brackets bold ત ો bold space bold AA to the power of bold T bold space bold equals bold space bold. bold. bold. bold. bold. bold space

A
I
A^T
એક પણ નહિ.

37.

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

$open square brackets table row bold n bold mn row bold 0 bold n end table close square brackets$
$open square brackets table row bold n bold n row bold 0 bold n end table close square brackets$
$open square brackets table row bold 1 bold mn row bold 0 bold 1 end table close square brackets$
$open square brackets table row bold 1 cell bold m to the power of bold n end cell row bold 0 bold 1 end table close square brackets$