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CBSE

Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

41. જો $bold A bold space bold equals bold space open square brackets table row cell bold 3 bold a end cell bold b bold c row bold b cell bold 3 bold c end cell bold a row bold c bold a cell bold 3 bold b end cell end table close square brackets$ ; a,b,c ∈ R, abc = 1, AAT = 64 I અને |A| > તો (a³ + B³ + C³)³

42.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 1 bold cotθ row bold cotθ bold 1 end table close square brackets bold space bold મ ા ટ ે bold space bold left parenthesis bold A to the power of bold minus bold 1 end exponent bold right parenthesis to the power of bold 2 bold space bold F bold left parenthesis bold theta bold right parenthesis bold space open square brackets table row cell bold minus bold cos bold 2 bold theta end cell cell bold minus bold sin bold 2 bold theta end cell row cell bold sin bold 2 bold theta end cell cell bold minus bold cos bold 2 bold theta end cell end table close square brackets bold space bold ત ો bold space bold f bold left parenthesis bold theta bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

cos²θ
cos θ
sin θ
sin²θ

43. જો ચોરસ શ્રેણિક A અને B માટે AB અને BA = B તો B² = ......

44.

bold A bold space bold equals bold space open square brackets table row bold 1 bold 3 row bold 3 bold 4 end table close square brackets bold space bold અન ે bold space bold A to the power of bold 2 bold space bold minus bold space bold 5 bold A bold space bold equals bold space bold kI bold space bold ત ો bold space bold space bold k bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

Tips: -

bold A bold space bold equals bold space open square brackets table row bold 1 bold 3 row bold 3 bold 4 end table close square brackets bold space open square brackets table row bold 1 bold 3 row bold 3 bold 4 end table close square brackets bold space bold equals bold space open square brackets table row bold 10 bold 15 row bold 15 bold 25 end table close square brackets bold A to the power of bold 2 bold space end exponent bold minus bold space bold 5 bold A bold space bold equals bold space open square brackets table row bold 10 bold 15 row bold 15 bold 25 end table close square brackets bold space bold plus bold space open square brackets table row cell bold minus bold 5 end cell cell bold minus bold 15 end cell row cell bold minus bold 15 end cell cell bold minus bold 20 end cell end table close square brackets bold equals bold space open square brackets table row bold 5 bold 0 row bold 5 bold 0 end table close square brackets bold space bold minus bold space bold 5 open square brackets table row bold 1 bold 0 row bold 0 bold 1 end table close square brackets bold space bold equals bold space bold 5 bold I bold therefore bold space bold k bold space bold equals bold space bold 5

45.

જો સમીકરણ λx + 2y - 2z = I, 4x + 2λy - z = 2 અને 6x + 6y + λz = 3, નો અનન્ય ઉકેલ મળે તો,

λ#1
λ#2
λ#3
λ#-2

46.

bold જ ો 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 comma bold space bold B bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space bold જ ે થ ી bold space bold space bold AB bold space bold equals bold space bold BA bold. bold space bold જ ્ ય ાં bold space bold B bold space bold # bold space bold 1 bold space

$open square brackets table row bold x bold x row bold 1 bold x end table close square brackets$
$open square brackets table row bold x bold y row bold 0 bold y end table close square brackets$
$open square brackets table row bold x bold y row bold 0 bold x end table close square brackets$
$open square brackets table row bold x bold x row bold y bold 0 end table close square brackets$

47. જો $bold A bold space bold equals bold space open square brackets table row cell bold minus bold 1 end cell cell bold minus bold 2 end cell cell bold minus bold 2 end cell row bold 2 bold 1 cell bold minus bold 2 end cell row bold 2 cell bold minus bold 2 end cell bold 1 end table close square brackets$ તો adj A = .......

3A^T
3A
A^T
A

48.

bold જ ો bold space bold 2 bold space bold X bold space bold plus bold space open square brackets table row bold 1 bold 2 row bold 3 bold 4 end table close square brackets bold space bold equals bold space open square brackets table row bold 3 bold 8 row bold 7 bold 2 end table close square brackets bold space bold ત ો bold space bold X bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

$open square brackets table row bold 1 bold 3 row bold 2 cell bold minus bold 1 end cell end table close square brackets$
$open square brackets table row bold 1 cell bold minus bold 3 end cell row bold 2 cell bold minus bold 1 end cell end table close square brackets$
$bold 2 open square brackets table row bold 1 bold 3 row bold 2 cell bold minus bold 1 end cell end table close square brackets$
$bold 2 bold space open square brackets table row bold 1 cell bold minus bold 3 end cell row bold 2 cell bold minus bold 1 end cell end table close square brackets$