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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

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

42.

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

λ#2

Tips: -

λx + 2y - 2z = 1
4x + 2λy - z = 2
6x + 6y + λz = 3

$open square brackets table row bold lambda bold 2 cell bold minus bold 2 end cell row bold 4 cell bold 2 bold lambda end cell cell bold minus bold 1 end cell row bold 6 bold 6 bold lambda end table close square brackets bold space open square brackets table row bold x row bold y row bold z end table close square brackets bold space bold equals bold space open square brackets table row bold 1 row bold 2 row bold 3 end table close square brackets bold vertical line bold A bold vertical line bold space bold equals bold space open square brackets table row bold lambda bold 2 cell bold minus bold 2 end cell row bold 4 cell bold 2 bold lambda end cell cell bold minus bold 1 end cell row bold 6 bold 6 bold lambda end table close square brackets bold space bold # bold space bold 0 bold space bold હ ો ય bold space bold ત ો bold space bold A bold minus bold 1 bold space bold મળ ે bold space bold તથ ા bold space bold અનન ્ ય bold space bold ઉક ે લ bold space bold મળ ે bold. bold space$

▯λ(λ² + 6)‌ - 2 (4λ ‌ 6) - 2 (24 - 12λ) # 0

∴▯2λ³ + 22λ - 60 # 0

∴▯λ³ + 11 λ - 30 # 0

∴▯(λ -2)(λ² + 2λ + 15) # 0

વાસ્તવિક બીજ માટે λ # 2 $table row blank end table$

43.

bold જ ો bold space bold A bold space bold equals bold space bold left square bracket bold 2 bold space bold minus bold space bold 3 bold space bold 4 bold right square bracket bold comma bold space bold B bold space bold equals bold space open square brackets table row bold 3 row bold 2 row bold 1 end table close square brackets bold comma bold space bold X bold space bold equals bold space bold left square bracket bold 0 bold space bold 2 bold space bold 3 bold right square bracket bold space bold અન ે bold space bold Y bold space bold equals bold space open square brackets table row bold 2 row bold 2 row bold 4 end table close square brackets bold space bold ત ો bold space bold AB bold space bold plus bold space bold XY bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

20
-20
[-20]
[20]

44. જો A = diag [3 2 1], તો ઍ-1 ના ઘટકોનો સરવાળો ......... છે.

$bold 1 over bold 6$
$bold 5 over bold 6$
$bold 11 over bold 6$
6

45.

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

46.

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

47.

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

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

48. 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

49.

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

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

50. 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

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Gujarati JEE Mathematics : શ્રેણિક

Multiple Choice Questions

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