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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.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row cell bold sin bold space bold alpha end cell cell bold minus bold cosec bold space bold alpha end cell row cell bold cos bold space bold alpha end cell cell bold sin bold space bold alpha end cell end table close square brackets bold space bold space bold તથ ા bold space bold A bold space bold plus bold space bold A bold apostrophe bold space bold equals bold space bold I bold space bold હ ો ય bold comma 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 0 bold space bold less than bold space bold alpha bold space bold less than bold space bold pi over bold 2 bold.

$bold pi over bold 2$
0
$bold pi over bold 6$
$bold pi over bold 3$

33.

bold જ ો bold space bold A bold space bold equals bold space open square brackets table row bold 4 bold 3 row bold 2 bold 5 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 mA bold space bold plus bold space bold nl bold space bold equals bold space bold 0 bold space bold ત ો bold comma bold space

m = 9, n = -14
m = 9, n = 14
m = -9, n = -14
m = -9. n = 14

m = 9, n = 14

Tips: -

$bold A to the power of bold 2 bold space bold equals bold space open square brackets table row bold 4 bold 3 row bold 2 bold 5 end table close square brackets open square brackets table row bold 4 bold 3 row bold 2 bold 5 end table close square brackets bold space bold equals bold space open square brackets table row bold 22 bold 27 row bold 18 bold 31 end table close square brackets bold space bold A to the power of bold 2 bold space end exponent bold minus bold space bold mA bold space bold plus bold space bold nI bold space bold equals bold space bold 0 bold space bold આથ ી bold space bold A to the power of bold 2 bold space bold equals bold space bold mA bold space bold minus bold space bold nI bold space open square brackets table row bold 22 bold 27 row bold 18 bold 31 end table close square brackets bold space bold equals bold space bold m bold space open square brackets table row bold 4 bold 3 row bold 2 bold 5 end table close square brackets bold space bold minus bold space open square brackets table row bold n bold 0 row bold 0 bold n end table close square brackets bold space bold space bold equals bold space open square brackets table row cell bold 4 bold m bold minus bold n end cell cell bold 3 bold m end cell row cell bold 2 bold m end cell cell bold 5 bold m bold minus bold n end cell end table close square brackets bold space$

∴ 4m-n=22 અને 3m = 27 પરથી m = 9, n = 14, તે 2m = 18, 5m - n = 31 નું સમાધાન પણ કરે છે.

નોંધ : ખરેખર તો $bold A bold space bold equals bold space open square brackets table row bold a bold b row bold c bold d end table close square brackets$ તો A² - (a + d) A + |A| I = 0
∴ m = a+d = 9 n = |A| = 14

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 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

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

37.

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

38.

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.

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