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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

31. $open vertical bar table row bold a bold b bold c row bold x bold y bold z row bold p bold q bold r end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold.$

$open vertical bar table row bold y bold b bold q row bold x bold a bold p row bold z bold c bold r end table close vertical bar$
$open vertical bar table row bold y bold q bold b row bold x bold p bold a row bold z bold c bold r end table close vertical bar$
$open vertical bar table row bold b bold y bold q row bold a bold p bold x row bold c bold z bold r end table close vertical bar$
આપેલ પૈકી એક પણ નહી

32.

સમીકરણો 2x + 3y + 5 = 0, x + ky + 5 = 0 અને kx - 12y - 14 = 0 સુસંગત હોય તો k = ....... .

$bold 6 bold comma bold space bold 17 over bold 5$
$bold minus bold 2 bold comma bold space bold 12 over bold 5$
$bold minus bold 6 bold comma bold space bold 17 over bold 5$
$bold minus bold 6 bold comma bold minus bold 17 over bold 5$

33. $bold D bold space bold equals bold space open vertical bar table row bold bc cell bold a to the power of bold 2 end cell cell bold a to the power of bold 2 end cell row cell bold b to the power of bold 2 end cell bold ca cell bold b to the power of bold 2 end cell row cell bold c to the power of bold 2 end cell cell bold c to the power of bold 2 end cell bold ab end table close vertical bar bold space bold અન ે bold space bold D bold apostrophe bold space bold equals bold space open vertical bar table row bold bc bold ab bold ca row bold ab bold ca bold bc row bold ca bold bc bold ab end table close vertical bar$ તો ........ .

D = D'
aD + bD' = 0
bD + aD' = 0
D + D' = 0

34. જો $open vertical bar table row cell bold 1 bold plus bold x end cell bold 1 bold 1 row bold 1 cell bold 1 bold plus bold x end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold x end cell end table close vertical bar bold space bold equals bold space bold 0 bold comma bold space$ તો = ........ .

0, 3
0, ± 3
0, -3
આપેલ પૈકી એક પણ નહી

35.

જો સમીકરણો a(y+z) x; b (z+x) = y, c(x+y) = z નો અનન્ય ઉકેલ મળે, તો $fraction numerator bold 1 over denominator bold 1 bold plus bold a end fraction bold plus fraction numerator bold 1 over denominator bold 1 bold plus bold b end fraction bold plus fraction numerator bold 1 over denominator bold a bold plus bold c end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold left parenthesis bold x bold space bold greater than bold space bold 0 bold comma bold space bold y bold space bold greater than bold space bold 0 bold comma bold space bold z bold space bold greater than bold space bold 0 bold right parenthesis$

-2
-2
1
2

Tips: -

x ≠ 0, y ≠ 0 અને z ≠ 0

ધારો કે $bold a bold space bold equals bold space fraction numerator bold x over denominator bold y bold plus bold z end fraction bold space bold space bold space bold space bold b bold space bold equals bold space fraction numerator bold y over denominator bold z bold plus bold x end fraction bold space bold space bold space bold space bold space bold space bold space bold c bold space bold equals bold space fraction numerator bold z over denominator bold x bold plus bold y end fraction$

$bold 1 bold space bold plus bold space bold a bold space bold equals bold space fraction numerator bold x bold plus bold y bold plus bold z over denominator bold y bold plus bold z end fraction bold semicolon bold space bold 1 bold space bold plus bold space bold b bold space bold equals bold space fraction numerator bold x bold plus bold y bold plus bold z over denominator bold z bold plus bold x end fraction bold space bold 1 bold space bold plus bold space bold c bold space bold equals bold space fraction numerator bold x bold plus bold y bold plus bold z over denominator bold x bold plus bold y end fraction$

હવે $fraction numerator bold 1 over denominator bold 1 bold plus bold a end fraction bold space bold plus bold space fraction numerator bold 1 over denominator bold 1 bold plus bold b end fraction bold space bold plus bold space fraction numerator bold 1 over denominator bold 1 bold plus bold c end fraction$

$bold equals bold space fraction numerator bold y bold plus bold z over denominator bold x bold plus bold y bold plus bold z end fraction bold space bold plus bold space fraction numerator bold z bold plus bold x over denominator bold x bold plus bold y bold plus bold z end fraction bold space bold plus bold space fraction numerator bold x bold plus bold y over denominator bold x bold plus bold y bold plus bold z end fraction bold equals bold space fraction numerator bold 2 bold left parenthesis bold x bold plus bold y bold plus bold z bold right parenthesis over denominator bold x bold plus bold y bold plus bold z end fraction bold space bold equals bold space bold 2$

36. જો $open vertical bar table row cell bold y bold plus bold z end cell cell bold z bold plus bold x end cell cell bold x bold plus bold y end cell row cell bold x bold plus bold y end cell cell bold y bold plus bold z end cell cell bold z bold plus bold x end cell row cell bold z bold plus bold x end cell cell bold x bold plus bold y end cell cell bold y bold plus bold z end cell end table close vertical bar bold space bold equals bold space bold k bold space open vertical bar table row bold x bold y bold z row bold z bold x bold y row bold y bold z bold x end table close vertical bar$ તો k = ......... (x=y=zનથી, x+y+x ≠0)

-4
2
1
4

37. જો $bold D bold space bold equals bold space open vertical bar table row bold 1 bold cosθ bold 1 row cell bold minus bold cosθ end cell bold 1 bold cosθ row cell bold minus bold 1 end cell bold cosθ bold 1 end table close vertical bar$ તો D .......અંતરાલમાં છે.

[1, 4]
[0, 2]
[2, 4]
[0, 4]

38. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold 1 bold x cell bold x bold plus bold 1 end cell row cell bold 2 bold x end cell cell bold x bold left parenthesis bold x bold minus bold 1 bold right parenthesis end cell cell bold left parenthesis bold x bold plus bold 1 bold right parenthesis bold x end cell row cell bold 3 bold x bold left parenthesis bold x bold minus bold 1 bold right parenthesis end cell cell bold x bold left parenthesis bold x bold minus bold 1 bold right parenthesis bold left parenthesis bold x bold minus bold 2 bold right parenthesis end cell cell bold x bold left parenthesis bold x bold plus bold 1 bold right parenthesis bold left parenthesis bold x bold minus bold 1 bold right parenthesis end cell end table close vertical bar$ તો f(100) = .......

1
0
100
-100

39. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row bold 1 bold x cell bold x to the power of bold 2 end cell row bold x cell bold x to the power of bold 2 end cell bold 1 row cell bold x to the power of bold 2 end cell bold 1 bold x end table close vertical bar$ હોય તો $bold f open parentheses root index bold 3 of bold 3 close parentheses$ = ...... .

4
2
-2
-4

40. જો $bold D bold space bold equals bold space open vertical bar table row bold 1 cell bold 3 bold cosθ end cell bold 1 row cell bold sin bold space bold theta end cell bold 1 cell bold 3 bold cosθ end cell row bold 1 bold sinθ bold 1 end table close vertical bar$ તો D નું મહત્તમ મૂલ્ય ........ છે.

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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