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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

51.

જો (k, 5), (6,7), (2, 3) શિરોબિંદુવાળા ત્રિકોણનું ક્ષેત્રફળ 10 હોય તો k = .......... છે.

9 અથવા 1
-9 અથવા 1
9 અથવા -1
-9 અથવા -1

52. $open vertical bar table row bold x cell bold x bold plus bold y end cell cell bold x bold plus bold 2 bold y end cell row cell bold x bold plus bold 2 bold y end cell bold x cell bold x bold plus bold y end cell row cell bold x bold plus bold y end cell cell bold x bold plus bold 2 bold y end cell bold x end table close vertical bar$ નું મૂલ્ય ...... છે.

x² (x+y)
y² (x+y)
9y² (x+y)
9x² (x+y)

53.

open vertical bar table row cell bold 3 to the power of bold 2 end cell cell bold 4 to the power of bold 2 end cell cell bold 5 to the power of bold 2 end cell row cell bold 9 to the power of bold 2 end cell cell bold 40 to the power of bold 2 end cell cell bold 41 to the power of bold 2 end cell row cell bold 5 to the power of bold 2 end cell cell bold 12 to the power of bold 2 end cell cell bold 13 to the power of bold 2 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space

25
13²
0
41²

54. જો $open vertical bar table row cell bold f bold left parenthesis bold alpha bold right parenthesis end cell cell bold sin bold space bold alpha end cell cell bold cos bold space bold alpha end cell row bold 1 cell bold cos bold space bold alpha end cell cell bold sin bold space bold alpha end cell row cell bold minus bold 1 end cell cell bold sin bold space bold alpha end cell cell bold minus bold cos bold space bold alpha end cell end table close vertical bar bold space bold equals bold space bold 0$ તો f(α) નિ વિસ્તાર ...... છે.

$bold left square bracket bold minus square root of bold 2 bold comma bold space square root of bold 2 bold right square bracket$
$bold left parenthesis bold minus bold 2 bold comma bold space square root of bold 2 bold right parenthesis$
[0, 2]
(0, 2)

bold left square bracket bold minus square root of bold 2 bold comma bold space square root of bold 2 bold right square bracket

Tips: -

f(α) (-cos²^{α - sin2}α) - sin α (-cos α + sin α)+cos α (sin α + cos α) = 0

∴ f(α) = cos 2α + sin2 α

cos 2α + sin2 α નો વિસ્તાર $bold left square bracket bold minus bold space square root of bold 2 bold comma bold space square root of bold 2 bold right square bracket$ છે.

∴ f(α) નો વિસ્તાર $bold left square bracket bold minus square root of bold 2 bold comma bold space square root of bold 2 bold right square bracket$

55. $open vertical bar table row cell bold 1 bold plus bold sin to the power of bold 2 bold theta end cell cell bold sin to the power of bold 2 bold theta end cell cell bold sin to the power of bold 2 bold theta end cell row cell bold cos to the power of bold 2 bold theta end cell cell bold 1 bold plus bold cos to the power of bold 2 bold theta end cell cell bold cos to the power of bold 2 bold theta end cell row cell bold 4 bold sin bold 4 bold theta end cell cell bold 4 bold sin bold 4 bold theta end cell cell bold 1 bold plus bold 4 bold sin bold space bold 4 bold theta end cell end table close vertical bar bold space bold equals bold space bold 0$ અને $bold minus bold pi over bold 2 bold space bold less or equal than bold space bold theta bold space bold less or equal than bold space bold 0$ હોય,તો θ = ....

$bold minus bold pi over bold 24 bold comma fraction numerator bold minus bold 5 bold pi over denominator bold 24 end fraction$
$bold minus bold pi over bold 16 bold comma bold space fraction numerator bold minus bold pi over denominator bold 48 end fraction$
$bold minus bold pi over bold 16 bold minus bold pi over bold 3$
કિંમત મળે નહી.

56.

2x + 5y = 9xy, 4x + 3y = 11xy(y#0)(x#0) નો ઉકેલ ....... છે.

$open parentheses bold minus bold 1 over bold 3 bold comma bold 2 close parentheses$
$open parentheses bold 1 bold comma bold 1 over bold 2 close parentheses$
$open parentheses bold minus bold 1 bold comma bold space bold 1 over bold 2 close parentheses$
$open parentheses bold minus bold 1 over bold 3 bold comma bold space bold minus bold 2 close parentheses$

57. a = 2 sin θ તો $open vertical bar table row bold a bold 1 bold 0 row bold 1 bold a bold 1 row bold 0 bold 1 bold a end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.$

$bold 4 bold space bold sin to the power of bold 2 bold space bold theta bold space bold left parenthesis bold cosθ bold space bold minus bold space bold 1 bold right parenthesis$
$bold minus fraction numerator bold sin bold 4 bold theta over denominator bold cosθ end fraction$
$bold minus fraction numerator bold 2 bold space bold sin to the power of bold 2 bold space bold 2 bold theta over denominator bold cosθ end fraction$
આપેલ પૈકી એક પણ નહી

58.

જો $open vertical bar table row bold x bold 5 bold 9 row bold 16 cell bold 3 bold x bold plus bold 8 end cell bold 36 row bold 3 cell bold ` bold 1 end cell bold 7 end table close vertical bar bold space bold equals bold space bold 0$ હોય તો x= ..............

4 અથવા $bold minus bold space bold 23 over bold 21$
-4 અથવા $bold minus bold 23 over bold 21$
4 અથવા $bold 23 over bold 21$
-4 અથવા $bold 23 over bold 21$

59. $open vertical bar table row cell bold 2 bold x bold plus bold 3 bold y end cell cell bold y bold plus bold z end cell cell bold z bold plus bold x end cell row cell bold 2 bold y bold plus bold 3 bold z end cell cell bold z bold plus bold x end cell cell bold x bold plus bold y end cell row cell bold 2 bold z bold plus bold 3 bold x end cell cell bold x bold plus bold y end cell cell bold y bold plus bold z end cell end table close vertical bar bold space bold equals bold space bold k bold space open vertical bar table row bold x bold y bold z row bold y bold z bold x row bold z bold x bold y end table close vertical bar$ તો k = ....... .

60.

bold જ ો bold space open vertical bar table row cell bold 6 bold i end cell cell bold minus bold 3 bold i end cell bold 1 row bold 4 cell bold 3 bold i end cell cell bold minus bold 1 end cell row bold 20 bold 3 bold i end table close vertical bar bold equals bold space bold c bold space bold plus bold space bold ib bold space bold હ ો ય bold comma bold space bold ત ો bold space bold left parenthesis bold c bold comma bold space bold b bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold.

(-1, 0)
(1,3)
(0, 3)
(0,0)

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

2x + 5y = 9xy, 4x + 3y = 11xy(y#0)(x#0) નો ઉકેલ ....... છે.

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