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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

81.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold x to the power of bold 2 end cell bold sinx bold cosx row bold 2 bold 0 cell bold minus bold 1 end cell row bold a cell bold a to the power of bold 2 end cell cell bold a to the power of bold 3 end cell end table close vertical bar bold space bold ત ો bold space bold f bold " bold space bold left parenthesis bold 0 bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold space$

0
a + a²
a³
a પર આધારિત છે.

82.

જો $bold D subscript bold 1 bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row cell bold x to the power of bold 2 end cell cell bold y to the power of bold 2 end cell cell bold z to the power of bold 2 end cell row bold x bold y bold z end table close vertical bar bold space bold અન ે bold space bold space bold D subscript bold 2 bold space bold equals bold space open vertical bar table row bold 1 bold 1 bold 1 row bold yz bold zx bold xy row bold x bold y bold z end table close vertical bar bold space bold ત ો bold space bold equals bold space bold. bold. bold. bold. bold. bold.$

D₁ = D₂
D₂ = 2D₁
D₁ = -2D₂
D₁ = -D₂

83.

open vertical bar table row cell bold log subscript bold 3 bold 1024 end cell cell bold log subscript bold 8 bold 3 end cell row cell bold log subscript bold 3 bold 8 end cell cell bold log subscript bold 4 bold 9 end cell end table close vertical bar bold space bold cross times bold space bold space open vertical bar table row cell bold log subscript bold 2 bold 3 end cell cell bold log subscript bold 4 bold 3 end cell row cell bold log subscript bold 3 bold 4 end cell cell bold log subscript bold 3 bold 4 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.

84.

λ ની કઈ કિંમત માટે સમીકરણો x - 2y + 3z = 0, -2x + 3y + 2z = 0 અને -8x + λy = 0 નો શૂન્યોત્તર ઉકેલ મળે ? (x#0; y#o;z#0)

85.

open vertical bar table row cell bold 1 bold plus bold x end cell cell bold 1 bold minus bold x end cell cell bold 1 bold minus bold x end cell row cell bold 1 bold minus bold x end cell cell bold 1 bold plus bold x end cell cell bold 1 bold minus bold x end cell row cell bold 1 bold minus bold x end cell cell bold 1 bold minus bold x end cell cell bold 1 bold minus bold x end cell end table close vertical bar bold space bold equals bold space bold 0

નાં બીજ ......... છે.

0,-1
0,1
0,3
0,-3

86.

open vertical bar table row bold a bold b bold c row cell bold a to the power of bold 2 end cell cell bold b to the power of bold 2 end cell cell bold c to the power of bold 2 end cell row bold bc bold ca bold ab end table close vertical bar bold space

નું મુલ્ય ............ છે.

0
(a-b)(b-c)(c-a) (ab + bc + ca)
abc(a-b)(b-c)(c-a)
abc (ab + bc + ca)

(a-b)(b-c)(c-a) (ab + bc + ca)

Tips: -

$open vertical bar table row bold a bold b bold c row cell bold a bold minus bold b end cell cell bold b bold minus bold c end cell cell bold c bold minus bold a end cell row cell bold b bold plus bold c end cell cell bold c bold plus bold a end cell cell bold a bold plus bold b bold space end cell end table close vertical bar bold space bold equals bold space open vertical bar table row cell bold a bold minus bold b end cell cell bold b bold minus bold c end cell bold c row cell bold a to the power of bold 2 bold minus bold b to the power of bold 2 end cell cell bold b to the power of bold 2 bold minus bold c to the power of bold 2 end cell cell bold c to the power of bold 2 end cell row cell bold minus bold c bold left parenthesis bold a bold minus bold b bold right parenthesis end cell cell bold minus bold a bold left parenthesis bold b bold minus bold c bold right parenthesis end cell bold ab end table close vertical bar bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold C subscript bold 12 bold left parenthesis bold minus bold 1 bold right parenthesis bold comma bold space bold C subscript bold 32 bold left parenthesis bold minus bold 1 bold right parenthesis bold space bold equals bold space bold left parenthesis bold a bold minus bold b bold right parenthesis bold left parenthesis bold b bold minus bold c bold right parenthesis bold space open vertical bar table row bold 1 bold 1 bold c row cell bold c bold plus bold b end cell cell bold b bold plus bold c end cell cell bold c to the power of bold 2 end cell row cell bold minus bold c end cell cell bold minus bold a end cell bold ab end table close vertical bar bold space bold equals bold space bold left parenthesis bold a bold minus bold b bold right parenthesis bold left parenthesis bold b bold space bold minus bold c bold right parenthesis bold space open vertical bar table row bold 0 bold 1 bold c row cell bold a bold minus bold c end cell cell bold b bold plus bold c end cell cell bold c to the power of bold 2 end cell row cell bold a bold minus bold c end cell cell bold minus bold a end cell bold ab end table close vertical bar bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold C subscript bold 21 bold left parenthesis bold minus bold 1 bold right parenthesis bold equals bold space bold left parenthesis bold a bold minus bold b bold right parenthesis bold left parenthesis bold b bold minus bold c bold right parenthesis bold left parenthesis bold c bold minus bold a bold right parenthesis bold space open vertical bar table row bold 0 bold 1 bold c row cell bold minus bold 1 end cell cell bold b bold plus bold c end cell cell bold c to the power of bold 2 end cell row cell bold minus bold 1 end cell cell bold minus bold a end cell bold ab end table close vertical bar$

= (a-b)(b-c)(c-a) {ab - c² + ac + bc + c²}

= (a-b)(b-c)(c-a)(ab + bc + ca)

87. $open vertical bar table row cell bold q bold plus bold r end cell bold p bold p row bold q cell bold r bold plus bold p end cell bold q row bold r bold r cell bold p bold plus bold q end cell end table close vertical bar$ નું મૂલ્ય ....... છે.

pqr
0
p+q+r
4 pqr

88. જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold x bold plus bold p end cell bold x bold x row bold x cell bold x bold plus bold p end cell bold x row bold x bold x cell bold x bold plus bold p end cell end table close vertical bar bold space bold ત ો bold space bold f bold left parenthesis bold 2 bold x bold right parenthesis bold space bold minus bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space$

3p²x
3xp³
4px²
6px²

89.

જો $open vertical bar table row bold a bold b bold c row cell bold a bold minus bold b end cell cell bold b bold minus bold c end cell cell bold c bold minus bold a end cell row cell bold b bold plus bold c end cell cell bold c bold plus bold a end cell cell bold a bold plus bold b end cell end table close vertical bar bold space bold equals bold space bold a to the power of bold 3 bold space bold plus bold space bold b to the power of bold 3 bold space bold plus bold space bold c to the power of bold 3 bold space end exponent bold plus bold space bold kabc bold space bold હ ો ય bold comma bold space bold ત ો bold space bold k bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left parenthesis bold a bold # bold 0 bold comma bold space bold b bold # bold 0 bold comma bold space bold c bold # bold 0 bold right parenthesis bold space$

-3
3
-4
4

90.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space open vertical bar table row cell bold sec bold space bold x end cell bold x bold 1 row cell bold 2 bold space bold sinx end cell cell bold x to the power of bold 2 end cell cell bold 2 bold x end cell row cell bold tan bold space bold x end cell bold x bold 1 end table close vertical bar bold space bold ત ો bold space bold lim with bold x bold rightwards arrow bold 0 below bold space fraction numerator bold f bold apostrophe bold left parenthesis bold x bold right parenthesis over denominator bold x end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space$

1
-1
2
-2

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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