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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

21. $open vertical bar table row cell bold a bold minus bold b bold minus bold c end cell cell bold 2 bold a end cell cell bold 2 bold a end cell row cell bold 2 bold b end cell cell bold b bold minus bold c bold minus bold a end cell cell bold 2 bold b end cell row cell bold 2 bold c end cell cell bold 2 bold c end cell cell bold c bold minus bold a bold minus bold b end cell end table close vertical bar bold space bold equals bold space bold left parenthesis bold a bold plus bold b bold plus bold c bold right parenthesis to the power of bold k$ તો k = ....... (a+b+c≠1)

22. જો $bold A subscript bold r bold space bold equals bold space open vertical bar table row bold r cell bold r bold minus bold 1 end cell row cell bold r bold minus bold 1 end cell bold r end table close vertical bar$ જ્યાં r ∈ N તો $bold sum from bold r bold equals bold 1 to bold 15 of bold A subscript bold r bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space bold.$

225
25
15
આપેલ પૈકી એક પણ નહી

23. $open vertical bar table row cell bold x bold minus bold 2 end cell cell bold 2 bold x bold minus bold 3 end cell cell bold 3 bold x bold minus bold 4 end cell row cell bold x bold minus bold 4 end cell cell bold 2 bold x bold minus bold 9 end cell cell bold 3 bold x bold minus bold 16 end cell row cell bold x bold minus bold 8 end cell cell bold 2 bold x bold minus bold 27 end cell cell bold 3 bold x bold minus bold 64 end cell end table close vertical bar bold space bold equals bold space bold 0$ નો ઉકેલગણ ........ છે.

{4}
{2}
{3}
{1}

24. $open vertical bar table row cell bold 10 bold factorial end cell cell bold 11 bold factorial end cell cell bold 12 bold factorial end cell row cell bold 11 bold factorial end cell cell bold 12 bold factorial end cell cell bold 13 bold factorial end cell row cell bold 12 bold factorial end cell cell bold 13 bold factorial end cell cell bold 14 bold factorial end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold space$

2 (10 ! 12 ! 13 !)
2 (10! 11! 12!)
2 (10! 11!)
2 (10! × 13!)

25. જો l,m,n એવી વાસ્તવિક સંખ્યાઓ હોય, કે જેથી l² + m² + n² = 0 તો $open vertical bar table row cell bold 1 bold plus bold l to the power of bold 2 end cell bold lm bold ln row bold lm cell bold 1 bold plus bold m to the power of bold 2 end cell bold mn row bold nl bold mn cell bold 1 bold plus bold n to the power of bold 2 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold. bold space$

l + m + n + 2
lmn - 1
0
1

26. $open vertical bar table row cell bold 1 bold plus bold a end cell bold 1 bold 1 row bold 1 cell bold 1 bold plus bold b end cell bold 1 row bold 1 bold 1 cell bold 1 bold plus bold c end cell end table close vertical bar bold space bold equals bold space bold 0$ તો a^-1 + b^-1 + c^-1 = ....

(abc)^-1
1
-1
abc

-1

Tips: -

$open vertical bar table row bold a cell bold minus bold b end cell bold 0 row bold 0 bold b cell bold minus bold c end cell row bold 1 bold 1 cell bold 1 bold plus bold c end cell end table close vertical bar bold space bold equals bold space bold 0 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left parenthesis bold R subscript bold 21 bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold comma bold space bold R subscript bold 32 bold left parenthesis bold minus bold 1 bold right parenthesis$

∴ a (b + bc + c) + b (c) = 0

ab + abc + ac + bc = 0

ab + bc + ca = -abc

bold therefore bold space bold 1 over bold a bold space bold plus bold space bold 1 over bold b bold space bold plus bold space bold 1 over bold c bold space bold equals bold space bold minus bold 1

27. $open vertical bar table row cell bold a bold plus bold x end cell bold b bold c row bold a cell bold b bold plus bold y end cell bold c row bold a bold b cell bold c bold plus bold z end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold.$

$bold abc bold space open parentheses bold 1 bold plus bold a over bold x bold plus bold b over bold y bold plus bold c over bold z close parentheses$
$bold xyz bold space open parentheses bold 1 bold plus bold a over bold x bold plus bold b over bold y bold plus bold c over bold z close parentheses$
$bold abc bold space open parentheses bold 1 bold plus bold x over bold a bold plus bold y over bold b bold plus bold z over bold c close parentheses$
$bold xyz bold space open parentheses bold 1 bold plus bold x over bold a bold plus bold y over bold b bold plus bold z over bold c close parentheses$

28. જો $open vertical bar table row bold a bold b cell bold a bold minus bold b end cell row bold b bold c cell bold b bold minus bold c end cell row bold 2 bold 1 bold 0 end table close vertical bar bold space bold equals bold space bold 0$ તો a, b, c એ ....... માં છે.

સમગુણોત્તર શ્રેણી
સમાંતર શ્રેણી
સ્વરિત શ્રેણી
આપેલ પૈકી એક પણ નહી

29. જો $bold D subscript bold r bold space bold equals bold space open vertical bar table row bold 1 bold n bold n row cell bold 2 bold r end cell cell bold n to the power of bold 2 bold plus bold n bold plus bold 1 end cell cell bold n to the power of bold 2 bold plus bold n end cell row cell bold 2 bold r bold minus bold 1 end cell cell bold n to the power of bold 2 end cell cell bold n to the power of bold 2 bold plus bold n bold plus bold 1 end cell end table close vertical bar$ અને $bold sum from bold r bold equals bold 1 to bold n of bold space bold D subscript bold r bold space bold equals bold space bold 56$ તો n = ........ .

30. $open vertical bar table row cell square root of bold 14 bold plus square root of bold 3 end cell cell square root of bold 20 end cell cell square root of bold 5 end cell row cell square root of bold 15 bold plus square root of bold 28 end cell cell square root of bold 25 end cell cell square root of bold 10 end cell row cell bold 3 bold plus square root of bold 70 end cell cell square root of bold 15 end cell cell square root of bold 25 end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space bold.$

$bold 25 bold space square root of bold 3 bold space bold minus bold space bold 15 bold space square root of bold 2$
$bold 15 bold space square root of bold 2 bold space bold minus bold space bold 25 bold space square root of bold 3$
$bold 15 bold space square root of bold 2 bold space bold plus bold space bold 25 bold space square root of bold 3$
$bold minus bold 25 bold space square root of bold 3 bold space bold minus bold space bold 15 bold space square root of bold 2$

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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

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