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Gujarati JEE Mathematics : નિશ્વાયક

Multiple Choice Questions

41. $bold minus bold pi over bold 4 bold space bold less or equal than bold space bold x bold space bold less or equal than bold space bold pi over bold 4$ અંતરાલમાં $open vertical bar table row bold sinx bold cosx bold cosx row bold cosx bold sinx bold cosx row bold cosx bold cosx bold sinx end table close vertical bar bold space bold equals bold space bold 0$ ના ભિન્ન ઉકેલની સખ્યા ...... છે.

42. જો $open vertical bar table row bold 1 bold x cell bold x to the power of bold 2 end cell row cell bold x to the power of bold 2 end cell bold 1 bold x row bold x cell bold x to the power of bold 2 end cell bold 1 end table close vertical bar bold space bold equals bold space bold k to the power of bold 2 bold space bold left parenthesis bold x to the power of bold 2 bold space bold plus bold space bold x bold space bold plus bold space bold 1 bold right parenthesis to the power of bold 2 bold space$ તો k = ...... . (k એ x નું વિધેય છે.)

x
|x-1|
1
0

43. જો a = 1 + 2 + 4 + ... + n પદ સુધી, b = 1 + 3 + 9 + ...+ n પદ સુધી, c = 1 + 5 + 25 + ... + n પદ સુધી, તો $open vertical bar table row bold a cell bold 2 bold b end cell cell bold 4 bold c end cell row bold 2 bold 2 bold 2 row cell bold 2 to the power of bold n end cell cell bold 3 to the power of bold n end cell cell bold 5 to the power of bold n end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold space$

(10)ⁿ
(30)ⁿ
0
2ⁿ + 3ⁿ + 5ⁿ

44.

open vertical bar table row cell bold sum from bold r bold equals bold 1 to bold 16 of bold 2 to the power of bold r end cell bold a cell bold 2 to the power of bold 16 bold minus bold 1 end cell row cell bold 3 bold sum from bold r bold equals bold 1 to bold 16 of bold 4 to the power of bold r end cell bold b cell bold 2 bold left parenthesis bold 4 to the power of bold 16 bold minus bold 1 bold right parenthesis end cell row cell bold 7 bold sum from bold r bold equals bold 1 to bold 16 of bold 8 to the power of bold r end cell bold c cell bold 4 bold left parenthesis bold 8 to the power of bold 16 bold minus bold 1 bold right parenthesis end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space bold.

0
1
a + b + c
ab + bc + ca

45. $open vertical bar table row cell bold a bold plus bold plus bold 2 bold c end cell bold a bold b row bold c cell bold 2 bold a bold plus bold b bold plus bold c end cell bold b row bold c bold a cell bold a bold plus bold 2 bold b bold plus bold c end cell end table close vertical bar bold space bold equals bold space bold k bold space bold left parenthesis bold a bold space bold plus bold space bold b bold space bold plus bold space bold c bold right parenthesis to the power of bold m$ તો k + m = ........ .

46.

$open vertical bar table row cell bold x to the power of bold 2 end cell cell bold y to the power of bold 2 end cell cell bold z to the power of bold 2 end cell row cell bold left parenthesis bold x bold plus bold 1 bold right parenthesis to the power of bold 2 end cell cell bold left parenthesis bold y bold plus bold 1 bold right parenthesis to the power of bold 2 end cell cell bold left parenthesis bold z bold plus bold 1 bold right parenthesis to the power of bold 2 end cell row cell bold left parenthesis bold x bold minus bold 1 bold right parenthesis to the power of bold 2 end cell cell bold left parenthesis bold y bold minus bold 1 bold right parenthesis to the power of bold 2 end cell cell bold left parenthesis bold z bold minus bold 1 bold right parenthesis to the power of bold 2 end cell end table close vertical bar bold space bold equals bold space bold k bold space bold left parenthesis bold x bold space bold minus bold space bold y bold right parenthesis bold space bold left parenthesis bold y bold space bold minus bold space bold z bold right parenthesis bold space bold left parenthesis bold z bold space bold minus bold space bold x bold right parenthesis bold comma$ તો k = ...... x≠y, y≠z, z≠x.

-3
4
3
-4

47. જો m = ...... હોય તો $open vertical bar table row cell open parentheses table row bold 9 row bold 4 end table close parentheses end cell cell open parentheses table row bold 9 row bold 5 end table close parentheses end cell cell open parentheses table row bold 10 row bold m end table close parentheses end cell row cell open parentheses table row bold 10 row bold 6 end table close parentheses end cell cell open parentheses table row bold 10 row bold 7 end table close parentheses end cell cell open parentheses table row bold 11 row cell bold m bold plus bold 2 end cell end table close parentheses end cell row cell open parentheses table row bold 11 row bold 8 end table close parentheses end cell cell open parentheses table row bold 11 row bold 9 end table close parentheses end cell cell open parentheses table row bold 12 row cell bold m bold plus bold 4 end cell end table close parentheses end cell end table close vertical bar bold space bold equals bold space bold 0 bold space$

Tips: -

$open vertical bar table row cell open parentheses table row bold 9 row bold 4 end table close parentheses end cell cell open parentheses table row bold 9 row bold 5 end table close parentheses end cell cell open parentheses table row bold 10 row bold m end table close parentheses end cell row cell open parentheses table row bold 10 row bold 6 end table close parentheses end cell cell open parentheses table row bold 10 row bold 7 end table close parentheses end cell cell open parentheses table row bold 11 row cell bold m bold plus bold 2 end cell end table close parentheses end cell row cell open parentheses table row bold 11 row bold 8 end table close parentheses end cell cell open parentheses table row bold 11 row bold 9 end table close parentheses end cell cell open parentheses table row bold 12 row cell bold m bold plus bold 4 end cell end table close parentheses end cell end table close vertical bar bold space bold equals bold space bold 0 bold space bold therefore bold space open vertical bar table row cell open parentheses table row bold 10 row bold 5 end table close parentheses end cell cell open parentheses table row bold 9 row bold 5 end table close parentheses end cell cell open parentheses table row bold 10 row bold m end table close parentheses end cell row cell open parentheses table row bold 11 row bold 7 end table close parentheses end cell cell open parentheses table row bold 10 row bold 7 end table close parentheses end cell cell open parentheses table row bold 11 row cell bold m bold plus bold 2 end cell end table close parentheses end cell row cell open parentheses table row bold 12 row bold 9 end table close parentheses end cell cell open parentheses table row bold 11 row bold 9 end table close parentheses end cell cell open parentheses table row bold 12 row cell bold m bold plus bold 4 end cell end table close parentheses end cell end table close vertical bar bold space bold equals bold space bold 0 bold space$

જો m = 5 હોય, C₁ = C₃ તો થાય અને નિશ્વાયકનું મૂલ્ય 0 થાય.

(જો D = 0 હોય, તો m = 5 કહેતા નથી.)

48.

open vertical bar table row cell bold 1 bold plus bold i end cell cell bold 1 bold minus bold i end cell bold i row cell bold 1 bold minus bold i end cell bold i cell bold 1 bold plus bold i end cell row bold i cell bold 1 bold plus bold i end cell cell bold 1 bold minus bold i end cell end table close vertical bar bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold. bold. bold.

-4 - 7i
4 + 7i
3 + 7i
7 + 4i

49.

∆ ABC માટે a + b + c ≠ c હોય અને $open vertical bar table row bold a bold b bold c row bold b bold c bold a row bold c bold a bold b end table close vertical bar bold space bold equals bold space bold 0$ હોય, તો sin² A + sin²B + sin² C = ...... .