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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

61.

open parentheses table row bold 20 row bold 0 end table close parentheses bold minus open parentheses table row bold 20 row bold 1 end table close parentheses bold plus open parentheses table row bold 20 row bold 2 end table close parentheses bold minus open parentheses table row bold 20 row bold 3 end table close parentheses bold plus bold. bold. bold. bold plus open parentheses table row bold 20 row bold 10 end table close parentheses bold equals bold space bold. bold. bold. bold. bold. bold space

$bold 1 over bold 2 open parentheses table row bold 20 row bold 10 end table close parentheses$
0
$open parentheses table row bold 20 row bold 10 end table close parentheses$
$bold minus open parentheses table row bold 20 row bold 10 end table close parentheses$

62.

(1 + ax + bx²) (1 - 2x)¹⁸ નું x ની ઘાતના સ્વરૂપમાં વિસ્તરણ કરતાં x³ અને x⁴ ના સહગુણકો 0 હોય, તો (a, b) = ........

$open parentheses bold 14 bold comma bold 272 over bold 3 close parentheses$
$open parentheses bold 14 bold comma bold 251 over bold 3 close parentheses$
$open parentheses bold 16 bold comma bold 272 over bold 3 close parentheses$
$open parentheses bold 16 bold comma bold 251 over bold 3 close parentheses$

63.

(10 + 3x)¹² ના વિસ્તરણમાં x = 4 હોય, ત્યારે મોટામાં મોટું પદ ....... છે. તથા તેનું મૂલ્ય ....... છે.

$bold T subscript bold 7 bold comma bold space open parentheses table row bold 12 row bold 5 end table close parentheses bold space bold 10 to the power of bold 5 bold space bold cross times bold space bold 12 to the power of bold 7$
$bold T subscript bold 8 bold comma bold space open parentheses table row bold 12 row bold 5 end table close parentheses bold space bold left parenthesis bold 120 bold right parenthesis to the power of bold 5 bold space bold cross times bold space bold 144$
$bold T subscript bold 7 bold comma bold space open parentheses table row bold 12 row bold 7 end table close parentheses bold space bold 10 to the power of bold 5 bold space bold cross times bold space bold 12 to the power of bold 8$
$bold T subscript bold 7 bold space bold equals bold space bold T subscript bold 8 bold comma bold space open parentheses table row bold 12 row bold 8 end table close parentheses bold space bold 10 to the power of bold 5 bold times bold 12 to the power of bold 7$

64. $open curly brackets bold x bold plus bold left parenthesis bold x to the power of bold 3 bold minus bold 1 bold right parenthesis to the power of begin inline style bold 1 over bold 2 end style end exponent close curly brackets to the power of bold 5 bold space bold plus bold space open curly brackets bold x bold minus bold x to the power of bold 3 bold minus bold 1 bold right parenthesis to the power of begin inline style bold 1 over bold 2 end style end exponent close curly brackets to the power of bold 5$ એ x માં ...... ઘાતની બહુપદી છે.

65.

$bold left parenthesis bold 1 bold space bold minus bold space bold 2 square root of bold x bold right parenthesis to the power of bold 20$ ના દ્વિપદી વિસ્તરણમાં x ના પૂર્ણાંક ઘાતાંકવાળાં પદોના સહગુણકોનો સરવાળો ....... છે.

$bold 1 over bold 2 bold space bold left parenthesis bold 3 to the power of bold 50 bold plus bold 1 bold right parenthesis$
$bold 1 over bold 2 bold space bold left parenthesis bold 3 to the power of bold 50 bold right parenthesis$
$bold 1 over bold 2 bold space bold left parenthesis bold 3 to the power of bold 50 bold minus bold 1 bold right parenthesis$
$bold 1 over bold 2 bold space bold left parenthesis bold 3 to the power of bold 50 bold plus bold 1 bold right parenthesis$

bold 1 over bold 2 bold space bold left parenthesis bold 3 to the power of bold 50 bold plus bold 1 bold right parenthesis

Tips: -

$bold left parenthesis bold 1 bold minus square root of bold 2 bold x bold right parenthesis to the power of bold 50 bold space bold equals bold space open parentheses table row bold 50 row bold 0 end table close parentheses bold minus open parentheses table row bold 50 row bold 1 end table close parentheses bold space bold left parenthesis bold 2 square root of bold x bold right parenthesis to the power of bold 1 bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold left parenthesis bold 2 square root of bold x bold right parenthesis to the power of bold 2 bold space bold minus bold space open parentheses table row bold 50 row bold 3 end table close parentheses bold space bold left parenthesis bold 2 square root of bold x bold right parenthesis to the power of bold 3 bold space bold plus bold space bold. bold. bold. bold space$
k = x ના પૂર્ણાંક ઘાતાંકવાળાં પદોના સહગુણકોનો સરવાળો

$open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold left parenthesis bold 2 bold right parenthesis to the power of bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold left parenthesis bold 2 bold right parenthesis to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold 2 to the power of bold 50$

હવે $bold left parenthesis bold 1 bold space bold plus bold space bold x bold right parenthesis to the power of bold 50 bold space bold equals bold space open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 50 row bold 1 end table close parentheses bold space bold x bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold x to the power of bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 3 end table close parentheses bold space bold x to the power of bold 3 bold space bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold x to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold x to the power of bold 50 bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 1 bold right parenthesis bold space$

(1) માં x = 2 લેતાં $bold 3 to the power of bold 50 bold space bold equals bold space open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 50 row bold 1 end table close parentheses bold space bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 3 end table close parentheses bold space bold 2 to the power of bold 3 bold space bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold 2 to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold 2 to the power of bold 50 bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 2 bold right parenthesis$
(1) માં x = -2 લેતાં

$bold 1 to the power of bold 50 bold space bold equals bold space open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold minus bold space open parentheses table row bold 50 row bold 1 end table close parentheses bold space bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold space bold minus bold space open parentheses table row bold 50 row bold 3 end table close parentheses bold space bold 2 to the power of bold 3 bold space bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold 2 to the power of bold 4 bold space bold minus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold 2 to the power of bold 50 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 3 bold right parenthesis$

(2) + (3) કરતાં,

$bold 3 to the power of bold 50 bold plus bold 1 bold equals bold 2 bold space open square brackets open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold 2 to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold 2 to the power of bold 50 close square brackets fraction numerator bold 3 to the power of bold 50 bold plus bold 1 over denominator bold 2 end fraction bold space bold equals bold space open square brackets open parentheses table row bold 50 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 50 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold space bold plus bold space open parentheses table row bold 50 row bold 4 end table close parentheses bold space bold 2 to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 50 row bold 50 end table close parentheses bold space bold 2 to the power of bold 50 close square brackets bold space bold equals bold space bold k bold space bold therefore bold space bold k bold space bold equals bold space fraction numerator bold 3 to the power of bold 50 bold plus bold 1 over denominator bold 2 end fraction$

66.

આપેલ ધન પૂર્ણાંક r > 1, n > 2 માટે(1 + x)²ⁿ ના દ્વિપદી વિસ્તરણમાં (3r) માં અને (r+2) માં પદોના સહગુણકો સમાન હોય તો .......

n = 3r
n = 2r
n = 2r + 1
આપેલ પૈકી એક પણ નહી

67. જો n ધન પૂર્ણાંક હોય, તો $bold left parenthesis square root of bold 3 bold space bold plus bold space bold 1 bold right parenthesis to the power of bold 2 bold n end exponent bold space bold minus bold space bold left parenthesis square root of bold 3 bold space bold minus bold space bold 1 bold right parenthesis to the power of bold 2 bold n end exponent$ ....... છે.

એક અયુગ્મ ધન પૂર્ણાંક
એક યુગ્મ ધન પૂર્ણાંક
એક અસંમેય સંખ્યા
એક ધન પૂર્ણાંક સિવાયની સંમેય સંખ્યા

68. $open parentheses fraction numerator bold x bold plus bold 1 over denominator bold x to the power of bold 2 over bold 3 end exponent bold minus bold x to the power of bold 1 over bold 3 end exponent bold plus bold 1 end fraction bold minus fraction numerator bold x bold minus bold 1 over denominator bold x bold minus bold x to the power of bold 1 over bold 2 end exponent end fraction close parentheses to the power of bold 10$ ના વિસ્તરણમાં અચળ પદ ..... છે.

210
310
120
4

69.

જ્યારે m = ...... ત્યારે સરવાળો $bold sum from bold i bold equals bold 0 to bold m of bold space open parentheses table row bold 10 row bold i end table close parentheses bold space open parentheses table row bold 20 row cell bold m bold minus bold i end cell end table close parentheses$ મહત્તમ છે. (જ્યાં જો p < q તો $open parentheses table row bold p row bold q end table close parentheses bold space bold equals bold space bold 0$ )

70. 8²ⁿ-(62)²ⁿ⁺¹ ને 9 વડે ભાગતાં....... શેષ મળે.

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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

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