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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

61.

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

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

open parentheses bold 16 bold comma bold 272 over bold 3 close parentheses

Tips: -

$bold left parenthesis bold 1 bold space bold plus bold space bold ax bold space bold plus bold space bold bx to the power of bold 2 bold space bold right parenthesis bold space bold left parenthesis bold 1 bold space bold minus bold space bold 2 bold x bold right parenthesis to the power of bold 18 bold space bold equals bold space bold left parenthesis bold 1 bold space bold plus bold space bold ax bold space bold plus bold space bold bx to the power of bold 2 bold right parenthesis bold space open parentheses bold 1 bold minus open parentheses table row bold 18 row bold 1 end table close parentheses bold space bold 2 bold x bold plus open parentheses table row bold 18 row bold 2 end table close parentheses bold space bold left parenthesis bold 2 bold x bold right parenthesis to the power of bold 2 bold minus open parentheses table row bold 18 row bold 3 end table close parentheses bold space bold left parenthesis bold 2 bold x bold right parenthesis to the power of bold 3 bold space bold plus bold space open parentheses table row bold 18 row bold 4 end table close parentheses bold space bold left parenthesis bold 2 bold x bold right parenthesis to the power of bold 4 bold space bold minus bold space bold. bold. bold. close parentheses$

હવે x³ નો સહગુણક $bold equals bold space bold minus bold space open parentheses table row bold 18 row bold 3 end table close parentheses bold space bold 2 to the power of bold 3 bold space bold plus bold space bold a bold space open parentheses table row bold 18 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold space bold minus bold space bold b bold space open parentheses table row bold 18 row bold 1 end table close parentheses bold space bold 2 bold space bold equals bold space bold 0 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 1 bold right parenthesis$

x⁴ નો સહગુણક $bold equals bold space open parentheses table row bold 18 row bold 4 end table close parentheses bold space bold 2 to the power of bold 4 bold space bold plus bold space bold a bold space open parentheses bold minus open parentheses table row bold 18 row bold 3 end table close parentheses bold space bold 2 to the power of bold 3 close parentheses bold space bold plus bold space bold b bold space open parentheses table row bold 18 row bold 2 end table close parentheses bold space bold 2 to the power of bold 2 bold space bold equals bold space bold 0 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 2 bold right parenthesis$

(1) પરથી - 153 a + 9b + 1632 = 0 આથી -51 a + 3b + 544 = 0

(2) પરથી 32 a - 3b - 240 = 0 આથી -19a + 304 = 0

$bold therefore bold space bold a bold space bold equals bold space bold 16 bold.$ આથી $bold b bold space bold equals bold space bold 272 over bold 3$

$bold therefore bold space bold left parenthesis bold a bold comma bold space bold b bold right parenthesis bold space bold equals bold space open parentheses bold 16 bold comma bold space bold 272 over bold 3 close parentheses$

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

210
310
120
4

63.

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

64.

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
$open parentheses table row bold 20 row bold 10 end table close parentheses$
$bold minus open parentheses table row bold 20 row bold 10 end table close parentheses$

65. 8²ⁿ-(62)²ⁿ⁺¹ ને 9 વડે ભાગતાં....... શેષ મળે.

66.

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

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

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.

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

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

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

70.

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 $open parentheses table row bold p row bold q end table close parentheses bold space bold equals bold space bold 0$ )

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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

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