(1 + 2x)-7 ના વિસ્તરણમાં x10 નો સહગુણક ....... છે. from Mathematics દ્વિપદી પ્રમેય

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE

Subject

Mathematics
Advertisement
zigya logo

Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

1. bold sum from bold r bold equals bold 0 to bold 70 of bold space open parentheses table row bold 70 row bold r end table close parentheses bold space bold left parenthesis bold x bold space bold minus bold space bold 5 bold right parenthesis to the power of bold 70 bold minus bold r end exponent bold space bold 4 to the power of bold r વિસ્તરણમાં x9 નો સહગુણક ....... છે.
  • open parentheses table row bold 70 row bold 9 end table close parentheses
  • bold minus open parentheses table row bold 70 row bold 61 end table close parentheses
  • 0
  • bold minus open parentheses table row bold 70 row bold 8 end table close parentheses

2. (1 + x)-n (n ∈ N) ના વિસ્તરણમાં xr નો સહગુણક ....... છે. ( |x|<1)
  • bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold r bold space open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row bold r end table close parentheses
  • open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row bold r end table close parentheses
  • open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row cell bold n bold plus bold 1 end cell end table close parentheses
  • open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row cell bold r bold minus bold 1 end cell end table close parentheses

3. (a + 2b)3 (2a - b)4 ના વિસ્તરણમાં a3b4 નો સહગુણક ........ છે.
  • 593
  • -16
  • -15
  • 15

Advertisement
4. (1 + 2x)-7 ના વિસ્તરણમાં x10 નો સહગુણક ....... છે.
  • open parentheses table row bold 16 row bold 6 end table close parentheses
  • bold 2 to the power of bold 10 bold space open parentheses table row bold 17 row bold 10 end table close parentheses
  • bold 2 to the power of bold 10 bold space open parentheses table row bold 16 row bold 10 end table close parentheses
  • bold 2 to the power of bold 10 bold space open parentheses table row bold 16 row bold 9 end table close parentheses

C.

bold 2 to the power of bold 10 bold space open parentheses table row bold 16 row bold 10 end table close parentheses

Tips: -

 અહીં bold T subscript bold r bold plus bold 1 end subscript bold space bold equals bold space bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold r bold space open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row bold r end table close parentheses bold space bold left parenthesis bold 2 bold x bold right parenthesis to the power of bold r

     bold T subscript bold 11 bold space bold equals bold space bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold 10 bold space open parentheses table row cell bold 7 bold plus bold 10 bold minus bold 1 end cell row bold 10 end table close parentheses bold space bold 2 to the power of bold 10 bold space bold x to the power of bold 10 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 square bracket bold space bold n bold space bold equals bold space bold 7 bold comma bold space bold r bold space bold equals bold space bold 10 bold right square bracket

          bold equals bold space bold 2 to the power of bold 10 bold space open parentheses table row bold 161 row bold 10 end table close parentheses bold space bold x to the power of bold 10

∴ x10 નો સહગુણક bold equals bold space bold 2 to the power of bold 10 bold space open parentheses table row bold 16 row bold 10 end table close parentheses

Advertisement
Advertisement
5. bold 1 bold space bold times bold space fraction numerator open parentheses table row bold n row bold 1 end table close parentheses over denominator open parentheses table row bold n row bold 0 end table close parentheses end fraction bold space bold plus bold space bold 2 bold space fraction numerator open parentheses table row bold n row bold 2 end table close parentheses over denominator open parentheses table row bold n row bold 1 end table close parentheses end fraction bold space bold plus bold space bold 3 bold space fraction numerator open parentheses table row bold n row bold 3 end table close parentheses over denominator open parentheses table row bold n row bold 2 end table close parentheses end fraction bold space bold plus bold space bold. bold. bold. bold space bold plus bold space bold 31 bold space fraction numerator open parentheses table row bold n row bold 31 end table close parentheses over denominator open parentheses table row bold n row bold 30 end table close parentheses end fraction bold space bold equals bold. bold. bold. bold. bold. bold. bold. bold space
  • 31 (n - 15)
  • 31n - 15
  • 15 (2n-31)
  • 30n-465

6. જો x > 0, y > 0 તો bold sum from bold r bold equals bold 1 to bold infinity of bold space open parentheses fraction numerator bold x over denominator bold 2 bold x bold plus bold 3 bold y end fraction close parentheses to the power of bold r bold minus bold 1 end exponent bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space
  • fraction numerator bold 2 bold x over denominator bold x bold plus bold 3 bold y end fraction
  • fraction numerator bold 2 bold x bold plus bold 3 bold y over denominator bold x bold plus bold 3 bold y end fraction
  • fraction numerator bold 3 bold y over denominator bold 2 bold x bold plus bold 3 bold y end fraction
  • fraction numerator bold 2 bold x bold plus bold 3 bold y over denominator bold 2 bold x bold plus bold y end fraction

7. (1 - x)-n (n ∈ N)ના વિસ્તરણમાં xr નો સહગુણક ......... છે. ( |x| < 1)
  • open parentheses table row cell bold n bold minus bold r bold plus bold 1 end cell row bold r end table close parentheses
  • open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row bold r end table close parentheses
  • open parentheses table row cell bold n bold plus bold r bold minus bold 1 end cell row straight n end table close parentheses
  • bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold r bold space open parentheses table row cell bold n bold minus bold r bold plus bold 1 end cell row bold r end table close parentheses

8. જો (1 - x + x2)-3 = a0 + a1x + a2x2 + ... તો bold sum from bold r bold equals bold 0 to bold 6 of bold space bold a subscript bold r bold space bold equals bold space bold. bold. bold. bold. bold space bold left parenthesis bold vertical line bold x bold vertical line bold space bold less than bold space bold 1 bold right parenthesis bold space
  • -10
  • -7
  • 10
  • 38

Advertisement
9. bold sum from bold r bold equals bold 0 to bold n of bold space bold r bold space open parentheses table row bold n row bold r end table close parentheses bold space open parentheses table row bold 2 row bold 7 end table close parentheses to the power of bold r bold space open parentheses bold 5 over bold 7 close parentheses to the power of bold n bold minus bold r end exponent bold space bold equals bold space bold. bold. bold. bold. bold.
  • 0
  • 1
  • fraction numerator bold 5 bold n over denominator bold 7 end fraction
  • fraction numerator bold 2 bold n over denominator bold 7 end fraction

10. bold left parenthesis bold 1 bold space bold plus bold space bold x bold right parenthesis to the power of bold 40 bold space open parentheses bold 1 bold plus bold 1 over bold x close parentheses to the power of bold 40 ના વિસ્તરણમાં x-2 નો સહગુણક ......છે.
  • open parentheses table row bold 80 row bold 37 end table close parentheses
  • fraction numerator bold 80 bold space bold factorial over denominator bold 38 bold space bold factorial end fraction
  • open parentheses table row bold 80 row bold 38 end table close parentheses
  • open parentheses table row bold 107 row bold 38 end table close parentheses

Advertisement

Switch