Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

How to solve 4th sum
question image
Asked by lovemaan5500 | 25 Jan, 2019, 03:54: PM
answered-by-expert Expert Answer
begin mathsize 12px style L e t space open parentheses 1 plus x plus x squared plus x cubed plus x to the power of 4................. plus x to the power of 9 plus x to the power of 10 close parentheses to the power of 4 space equals space open parentheses a plus b close parentheses to the power of 4
w h e r e space a space equals space 1 plus x plus x squared plus x cubed plus x to the power of 4 plus x to the power of 5 space space space a n d space b space equals space x to the power of 6 plus x to the power of 7 plus x to the power of 8 plus x to the power of 9 plus x to the power of 10
left parenthesis a plus b right parenthesis to the power of 4 space equals space a to the power of 4 plus C presuperscript 4 subscript 1 space a cubed b space plus space C presuperscript 4 subscript 2 space a squared b squared space plus space C presuperscript 4 subscript 3 space a b cubed plus b to the power of 4

l e t space a to the power of 4 space equals space open parentheses c plus d close parentheses to the power of 4 space equals space c to the power of 4 plus C presuperscript 4 subscript 1 space c cubed d space plus space C presuperscript 4 subscript 2 space c squared space d squared space plus space C presuperscript 4 subscript 3 space c space d cubed plus d to the power of 4 space
w h e r e space c space equals space 1 plus x plus x squared space space space a n d space space d space equals space x cubed plus x to the power of 4 plus x to the power of 5
w e space g e t space t e r m s space o f space x to the power of 10 space i n space c cubed d space space a s space a space p r o d u c t space o f space x to the power of 6 x to the power of 4 comma space space x to the power of 5 x to the power of 5
c o e f f i c i e n t space o f space x to the power of 6 x to the power of 4 space i n space c cubed d space equals space 1 cross times 1 space equals 1
c o e f f i c i e n t space o f space x to the power of 5 x to the power of 5 space i n space c cubed d space equals space 3 cross times 1 space equals 3
h e n c e space c o e f f i c i e n t space o f space x to the power of 10 space i n space C presuperscript 4 subscript 1 space c cubed d space equals space 4 left parenthesis 4 right parenthesis space equals space 16 space space.............. left parenthesis 1 right parenthesis

w e space g e t space t e r m s space o f space x to the power of 10 space i n space c squared d squared space space a s space a space p r o d u c t space o f space x to the power of 4 x to the power of 6 comma space space x squared x to the power of 8 comma space 1 x to the power of 10 comma space x cubed x to the power of 7 a n d space x x to the power of 9
h e n c e space c o e f f i c i e n t space o f space x to the power of 10 space i n space C presuperscript 4 subscript 2 space c squared space d squared space space equals space 6 left parenthesis 1 plus 9 plus 1 plus 4 plus 2 right parenthesis space equals space 102 space............................. left parenthesis 2 right parenthesis

w e space g e t space t e r m s space o f space x to the power of 10 space i n space c space d cubed space space a s space a space p r o d u c t space o f space space x x to the power of 9
h e n c e space c o e f f i c i e n t space o f space x to the power of 10 space i n space C presuperscript 4 subscript 3 space c space d cubed space space equals space 4 left parenthesis 1 right parenthesis space equals space 4 space............................. left parenthesis 3 right parenthesis end style
 
Let us calculate the coefficent of x10 in a3b
 
begin mathsize 12px style L e t space a cubed b space space equals space left parenthesis c plus d right parenthesis cubed left parenthesis x to the power of 6 plus x to the power of 7 plus x to the power of 8 plus x to the power of 9 plus x to the power of 10 right parenthesis
w h e r e space c space equals space left parenthesis 1 plus x plus x squared right parenthesis space space a n d space d space equals space x cubed plus x to the power of 4 plus x to the power of 5
w e space g e t space x to the power of 10 space t e r m space i n space a cubed b space a s space p r o d u c t s space o f space x to the power of 4 x to the power of 6 comma space space x cubed x to the power of 7 comma space a n d space x x to the power of 9 space
c o e f f i c i e n t space o f space x to the power of 10 space i n space C presuperscript 4 subscript 1 a cubed b space equals space 4 left parenthesis 1 plus 3 plus 1 right parenthesis space equals space 20 space..................... left parenthesis 4 right parenthesis end style
 
we will not get x10 in other terms of binomial expansion.
hence coefficient of x10  = 16+102+4+20 = 142
Answered by Thiyagarajan K | 28 Jan, 2019, 02:25: PM

Application Videos

CBSE 11-science - Maths
Asked by Manjeet | 23 Mar, 2024, 09:41: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by rambabum3372 | 21 Mar, 2024, 04:51: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by ambedkarrajesh5 | 18 Mar, 2024, 08:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by sukumeyoji | 15 Mar, 2024, 04:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by kanishkatutejasirsa | 09 Mar, 2024, 11:08: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by rajyothi64 | 05 Mar, 2024, 09:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by ghoshshawata62 | 04 Mar, 2024, 08:16: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by ns091764623 | 03 Mar, 2024, 08:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by nayaktapaswini2007 | 29 Feb, 2024, 09:10: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by kartikpramanik728 | 28 Feb, 2024, 07:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×