1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The total number of terms in the expansion of (x+y)50+(xâˆ’y)50 is

A
51
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
26
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
102
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
25
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## Consider given the expression,(x+y)50+(x−y)50We know that,(x+y)n=nC0xn+nC1xn−1y+nC2xn−2y2+......nCrxn−ryr.....nCnynNow,(x+y)50+(x−y)50=50C0x50+50C1x49y+50C2x48y2+.....50C50y50+50C0x50−50C1x49y+50C2x48y2+.....+50C50y50=2[50C0x50+50C2x50−2y+50C4x50−4y4+......50Crx50−ryr.....50C50y50]Here, 50C0,50C1,50C2,...50C49,50C50 contain 51 terms.In 26-coefficients , r is even.In 25-coefficients, r is odd.Therefore, there are 26 termsHence, Option B is correct.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
General Term
MATHEMATICS
Watch in App
Join BYJU'S Learning Program