JEE Main Questions
Find the coefficient of x9 in the expansion of (x2−3x1)9.
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are ositive, then prove that the coefficients of xpandxq
in the expansion of (1+x)p+q
will be equal.
If the sum of the coefficient in the expansion of (α2x2−2αx+1)51
vanishes, then find the value ofα
Show that the coefficient of the middle term in the expansion of (1+x)2nis equal to the sum of the coefficients of two middle terms in the expansion of (1+x)2n−1.
If the coefficients of (r−5)th and (2r−1)thterms of the expansion (1+x)34 are equal, find r.
If the coefficients of three consecutive terms in the expansion of (1+x)n
are in the ratio 1:7:42, then find the value of n˙
Find the number of terms which are free from radical signs in the expansion of (y1/5+x1/10)55˙
Show that the middle term in the expansion of (1+x)2nisn!(1.3.5(2n−1))2nxn,wheren
is a positive integer.