EASY
JEE Main/Advance
IMPORTANT
Earn 100

Using binomial theorem prove that 6n-5n always leaves the remainder 1 when divided by 25.

Important Questions on Binomial Theorem

EASY
JEE Main/Advance
IMPORTANT
Find the last digit, last two digits and last three digits of the number 2727.
MEDIUM
JEE Main/Advance
IMPORTANT
Find numerically greatest term(s) in the expansion of 3-5x15 when x=15.
MEDIUM
JEE Main/Advance
IMPORTANT
Which term is numerically the greatest term in the expansion of 2x+5y34, when x=3 and y=2?
EASY
JEE Main/Advance
IMPORTANT
Find the term in the expansion of 2x-56 which have
(i) Greatest binomial coefficient
(ii) Greatest numerical coefficient
(iii) Algebraically greatest coefficient
(iv) Algebraically least coefficient
EASY
JEE Main/Advance
IMPORTANT

If C0, C1, C2, Cn are the binomial coefficients in the expansion of 1+xn, then prove that:

3·2-12C1+32·22-122C2+33·23-123C3+.+3n·2n-12nCn=23n-3n2n

EASY
JEE Main/Advance
IMPORTANT

If C0,C1,C2,Cn are the binomial coefficients in the expansion of 1+xn then prove that

 C1C0+2C2C1+3C3C2+..+nCnCn-1=nn+12

EASY
JEE Main/Advance
IMPORTANT

If C0,C1,C2,Cn are the binomial coefficients in the expansion of 1+xn then prove that:

C0+C1C1+C2C2+C3C3+C4.Cn-1+Cn=C0C1C2Cn-1n+1nn!

EASY
JEE Main/Advance
IMPORTANT

If C0,C1,C2,Cn are the binomial coefficients in the expansion of 1+xn then prove that

C0-2C1+3C2-4C3+.+-1nn+1Cn=0