Binomial Theorem · Question 30

JEE Main 2025 (Online) 2nd April Evening ShiftMCQMedium📈 Topic in 52% papers+4−1

If r=010 ( 10r+1 - 110r ) 11Cr+1 = 11 - 11111010, then is equal to :

Answer

(2) 20

Solution

10r+1 - 110r = 10 - 110r

LHS = 10 r=010 11Cr+1 - r=010 11Cr+110r

Put k = r + 1 (k = 1 to 11):

k=111 11Ck = 211 - 1

k=111 11Ck10k-1 = 10 k=111 11Ck ( 110 )k = 10 [ ( 1110 )11 - 1 ]

LHS = 10(211 - 1) - 10 ( 11111011 - 1 )

= 10 211 - 11111010

= 211 1011 - 11111010 = 2011 - 11111010

= 20

Answer: (2)

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Keep practising — Binomial Theorem

The least value of n for which the number of integral terms in the Binomial expansion of ( [3]7 + [12]11)n is 183, is :

2184
2172
2196
2148

JEE Main 2025 (Online) 29th January Morning Shift

If = 1 + r=16(-3)r-1 12C2r-1, then the distance of the point (12, 3) from the line x - 3y + 1 = 0 is .

JEE Main 2025 (Online) 28th January Morning Shift

Let the coefficients of three consecutive terms Tr, Tr+1 and Tr+2 in the binomial expansion of (a + b)12 be in a G.P. and let p be the number of all possible values of r. Let q be the sum of all rational terms in the binomial expansion of ( [4]3 + [3]4)12. Then p + q is equal to:

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