Binomial Theorem

JEE Main 2024 (Online) 29th January Morning ShiftNumericalMedium📈 Topic in 43% papers+4

Ques. 1JEE Main 2024, 29 January (Morning Shift)

If 11C12+ 11C23+ + 11C910= nm with (n,m)=1, then n+m is equal to .

Answer

2041

Solution

∵ 11Crr+1= 112 12Cr+1

Sum = 112 (12C2+12C3+ +12C10 )

= 112 (212-12C0-12C1-12C11-12C12 )

= 4096-2612= 20356

⇒ n = 2035, m = 6 ⇒ n + m = 2041

Answer: 2041

Keep practising — Binomial Theorem

Ques. 2JEE Main 2024, 29 January (Evening Shift)

Remainder when 643232 is divided by 9 is equal to .

Ques. 3JEE Main 2024, 27 January (Morning Shift)

If A denotes the sum of all the coefficients in the expansion of (1-3x+10x2 )n and B denotes the sum of all the coefficients in the expansion of (1+x2 )n, then :

B=A3
3A=B
A=3B
A=B3

Ques. 4JEE Main 2024, 27 January (Evening Shift)

The coefficient of x2012 in the expansion of (1-x)2008 (1+x+x2 )2007 is equal to .

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Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

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