Binomial Theorem

JEE Main 2024 (Online) 30th January Evening ShiftNumericalHard📈 Topic in 43% papers+4

Ques. 1JEE Main 2024, 30 January (Evening Shift)

Let = k=0n ( ( n Ck )2k+1 ) and = k=0n-1 ( n Ck n Ck+1k+2 ). If 5 =6 , then n equals .

Answer

Solution

∵ nCrr+1= n+1Cr+1n+1

= 1n+1 k=0nnCn-k n+1Ck+1= 2n+1Cn+1n+1

= 1n+1 k=0n-1nCn-k n+1Ck+2= 2n+1Cn+2n+1

∵ mCr nCs-r=m+nCs (lower indices add to n+1 and n+2)

= 2n+1Cn+22n+1Cn+1= nn+2

5 =6 nn+2= 56 n=10

Answer: 10

Keep practising — Binomial Theorem

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

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

Ques. 3JEE Main 2024, 29 January (Evening Shift)

Remainder when 643232 is divided by 9 is equal to .

Ques. 4JEE 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. 5JEE Main 2024, 27 January (Evening Shift)

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

All Binomial Theorem PYQs →

PDFDownload Binomial Theorem PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

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

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)