Binomial Theorem

JEE Main 2025 (Online) 22nd January Morning ShiftNumericalMedium📈 Topic in 47% papers+4

Ques. 1JEE Main 2025, 22 January (Morning Shift)

If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .

Answer

2035

Solution

11Ckk+1= 12Ck+112 with k=2r+1.

Sum = 112 (12C2+12C4+ +12C12 )

Even-place coefficients of (1+x)12 add to 211, so the bracket =211-1=2047

mn= 204712 (coprime) m-n=2035

Answer: 2035

Keep practising — Binomial Theorem

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Let , , and be the coefficients of x7,x5,x3 and x respectively in the expansion of (x+ x3-1 )5+ (x- x3-1 )5, x>1. If u and v satisfy the equations u+ v=18, u+ v=20, then u+v equals :

Ques. 3JEE Main 2025, 22 January (Evening Shift)

If r=130 r2 (30Cr )230Cr-1= 229, then 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)