Binomial Theorem · Question 2

JEE Advanced 2025 Paper 2NumericalMedium📈 Topic in 17% papers+4

Let a0,a1, ,a23 be real numbers such that (1+ 25x )23= i=023ai xi for every real number x. Let ar be the largest among the numbers aj for 0 j 23. Then the value of r is .

Answer

Solution

ak=23Ck ( 25 )k, all positive.

ak+1ak= 23-kk+1 25 1 46-2k 5k+5 k 417 5.86.

So ak increases up to k=6 and decreases after it: largest is a6.

Answer: 6

JEE Advanced 2025 Paper 2

Keep practising — Binomial Theorem

Let R denote the set of all real numbers. Consider the polynomial function f: R R defined by f(x)= d10dx10 ((x2-1)10 ), for all x R. Here d10dx10 ((x2-1)10 ) is the 10th order derivative of the function (x2-1)10. Then which of the following statements is (are) TRUE ?

The coefficient of x8 in the polynomial f(x) is (-10) ( 18!8! )
The value of f(1)+f(-1) is equal to 10! 211
The degree of the polynomial f(x) is 10
The constant term of the polynomial f(x) is - ( 10!5! )

JEE Advanced 2026 Paper 2

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All JEE Advanced Mathematics chapters

Class 11Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Conic Sections Limits and Derivatives Statistics

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)