For r = 0, 1, andhellip;, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 andndash; C10b)A10(B210C10A10)c)0d)C10andndash;B10Correct answer is option 'D'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

JEE Exam > JEE Questions > For r = 0, 1, …, 10, let Ar, Brand Cr ...

For r = 0, 1, …, 10, let A_r, B_rand C_r denote, respectively, the coefficient of x^r in the expansions of (1 + x)¹⁰ , (2010)

(1 + x)²⁰and (1 + x)³⁰. Then

is equal to

a)
B₁₀ – C₁₀
b)
A₁₀(B²₁₀C₁₀A₁₀)
c)
0
d)
C₁₀–B₁₀

Correct answer is option 'D'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the...

Clearly

Now expanding (1 + x )¹⁰and (1 + x )²⁰by bin om ial theorem and comparing the coefficients of x²⁰in their product, on both sides, we get

= coeff of x²⁰ in (1 + x )³⁰ = ³⁰ C₂₀= ³⁰C₁₀

Again expending (1 + x )¹⁰ and ( x + 1)¹⁰ by bin omial theorem and comparing the coefficients of x¹⁰ in their

product on both sides, we get

coeff of x¹⁰ in (1 + x)²⁰= ₂₀C₁₀

Substituting these values in equation (1), we get

View all questions of this test

View all answers Start learning for free

Explore Courses for JEE exam

Similar JEE Doubts

For r = 0, 1, …, 10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10,(1 + x)20 and (1 + x)30. is equal to

View answer

For a polynomial g(x) with real coefficient, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficient defined byS = {(x2 – 1)2 (a0 + a1x + a2x2 + a3x3) : a0, a1, a2, a3 ∈ R}.For a polynomial f, let f and f" denote its first and second order derivatives, respectively. Then the minimum possible value of (mf + mf"), where f ∈ S, is _______ Correct answer is '5.00'. Can you explain this answer?

View answer

For a polynomial g(x) with real coefficient, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficient defined by S= {(x2 – 1)2 (a0 + a1x + a2x2 + a3x3) : a0, a1, a2, a3 ∈ R}. For a polynomial f, let f and f" denote its first and second order derivatives, respectively. Then the minimum possible value of (mf + mf"), where f ∈ S, is _______ Correct answer is '5.00'. Can you explain this answer?

View answer

Let Crdenote the binomial coefficient of xrin the expansion of (1 + x)10. Ifα, β∈R. C1+ 3.2C2+ 5.3C3+ .... upto 10 terms =, then the value of α + β is equal to Correct answer is '286'. Can you explain this answer?

View answer

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and Crespectively. Suppose a = 6, b = 10 and the area of the triangle is . If ∠ACB is obtuse and if r denotesthe radius of the incircle of the triangle, then r2 is equal to Correct answer is '3'. Can you explain this answer?

View answer

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Mathematics (Maths) for JEE Main & Advanced

Chemistry for JEE Main & Advanced

Study Plan for JEE

Top Courses for JEE

View all

For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer?.

Solutions for For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.

Here you can find the meaning of For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer?, a detailed solution for For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice For r = 0, 1, …, 10, let Ar, Brand Cr denote, respectively, the coefficient of xr in the expansions of (1 + x)10 , (2010) (1 + x)20 and (1 + x)30. Then is equal toa)B10 – C10b)A10(B210C10A10)c)0d)C10–B10Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.

Explore Courses for JEE exam