Q84.If the coefficients of x and x2 in the expansion of (1 + x)p(1 −x)q, p, q ≤15 , are −3 and −5 respectively, then the coefficient of x3 is equal to ______.
What This Question Tests
This question requires expanding the product of two binomials up to x^3, collecting coefficients, and solving a system of equations to find the required coefficient.
Concepts Tested
Formulas Used
(1+x)^n = 1 + nx + n(n-1)/2! x^2 + n(n-1)(n-2)/3! x^3 + ...
(1-x)^n = 1 - nx + n(n-1)/2! x^2 - n(n-1)(n-2)/3! x^3 + ...
📚 NCERT Sections This Tests
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
8.2 — Name The Following Compounds According To Iupac System Of Nomenclature:
Chemistry Class 12 · Chapter 8
8.2 Name the following compounds according to IUPAC system of nomenclature: (i) CH3CH(CH3)CH2CH2CHO (ii) CH3CH2COCH(C2H5)CH2CH2Cl (iii) CH3CH=CHCHO (iv) CH3COCH2COCH3 (v) CH3CH(CH3)CH2C(CH3)2COCH3 (vi) (CH3)3CCH2COOH (vii) OHCC6H4CHO-p
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Binomial expansion of algebraic expressions
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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