Q66.The coefficient of x50 in the binomial expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + … +x1000 is: (1) (1000)! (2) (1000)! (50)(!95φ! (49)(!95)! (3) (1001)! (4) (1001)! (51)(!95ϕ! (50)(!95)!
What This Question Tests
This question tests the ability to simplify a series using the sum of a geometric progression formula, then find the coefficient of a specific term in a binomial expansion.
Concepts Tested
Formulas Used
Sum of GP = a(rⁿ-1)/(r-1)
(1+x)ⁿ = Σ nCr x^r
📚 NCERT Sections This Tests
5.28 — How Many Ions Are Produced From The Complex Co(Nh3)6Cl2 In Solution?
Chemistry Class 11 · Chapter 5
5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
📋 Question Details
- Chapter
- Binomial Theorem
- Topic
- Coefficient in binomial expansion
- Year
- 2014
- Shift
- 11 Apr Online
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 8: Binomial Theorem
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