Q63.Number of integral solutions to the equation x + y + z = 21 , where x ≥1, y ≥3, z ≥4 , is equal to _____ .
What This Question Tests
This question requires finding the number of integral solutions to a linear equation with specified lower bounds for each variable, typically solved using the stars and bars method after a variable transformation.
Concepts Tested
Formulas Used
Number of non-negative integral solutions = (n+r-1)C(r-1)
📚 NCERT Sections This Tests
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
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?
📋 Question Details
- Chapter
- Permutation & Combination
- Topic
- Integral solutions of linear equations
- Year
- 2023
- Shift
- 01 Feb Shift 2
- Q Number
- Q63
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 7: Permutations and Combinations
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