Q83.The total number of 3 -digit numbers, whose greatest common divisor with 36 is 2 , is ______.
What This Question Tests
This problem combines number theory (GCD, divisibility) with counting principles. It requires understanding the properties of GCD and applying the principle of inclusion-exclusion to count 3-digit numbers with specific divisibility conditions.
Concepts Tested
Formulas Used
GCD(A,B) = d implies A = kd and B = md with GCD(k,m)=1
๐ NCERT Sections This Tests
1.18 โ A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 ยท Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
12.5 โ A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 ยท 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.
8.17 โ Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 ยท Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
๐ Question Details
- Chapter
- Permutation & Combination
- Topic
- Number Theory, Divisibility Rules
- Year
- 2022
- Shift
- 26 Jun Shift 2
- Q Number
- Q83
- Type
- Numerical
- NCERT Ref
- Class 10 Mathematics Ch 1: Real Numbers (GCD concept), Class 11 Mathematics Ch 7: Permutations and Combinations (Counting techniques)
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