In a class of 140 students numbered 1 to 140 , all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :
102
42
1
38
Correct Option: , 4
Let $n(A)=$ number of students opted Mathematics $=70$,
$\mathrm{n}(\mathrm{B})=$ number of students opted Physics $=46$,
$\mathrm{n}(\mathrm{C})=$ number of students opted Chemistry
$=28$
$\mathrm{n}(\mathrm{A} \cap \mathrm{B})=23$
$\mathrm{n}(\mathrm{B} \cap \mathrm{C})=9$
$\mathrm{n}(\mathrm{A} \cap \mathrm{C})=14$
$\mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=4$
Now $\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})$
$=n(A)+n(B)+n(C)-n(A \cap B)-n(B \cap C)$
$-n(A \cap C)+n(A \cap B \cap C)$
$=70+46+28-23-9-14+4=102$
So number of students not opted for any course
$=$ Total $-\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})$
$=140-102=38$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,