Question:
Which of the following are true of false?
(i) $(2+3) !=2 !+3 !$
(ii) $(2 \times 3) !=(2 !) \times(3 !)$
Solution:
Option (i) and (ii) both are false
Proofs :
For option (i)
L.H.S. $=(2+3) !=(5 !)=120$
R.H.S. $=(2 !)+(3 !)=2+6=8$
$\therefore$ L.H.S. \neqR.H.S.
For option (ii),
L.H.S. $=(2 \times 3) !=(6 !)=720$
R.H.S $=(2 !) \times(3 !)=4 \times 6=24$
$\therefore$ L.H.S. $\neq$ R.H.S.
Important Notes : for any two whole numbers a and b,
- $(a+b) ! \neq(a !)+(b !)$
$\cdot(a \times b) ! \neq(a !) \times(b !)$
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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,
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