Question:
Find the sixth term of the expansion $\left(y^{\frac{1}{2}}+x^{\frac{1}{3}}\right)^{n}$ if the binomial coefficient of the third term from the end is 45 .
Solution:
Given $\left(y^{1 / 2}+x^{1 / 3}\right)^{n}$
Also given that binomial coefficient of third term from the end $=45$ Therefore,
${ }^{n} C_{n-2}=45$
The above expression can be written as
${ }^{n} C_{2}=45$
$\Rightarrow \frac{n(n-1)(n-2) !}{2 !(n-2) !}=45$
$\Rightarrow \quad n(n-1)=90$
$\Rightarrow \quad n^{2}-n-90=0$
$\Rightarrow(n-10)(n+9)=0$
Therefore $n=10$
Now, sixth term $={ }^{10} C_{5}\left(y^{1 / 2}\right)^{10-5}\left(x^{1 / 3}\right)^{5}=252 y^{5 / 2} \cdot x^{5 / 3}$
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- 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
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- Chemical Effects of Electric Current,
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