Question:
Given the integers $r>1, n>2$, and coefficients of $(3 r)^{\text {th }}$ and $(r+2)^{\text {nd }}$ terms in the binomial expansion of $(1+x)^{2 n}$ are equal, then
(A) $n=2 r$
(B) $n=3 r$
(C) $n=2 r+1$
(D) none of these
Solution:
(A) $n=2 r$
Explanation:
Given $(1+x)^{2 n}$
$T_{3 r}=T_{(3 r-1)+1}={ }^{2 n} \mathrm{C}_{3 r-1} x^{3 r-1}$
$T_{r+2}=T_{(r+1)+1}={ }^{2 n} C_{r+1} x^{r+1}$
${ }^{2 n} C_{3 r-1}={ }^{2 n} C_{r+1}$
$3 r-1+r+1=2 n$
$n=2 r$
Hence option A is the correct answer.
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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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