Question:
If the fourth term in the binomial expansion of
$\left(\sqrt{\frac{1}{x^{1+\log _{10} x}}}+x^{\frac{1}{12}}\right)^{6}$ is equal to 200 , and $x>1$,
then the value of x is :
$10^{3}$
100
$10^{4}$
10
Correct Option: , 4
Solution:
$200={ }^{6} \mathrm{C}_{3}\left(\mathrm{x}^{\frac{1}{x+\log _{10} x}}\right)^{\frac{3}{2}} \times \mathrm{x}^{\frac{1}{4}}$
$\Rightarrow 10=x^{\frac{3}{2\left(1+\log _{10} x\right)}+\frac{1}{4}}$
$\Rightarrow 1=\left(\frac{3}{2(1+t)}+\frac{1}{4}\right) t$
where $t=\log _{10} x$
$\Rightarrow t^{2}+3 t-4=0$
$\Rightarrow t=1,-4$
$\Rightarrow x=10,10^{-4}$
$\Rightarrow x=10($ As $x>1)$
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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
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- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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