Question:
Write
(i) the coefficient of $x^{3}$ in $x+3 x^{2}-5 x^{3}+x^{4}$.
(ii) the coefficient of $x$ in $\sqrt{3}-2 \sqrt{2} x+6 x^{2}$.
(iii) the coefficient of $x^{2}$ in $2 x-3+x^{3}$.
(iv) the coefficient of $x$ in $\frac{3}{8} x^{2}-\frac{2}{7} x+\frac{1}{6}$.
(v) the constant term in $\frac{\pi}{2} x^{2}+7 x-\frac{2}{5} \pi$.
Solution:
(i) The coefficient of $x^{3}$ in $x+3 x^{2}-5 x^{3}+x^{4}$ is $-5$.
(ii) The coefficient of $x$ in $\sqrt{3}-2 \sqrt{2} x+6 x^{2}$ is $-2 \sqrt{2}$.
(iii) $2 x-3+x^{3}=-3+2 x+0 x^{2}+x^{3}$
The coefficient of $x^{2}$ in $2 x-3+x^{3}$ is 0 .
(iv) The coefficient of $x$ in $\frac{3}{8} x^{2}-\frac{2}{7} x+\frac{1}{6}$ is $-\frac{2}{7}$.
(v) The constant term in $\frac{\pi}{2} x^{2}+7 x-\frac{2}{5} \pi$ is $-\frac{2}{5} \pi$.
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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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