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Questions and Answers
What is the initial force acting on the particle at rest at the origin?
What is the initial force acting on the particle at rest at the origin?
- 0 Newtons (correct)
- 12 Newtons
- 10 Newtons
- None of the above
An α-particle accelerated by 104V does not change its direction when entering a magnetic field.
An α-particle accelerated by 104V does not change its direction when entering a magnetic field.
False (B)
What is the density of water used in the calculation of height rise in the capillary?
What is the density of water used in the calculation of height rise in the capillary?
1 gm/cc
The thickness of the region where the α-particle enters is _____ m.
The thickness of the region where the α-particle enters is _____ m.
Match the following components to their respective values or properties:
Match the following components to their respective values or properties:
How does the source EMF behave when switch S is at position 1?
How does the source EMF behave when switch S is at position 1?
What is the change in direction (in degrees) of motion for the α-particle?
What is the change in direction (in degrees) of motion for the α-particle?
The water will rise higher in the capillary due to the larger diameter of the glass rod.
The water will rise higher in the capillary due to the larger diameter of the glass rod.
What expression represents the potential energy of a body in a conservative force field?
What expression represents the potential energy of a body in a conservative force field?
A small ball falling at a constant velocity will accelerate when it strikes another object.
A small ball falling at a constant velocity will accelerate when it strikes another object.
What is the velocity of the small ball before it strikes the inclined cart?
What is the velocity of the small ball before it strikes the inclined cart?
During the elastic collision, the speed of rebound of the small ball will be __________.
During the elastic collision, the speed of rebound of the small ball will be __________.
If the cylindrical drum rolls forward without slipping when pushed by the board, what distance does the man move on the ground?
If the cylindrical drum rolls forward without slipping when pushed by the board, what distance does the man move on the ground?
Match the following expressions with their correct variables:
Match the following expressions with their correct variables:
The distance moved by the drum is equal to half the distance moved by the man on the ground.
The distance moved by the drum is equal to half the distance moved by the man on the ground.
What is the approximate rebound speed of the ball after colliding with the inclined cart?
What is the approximate rebound speed of the ball after colliding with the inclined cart?
If a positive charged particle collides inelastically at point Q with a coefficient of restitution of e = 1/2, where will the particle likely strike next?
If a positive charged particle collides inelastically at point Q with a coefficient of restitution of e = 1/2, where will the particle likely strike next?
The speed of sound is assumed to be 340 m/s in all conditions.
The speed of sound is assumed to be 340 m/s in all conditions.
What is the minimum height of water required for resonance in a cylindrical tube if the frequency is 340 Hz?
What is the minimum height of water required for resonance in a cylindrical tube if the frequency is 340 Hz?
The charge flowing to earth when three plates have initial charges Q, 2Q, and 4Q is __________.
The charge flowing to earth when three plates have initial charges Q, 2Q, and 4Q is __________.
Match the following terms with the correct description:
Match the following terms with the correct description:
Which of the following statements about the coefficient of restitution for the particle is correct?
Which of the following statements about the coefficient of restitution for the particle is correct?
The frequency of the tuning fork must match the natural frequency of the air column in the tube for resonance to occur.
The frequency of the tuning fork must match the natural frequency of the air column in the tube for resonance to occur.
The cylindrical tube is __________ cm long.
The cylindrical tube is __________ cm long.
What is the resistance per unit length of the rods?
What is the resistance per unit length of the rods?
The rods are arranged in a triangular formation.
The rods are arranged in a triangular formation.
What is the velocity at which the rods start moving?
What is the velocity at which the rods start moving?
The voltage drop across the capacitor is _____ times the voltage drop across the inductor.
The voltage drop across the capacitor is _____ times the voltage drop across the inductor.
Match the following thermal properties with their respective values:
Match the following thermal properties with their respective values:
At what height does the center of mass of the two bodies reach when one is projected upwards?
At what height does the center of mass of the two bodies reach when one is projected upwards?
The impendence of the circuit is directly related to its voltage drop.
The impendence of the circuit is directly related to its voltage drop.
What is the impedance of the circuit if the power factor is 0.8 and L is 5 henry?
What is the impedance of the circuit if the power factor is 0.8 and L is 5 henry?
The surface charge density $ heta$ of the sheet is proportional to which of the following?
The surface charge density $ heta$ of the sheet is proportional to which of the following?
What is the ratio of the circumference of the first Bohr orbit for the electron in the hydrogen atom to the de-Broglie wavelength of electrons with the same velocity?
What is the ratio of the circumference of the first Bohr orbit for the electron in the hydrogen atom to the de-Broglie wavelength of electrons with the same velocity?
A glass prism with a refractive index of 1.5 can be totally reflective in water.
A glass prism with a refractive index of 1.5 can be totally reflective in water.
The refractive index $ ext{n}$ of a glass prism is ______.
The refractive index $ ext{n}$ of a glass prism is ______.
What happens when a light beam hits the face AB of a prism normally?
What happens when a light beam hits the face AB of a prism normally?
Match the following refractive indices with the corresponding medium:
Match the following refractive indices with the corresponding medium:
What is the correct electronic configuration of Mn, Fe, and Co metal ion in the complexes, respectively?
What is the correct electronic configuration of Mn, Fe, and Co metal ion in the complexes, respectively?
When light is incident on face BC of a glass prism, what is the condition for total internal reflection?
When light is incident on face BC of a glass prism, what is the condition for total internal reflection?
The complementary strand for a given single strand of DNA can be determined using base-pairing rules.
The complementary strand for a given single strand of DNA can be determined using base-pairing rules.
The sine condition for total reflection at the interface is independent of the refractive indices.
The sine condition for total reflection at the interface is independent of the refractive indices.
What is the correct order of pKa for the following compounds?
What is the correct order of pKa for the following compounds?
The rate constant values for the decay of radioisotopes X and Y are __________ h–1.
The rate constant values for the decay of radioisotopes X and Y are __________ h–1.
At what time will the activities of radioisotopes X and Y be approximately equal?
At what time will the activities of radioisotopes X and Y be approximately equal?
What is the minimum pressure required for desalinating sea water containing 1 M NaCl at 300 K?
What is the minimum pressure required for desalinating sea water containing 1 M NaCl at 300 K?
Match the substances with their corresponding categories:
Match the substances with their corresponding categories:
All isotopes of the same element have the same half-life.
All isotopes of the same element have the same half-life.
Flashcards
Potential Energy and Acceleration
Potential Energy and Acceleration
The potential energy of a body in a conservative force field is given by U = x – y, where x and y are the position coordinates. The acceleration of the body can be calculated using the negative gradient of the potential energy.
Elastic Collision
Elastic Collision
In an elastic collision, both momentum and kinetic energy are conserved. The ball's initial vertical velocity is canceled by the horizontal velocity of the cart, resulting in a rebound speed determined by the Pythagorean theorem.
Rolling Motion
Rolling Motion
When the drum rolls forward, the point of contact between the drum and the ground is momentarily stationary. The distance moved by the man is equal to the distance the drum rolls plus the length of the board.
Surface Charge Density and Angle
Surface Charge Density and Angle
The surface charge density (σ) of a sheet is directly proportional to the sine of the angle (θ) between the electric field and the surface normal. This means as the angle increases, the surface charge density also increases.
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Circumference to de Broglie Wavelength Ratio
Circumference to de Broglie Wavelength Ratio
The ratio of the circumference of the first Bohr orbit to the de Broglie wavelength of an electron with the same velocity is 2:1. This arises from the quantization of angular momentum in the Bohr model.
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Total Internal Reflection Condition
Total Internal Reflection Condition
When light travels from a denser medium (glass, refractive index 1.5) to a rarer medium (water, refractive index 4/3), total internal reflection occurs if the angle of incidence exceeds the critical angle. The critical angle is determined by the ratio of refractive indices.
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Total Internal Reflection in a Prism
Total Internal Reflection in a Prism
For a glass prism immersed in water, total internal reflection occurs when the angle of incidence (θ) at the BC face is greater than or equal to the critical angle. This condition is based on Snell's law and the refractive indices of glass and water.
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Quantized Angular Momentum in Hydrogen Atom
Quantized Angular Momentum in Hydrogen Atom
The angular momentum of an electron in a hydrogen atom is quantized, meaning it can only take on discrete values. This quantization leads to the existence of specific energy levels for the electron.
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De Broglie Wavelength and Momentum
De Broglie Wavelength and Momentum
The de Broglie wavelength of a particle is inversely proportional to its momentum. This means lighter particles or particles with higher velocities have shorter wavelengths.
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First Bohr Orbit and Ground State
First Bohr Orbit and Ground State
The first Bohr orbit of a hydrogen atom represents the ground state, the lowest possible energy level for the electron. The electron can only exist in specific energy levels.
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Refractive Index and Light Bending
Refractive Index and Light Bending
The refractive index of a medium is a measure of how much light bends when it passes from one medium to another. It represents the ratio of the speed of light in vacuum to the speed of light in the medium.
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Force on a moving wire in a magnetic field
Force on a moving wire in a magnetic field
The force required to maintain a constant velocity on the wire is determined by the interaction of the magnetic field and the current flowing through the wire. The magnitude of this force is given by F = I l B, where I is the current, l is the length of the wire, and B is the magnetic field strength.
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Impedance of a circuit
Impedance of a circuit
The impendence of a circuit is a measure of its resistance to the flow of alternating current. It combines the effects of resistance, capacitance, and inductance.
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Maximum height of a center of mass
Maximum height of a center of mass
The center of mass of a system rises to a maximum height, which is directly proportional to the square of the initial velocity and inversely proportional to the acceleration due to gravity. This is consistent with the principles of projectile motion.
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Heat flow and balance in a rod
Heat flow and balance in a rod
The position of a point on a rod that maintains equal rates of ice melting and water evaporation is determined by the balance of heat flow. The thermal conductivity of the rod, along with the latent heat of fusion and vaporization, determine the temperature gradient and the position of the point.
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Electric field within a charged dielectric disc
Electric field within a charged dielectric disc
The charge density of a dielectric disc in a specific region can be used to calculate the electric field within the disc. The electric field is dependent on the geometry of the charge distribution.
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Coefficient of restitution (e)
Coefficient of restitution (e)
The coefficient of restitution (e) is a measure of how much kinetic energy is conserved in a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach.
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Motion of charged particle in a magnetic field
Motion of charged particle in a magnetic field
In this scenario, the charged particle enters a uniform magnetic field perpendicular to its motion. This causes the particle to move in a circular path. The inelastic collision with the wall means kinetic energy is lost.
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Resonance of sound waves in a tube
Resonance of sound waves in a tube
Resonance occurs when the frequency of the driving force (tuning fork) matches a natural frequency of the system (air column in the tube). This causes the amplitude of the vibrations to increase significantly.
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Conditions for resonance in a closed tube
Conditions for resonance in a closed tube
For resonance in a closed tube (one end closed, one end open), the length of the air column must be an odd multiple of a quarter wavelength of the sound wave. This is because the closed end must be a displacement node (no movement) and the open end a displacement antinode (maximum movement).
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Charge redistribution in parallel plates
Charge redistribution in parallel plates
The charge flowing to earth is equal to the difference in the initial charges of the plates. Due to charge redistribution, the final charge on each plate will be the same.
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Charge flow to earth
Charge flow to earth
When the switch is closed, charge will flow from the plates with higher initial charge to the plates with lower charge until the potential difference between them becomes equal. The charge flowing to earth is that which is released from the plates with higher initial charge.
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Particle Motion under a Time-Dependent Force
Particle Motion under a Time-Dependent Force
The force acting on a particle is given by F = (12 – 2t) Newton, where t is time. This force causes the particle to move along the x-axis starting from rest at the origin. The problem asks to find the time it takes for the particle to return to the origin.
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Alpha Particle Deflection in a Magnetic Field
Alpha Particle Deflection in a Magnetic Field
An alpha particle, which is a helium nucleus, is accelerated by a potential difference of 10^4 V. This acceleration causes the alpha particle to enter a region with a uniform magnetic field, where it experiences a change in its direction of motion due to the magnetic force. The problem requires finding the angle of this change in direction.
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Capillary Action and Water Rise
Capillary Action and Water Rise
A glass rod is inserted into a glass capillary, creating a narrow space. This arrangement is then brought into contact with water. The water rises inside the capillary due to surface tension and the cohesive forces between water molecules and the glass. The problem aims to determine the height the water will rise in the capillary.
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AC Circuit Analysis with Switch
AC Circuit Analysis with Switch
The given AC circuit has a switch that can be placed in two positions. In position 1, the source emf leads the current by an angle of pi/6. When the switch is moved to position 2, the source emf leads the current by an unknown angle. The task is to determine this angle, denoted as 'x'.
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Electric Field Intensity Calculation
Electric Field Intensity Calculation
The electric field intensity at a point P is determined by the distribution of charges around it. In this case, the problem provides the charge density (delta) and distances, and you need to calculate the electric field intensity at point P.
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Alpha Particle Deflection Angle
Alpha Particle Deflection Angle
The problem presents an alpha particle entering a magnetic field and experiencing a change in direction. The problem asks find the angle of deflection.
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Magnetic Force on a Charged Particle
Magnetic Force on a Charged Particle
The force on a particle due to a magnetic field is given by F = q * v * B, where q is the charge, v is the velocity, and B is the magnetic field. This force is perpendicular to both the velocity and the magnetic field, causing the particle to move in a circular path.
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Capillary Action and Surface Tension
Capillary Action and Surface Tension
The surface tension of water causes it to rise in a narrow tube, such as a capillary, due to the cohesive forces between water molecules and the adhesive forces between water molecules and the tube's walls. This phenomenon is called capillary action.
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Electronic Configuration of transition Metal ions in complexes
Electronic Configuration of transition Metal ions in complexes
The electronic configuration of a metal ion describes the arrangement of electrons in its orbitals. For Mn, Fe, and Co ions in complexes, the electrons occupy the t2g and eg orbitals based on crystal field theory, which explains how metal ions interact with ligands.
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Complementary DNA Strand
Complementary DNA Strand
The complementary strand of a single-stranded DNA molecule has a sequence that pairs with the original strand according to base pairing rules: Adenine (A) pairs with Thymine (T), and Guanine (G) pairs with Cytosine (C).
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Comparing pKa values of organic compounds
Comparing pKa values of organic compounds
pKa values indicate the acidity of a compound. A lower pKa value signifies a stronger acid. In this case, the pKa values are ranked based on the stability of the conjugate bases formed after deprotonation.
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Radioactive Decay and Half-life
Radioactive Decay and Half-life
Radioactive decay follows first-order kinetics, meaning its rate is proportional to the amount of radioactive material present. The rate constant is related to the half-life, which is the time it takes for half of the radioactive material to decay.
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Osmotic pressure and desalination
Osmotic pressure and desalination
Osmosis is the movement of water molecules across a semipermeable membrane from an area of high water concentration to an area of low water concentration. To prevent osmosis, a minimum pressure, called osmotic pressure, needs to be applied on the side with higher water concentration. The osmotic pressure can be calculated using the van't Hoff equation: π = iMRT, where π is the osmotic pressure, i is the van't Hoff factor, M is the molarity of the solution, R is the ideal gas constant, and T is the temperature.
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pKa values and stability of conjugate bases
pKa values and stability of conjugate bases
The correct order of pKa values for the given compounds (I - IV) depends on the stability of the conjugate bases formed after deprotonation. This stability is influenced by factors such as resonance and the electronegativity of the atoms involved. In general, more stable conjugate bases correspond to stronger acids and lower pKa values.
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Crystal Field Theory and Electronic Configuration
Crystal Field Theory and Electronic Configuration
The electronic configuration of a transition metal ion in a complex is influenced by the crystal field theory, which explains the splitting of d orbitals in the presence of ligands. The energy levels of these orbitals are then filled according to Hund's rule and the Aufbau principle.
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DNA base pairing and complementary strands
DNA base pairing and complementary strands
Complementary DNA strands are formed by base pairing, where adenine (A) pairs with thymine (T), and guanine (G) pairs with cytosine (C). The complementary strand is arranged antiparallel to the original strand, meaning that the 5' end corresponds to the 3' end of the original strand and vice versa.
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JEE Main 2024 - FIITJEE Full Test-I - Important Details
- Test Date: 28-12-2023
- Time Allotted: 3 hours
- Maximum Marks: 300
- Total Questions: 90
- Subjects: Physics (30 questions), Chemistry (30 questions), Mathematics (30 questions)
- Question Types: Multiple Choice (Section A), Numerical Answer Type (Section B)
- Marking Scheme:
- Correct Multiple Choice Answer: +4 marks
- Incorrect Multiple Choice Answer: -1 mark
- Correct Numerical Answer: +4 marks
- Incorrect Numerical Answer: -1 mark
- Sections:
- Part A (Physics, Chemistry, Mathematics):
- Section A (01-20, 31-50, 61-80): 60 Multiple Choice Questions
- Section B (21-30, 51-60, 81-90): 30 Numerical Questions
- Part A (Physics, Chemistry, Mathematics):
- Instructions:
- Attempt all questions in Section A
- Select any 5 questions from Section B
JEE Main 2024 - FIITJEE Full Test-I - Question Details (Pages 2-15)
- Detailed questions in Physics, Chemistry and Mathematics (pages 2-15)
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