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Questions and Answers
What is the net electric flux through a closed cylinder placed in a uniform electric field parallel to its axis?
What is the net electric flux through a closed cylinder placed in a uniform electric field parallel to its axis?
xπR^2E
What is the total outgoing flux from the spherical surface encloses a cube with point charges at its corners?
What is the total outgoing flux from the spherical surface encloses a cube with point charges at its corners?
4
What is the charge enclosed in a region with given electric field E?
What is the charge enclosed in a region with given electric field E?
xε0
The stable order of the free radicals allyl, benzyl, (5αH)3°, (3αH)2°, (2αH)1°, and CH3 is in the order: ________.
The stable order of the free radicals allyl, benzyl, (5αH)3°, (3αH)2°, (2αH)1°, and CH3 is in the order: ________.
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What happens to the volume of the concentrated solution as a result of osmosis?
What happens to the volume of the concentrated solution as a result of osmosis?
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Ice melts at 0°C, 1 atm if NaCl is poured on it, and the freezing point of water is lowered on addition of NaCl.
Ice melts at 0°C, 1 atm if NaCl is poured on it, and the freezing point of water is lowered on addition of NaCl.
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The correct order of increasing basicity of the given conjugate bases (R=CH3) is:
The correct order of increasing basicity of the given conjugate bases (R=CH3) is:
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Which of the following orders is not correct regarding the –𝐼𝐼 effect of the substituents?
Which of the following orders is not correct regarding the –𝐼𝐼 effect of the substituents?
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What is the vapour pressure of CCl4 solution when 0.5g of non-volatile solute (mol.wt = 65) is dissolved in 100mL CCl4? (Density of CCl4 = 1.58 g/cm3)
What is the vapour pressure of CCl4 solution when 0.5g of non-volatile solute (mol.wt = 65) is dissolved in 100mL CCl4? (Density of CCl4 = 1.58 g/cm3)
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The total number of isomeric carbocations possible for the formula C4H9+ is:
The total number of isomeric carbocations possible for the formula C4H9+ is:
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Which of the following statements about the electromeric effect is true?
Which of the following statements about the electromeric effect is true?
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The number of π-electrons involved in resonance in a benzene molecule is:
The number of π-electrons involved in resonance in a benzene molecule is:
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If log10 2 = 0.3010, then log5 64 is:
If log10 2 = 0.3010, then log5 64 is:
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A charge particle q1 is at position (2, –1, 3). The electrostatic force on another charged particle q2 at (0, 0, 0) is?
A charge particle q1 is at position (2, –1, 3). The electrostatic force on another charged particle q2 at (0, 0, 0) is?
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Two equal and like charges 5 cm apart experience a repulsive force of 0.144 newton. The magnitude of the charge in microcoulomb will be?
Two equal and like charges 5 cm apart experience a repulsive force of 0.144 newton. The magnitude of the charge in microcoulomb will be?
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Two spherical shells A and B of radii 2 cm and 4 cm are charged equally. What is the ratio of charge density on the surfaces of the two shells?
Two spherical shells A and B of radii 2 cm and 4 cm are charged equally. What is the ratio of charge density on the surfaces of the two shells?
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An electric dipole in stable equilibrium in an electric field requires what torque to maintain it at an angle θ from its initial position?
An electric dipole in stable equilibrium in an electric field requires what torque to maintain it at an angle θ from its initial position?
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The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be?
The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be?
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The expression $f(A) + \begin{bmatrix}1 & 0 \ 0 & 1 \end{bmatrix}$ is equal to
The expression $f(A) + \begin{bmatrix}1 & 0 \ 0 & 1 \end{bmatrix}$ is equal to
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Matrix A = $\begin{bmatrix}x & a & b + c \ x & b & c + a \ x & c & a + b \end{bmatrix}$, is non-invertible if
Matrix A = $\begin{bmatrix}x & a & b + c \ x & b & c + a \ x & c & a + b \end{bmatrix}$, is non-invertible if
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If $\begin{bmatrix}1 & 1 \ 1 & 0 \end{bmatrix} A = \begin{bmatrix}-3 & 2 \ 5 & -3 \end{bmatrix}$, then the matrix A equals
If $\begin{bmatrix}1 & 1 \ 1 & 0 \end{bmatrix} A = \begin{bmatrix}-3 & 2 \ 5 & -3 \end{bmatrix}$, then the matrix A equals
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The solution set of $x - 1 < 1 - x$, for $x \in \mathbb{R}$ is an empty set.
The solution set of $x - 1 < 1 - x$, for $x \in \mathbb{R}$ is an empty set.
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The set of values of $x$ for which the inequalities $x - 3 < 0$ and $10x - x - 16 > 0$ hold simultaneously, is ________.
The set of values of $x$ for which the inequalities $x - 3 < 0$ and $10x - x - 16 > 0$ hold simultaneously, is ________.
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If $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ is such that $|A| = 0$ and $A - (a+d)A + kI = O$, then k is equal to
If $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$ is such that $|A| = 0$ and $A - (a+d)A + kI = O$, then k is equal to
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Match the following matrices with their determinants:
Match the following matrices with their determinants:
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The number of real solutions of $2| x - 1 | = 3| x -1 |$ is
The number of real solutions of $2| x - 1 | = 3| x -1 |$ is
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Study Notes
JEE Milestone Test-01
General Instructions
- Duration: 3 hours
- Total marks: 300
- The test consists of 90 questions, divided into three sections: Physics, Chemistry, and Mathematics
- Each section has 30 questions, with the first 20 being multiple-choice and the last 10 being integer-type questions
- Each correct answer is worth 4 marks, and 1 mark will be deducted for each incorrect response
Physics Section
- Electric Charges and Fields
- Electric field intensity due to a uniformly charged sphere is zero at the centre and infinity
- The maximum electric field intensity on the axis of a uniformly charged ring is proportional to the charge and inversely proportional to the square of the distance
- Electric dipole moment is a product of charge and distance
- Electric field lines originate from positive charges and terminate on negative charges
- Electrostatic field lines at a point represent the direction of the force experienced by a positive test charge
Chemistry Section
- Solutions
- Raoult's law is applicable to ideal solutions
- Non-ideal solutions show positive or negative deviation from Raoult's law
- The freezing point of water is lowered on the addition of NaCl
- Organic Chemistry (GOC)
- No specific topics mentioned in the text
Mathematics Section
- Determinants
- No specific topics mentioned in the text
- Matrices
- No specific topics mentioned in the text
- Basic Mathematics
- No specific topics mentioned in the text### Chemistry
- Types of deviations from Raoult's law:
- Positive deviation: observed in mixtures of acetone and chloroform
- Negative deviation: observed in mixtures of water and nitric acid
- Stability of carbocations:
- Order of stability: III > II > I
- Factors affecting stability: resonance, hyperconjugation, electromeric effect
- Stability of carbanions:
- Order of stability: I > II > III
- Stability of free radicals:
- Order of stability: allyl > benzyl > 3° > 2° > 1° > CH3
Thermodynamics
- Freezing point depression:
- Formula: ΔT = Kb × m
- Kb: freezing point depression constant
- m: molality of the solution
- Boiling point elevation:
- Formula: ΔT = Kb × m
- Kb: boiling point elevation constant
- m: molality of the solution
- Vapour pressure:
- Formula: P = P° × X
- P°: vapour pressure of the pure solvent
- X: mole fraction of the solvent
Organic Chemistry
- Nucleophilic substitution:
- Example: CH3Br + CH3OH → CH3OCH3 + HBr
- Types: SN1, SN2, E1, E2
- Electrophiles:
- Definition: electron-loving species
- Examples: H+, NO2+, Br2
- Electromeric effect:
- Definition: temporary movement of electrons
- Examples: in benzene, in cyclohexene
- Resonance:
- Definition: delocalization of electrons
- Examples: in benzene, in cyclohexadiene
Physics
- Osmosis:
- Definition: movement of solvent molecules through a semipermitive membrane
- Types: positive, negative, and zero osmosis
- Gas laws:
- Ideal gas law: PV = nRT
- Formula: P = P° × (1 - X)
Mathematics
-
Matrix algebra:
- Inverse of a matrix: A^(-1)
- Determinant of a matrix: |A|
- Eigenvalues and eigenvectors
-
Logarithms:
- Properties: logarithmic identity, logarithmic inequality
- Applications: exponential growth and decay
-
Algebra:
- Quadratic equations: ax^2 + bx + c = 0
- Linear equations: ax + b = 0### Matrix Properties
-
If A = [[0, α, 2]], and A³ = 125, then the positive value of α is.
-
If A² = B, then the value of α is (1, -1, 4, or no real value).
Inequality Solution
- The set of all real x satisfying the inequality (x + 4)(3 - x)² > 0 is (x ∈ (-∞, 3) ∪ (4, ∞), x ∈ (-∞, -4) ∪ (4, ∞), x ∈ (-∞, -3) ∪ (4, ∞), or x ∈ (-∞, -3) ∪ (3, ∞)).
Function Values
- If f(x) = -1 / (x - 1)(x - 2), then the value of f(49) is.
- If x + 3y + λz = 0, x + 5y - 2z = 0 has a non-zero solution, then the value of λ is (1, -1, 0, or no real value).
Determinant Properties
- If A = [[α, 0], [0, 1]], and B = [[1, 0], [5, 1]], then the value of α is.
- If Δ = [[2, 5, 7]], and Δ' = [[2, 5, 7]], then Δ'/Δ is.
- If Δ = [[1, 2, 3]], and Δ' = [[3, 7, 10]], then Δ'/Δ is.
Logarithmic Equations
- If logx + logy + logz = 0, then x^(a-b) y^(b-c) z^(c-a) is.
Matrix Operations
- If A and B are square matrices of order 3, and A = -1, B = 3, then 3(AB) + 100 equals.
- The number of solutions of 3x = -x is.
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Description
A 3-hour milestone test covering Electric Charges and Fields in Physics, Solutions and Organic Chemistry, and Determinants, Matrices, and Basic Mathematics in Mathematics.
