26 Questions
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?
4
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: ________.
Benzyl > allyl > 3° > 2° > 1° > CH3
What happens to the volume of the concentrated solution as a result of osmosis?
Gradually increases
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.
True
The correct order of increasing basicity of the given conjugate bases (R=CH3) is:
R < HC ≡ C < RCOO < NH2
Which of the following orders is not correct regarding the –𝐼𝐼 effect of the substituents?
−NR3 < –OR < − F
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)
94.39 mm of Hg
The total number of isomeric carbocations possible for the formula C4H9+ is:
6
Which of the following statements about the electromeric effect is true?
Temporary effect
The number of π-electrons involved in resonance in a benzene molecule is:
6
If log10 2 = 0.3010, then log5 64 is:
233
A charge particle q1 is at position (2, –1, 3). The electrostatic force on another charged particle q2 at (0, 0, 0) is?
q1q2 / 56πε0
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?
20
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?
4 : 1
An electric dipole in stable equilibrium in an electric field requires what torque to maintain it at an angle θ from its initial position?
pE cos θ
The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be?
2q / 4πε0 * 3R²
The expression $f(A) + \begin{bmatrix}1 & 0 \ 0 & 1 \end{bmatrix}$ is equal to
$\begin{bmatrix}3 & 1 \ 0 & 1 \end{bmatrix}$
Matrix A = $\begin{bmatrix}x & a & b + c \ x & b & c + a \ x & c & a + b \end{bmatrix}$, is non-invertible if
x has any value
If $\begin{bmatrix}1 & 1 \ 1 & 0 \end{bmatrix} A = \begin{bmatrix}-3 & 2 \ 5 & -3 \end{bmatrix}$, then the matrix A equals
$\begin{bmatrix}1 & 1 \ 0 & 1 \end{bmatrix}$
The solution set of $x - 1 < 1 - x$, for $x \in \mathbb{R}$ is an empty set.
False
The set of values of $x$ for which the inequalities $x - 3 < 0$ and $10x - x - 16 > 0$ hold simultaneously, is ________.
(-2, 5)
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
b + c
Match the following matrices with their determinants:
$\begin{vmatrix}1 & 2 & 3 \ 3 & 7 & 10 \ 3 & 9 & 13 \end{vmatrix}$ = 3 $\begin{vmatrix}3 & 9 & 13 \ 3 & 9 & 13 \end{vmatrix}$ = 0
The number of real solutions of $2| x - 1 | = 3| x -1 |$ is
0
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.
A 3-hour milestone test covering Electric Charges and Fields in Physics, Solutions and Organic Chemistry, and Determinants, Matrices, and Basic Mathematics in Mathematics.
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