All flashcard decksJEE Main syllabus →
26 cardsJEE Main

JEE Main Mathematics & Physics Core Concepts

Essential formulas, theorems, shortcuts, and core concepts for JEE Main Mathematics and Physics.

Start studyingPlay Match
PDF study sheet

Free account needed to save, copy or download. We bring you back here.

1 / 26
0 known
TermClick or press Space to flip
Leibniz Rule for Differentiation Under the Integral Sign
GetMyMockTestQuestion side

Full list

Terms in this deck (26)

JEE Main mock tests →
1
Leibniz Rule for Differentiation Under the Integral Sign
d/dx [int_{u(x)}^{v(x)} f(t) dt] = f(v(x)) v'(x) - f(u(x)) u'(x).
2
Shortest Distance Between Two Skew Lines
For r = a1 + lambdab1 and r = a2 + mub2: d = |(a2 - a1) . (b1 x b2)| / |b1 x b2|. Lines are coplanar if (a2 - a1) . (b1 x b2) = 0.
3
Condition of Tangency for Conic Sections
Circle x^2 + y^2 = r^2: c^2 = r^2(1 + m^2); Parabola y^2 = 4ax: c = a/m; Ellipse x^2/a^2 + y^2/b^2 = 1: c^2 = a^2m^2 + b^2; Hyperbola x^2/a^2 - y^2/b^2 = 1: c^2 = a^2m^2 - b^2.
4
Properties of Matrix Adjoint and Determinant
A adj(A) = |A| I; |adj(A)| = |A|^(n - 1); adj(adj(A)) = |A|^(n - 2) * A; |adj(adj(A))| = |A|^((n - 1)^2) for an n x n non-singular matrix.
5
Definite Integral Reflection Property (King's Rule)
int_a^b f(x) dx = int_a^b f(a + b - x) dx. Adding both forms gives 2I = int_a^b [f(x) + f(a + b - x)] dx, often yielding an immediate elementary integrand.
6
Wallis Formula for Powers of Trigonometric Functions
int_0^{pi/2} sin^n(x) dx = int_0^{pi/2} cos^n(x) dx = [(n-1)/n] [(n-3)/(n-2)] ... (1/2) (pi/2) if n is even, or ... (2/3) 1 if n is odd.
7
Cauchy-Schwarz and AM-GM-HM Inequalities
(sum a_i^2)(sum b_i^2) >= (sum a_i * b_i)^2 with equality iff a_i / b_i = k. For positive reals: AM >= GM >= HM with equality iff all terms are equal.
8
Distance Between Parallel Planes and Distance of a Point from a Plane
Point (x0, y0, z0) to ax + by + cz + d = 0: d = |ax0 + by0 + cz0 + d| / sqrt(a^2 + b^2 + c^2). Between ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0: d = |d1 - d2| / sqrt(a^2 + b^2 + c^2).
9
Homogeneous Second-Degree Equation and Pair of Straight Lines
ax^2 + 2hxy + by^2 = 0 represents two lines through origin. Angle between them: tan(theta) = 2*sqrt(h^2 - ab) / |a + b|. Lines are perpendicular iff a + b = 0; coincident iff h^2 = ab.
10
Bayes' Theorem for Conditional Probability
P(A_i | B) = [P(B | A_i) P(A_i)] / [sum_{j=1}^n P(B | A_j) P(A_j)], updating the prior probability P(A_i) given observed evidence B.
11
Binomial Coefficient Sum Identities
sum_{r=0}^n C(n, r) = 2^n; sum_{r=0}^n (-1)^r C(n, r) = 0; sum_{r=1}^n r C(n, r) = n 2^(n - 1); sum_{r=0}^n C(n, r)^2 = C(2n, n).
12
Moment of Inertia Theorems
Parallel Axis Theorem: I = I_cm + M * d^2 (valid for all rigid bodies). Perpendicular Axis Theorem: I_z = I_x + I_y (valid only for planar laminar bodies in xy-plane).
13
Rolling Motion Without Slipping: Kinetic Energy and Acceleration
Total KE: K = 1/2Mv_cm^2 (1 + k^2 / R^2). Linear acceleration down an incline of angle theta: a = (g sin(theta)) / (1 + k^2 / R^2).
14
Simple Harmonic Motion: Velocity, Acceleration, and Energy
x = A sin(omegat + phi); v = omega sqrt(A^2 - x^2); a = -omega^2 x. Total energy E = 1/2 m omega^2 * A^2 (conserved; continuously converts between KE and PE).
15
Doppler Effect for Sound Waves
Observed frequency: f' = f * [(v +/- v_o) / (v -/+ v_s)], where v is sound speed in medium, v_o is observer velocity, and v_s is source velocity along line of sight.
16
Carnot Engine Efficiency and Maximum Work
Efficiency eta = 1 - T_C / T_H = W / Q_H, where temperatures T_H and T_C must be in absolute Kelvin. No engine operating between two heat reservoirs can exceed Carnot efficiency.
17
Gauss's Law and Electric Field of Standard Geometries
Infinite line charge: E = lambda / (2piepsilon_0r); Infinite non-conducting sheet: E = sigma / (2epsilon_0); Conducting surface: E = sigma / epsilon_0.
18
LC Oscillation Frequency and Energy Conservation
Natural angular frequency: omega = 1 / sqrt(L C). Energy oscillates between capacitor electric field (q^2 / (2C)) and inductor magnetic field (1/2 L * I^2) with total energy conserved.
19
Electromagnetic Waves and Poynting Vector
Wave speed c = 1 / sqrt(mu_0 epsilon_0) = E_0 / B_0. Poynting vector S = (1 / mu_0) (E x B), giving instantaneous directional power flow per unit area (W/m^2).
20
Brewster's Law and Polarization by Reflection
When unpolarized light strikes a dielectric interface at Brewster angle theta_p, reflected light is completely linearly polarized perpendicular to plane of incidence: tan(theta_p) = mu.
21
Lens Maker's Formula and Power of Combined Lenses
1/f = (mu_rel - 1) * (1/R1 - 1/R2). Two thin lenses in contact: 1/F = 1/f1 + 1/f2 and total optical power P = P1 + P2.
22
Photoelectric Effect: Einstein's Equation and Stopping Potential
K_max = h nu - phi = e V_s, where phi = h * nu_0 is work function. Slope of stopping potential V_s vs frequency nu graph equals h / e (universal constant).
23
Bohr Model of Hydrogen Atom: Radius, Velocity, and Energy
Radius r_n = 0.529 n^2 / Z A; Velocity v_n = 2.18 10^6 Z / n m/s; Total energy E_n = -13.6 Z^2 / n^2 eV.
24
Radioactive Decay Law and Half-Life / Mean-Life Relation
N(t) = N_0 exp(-lambda t); Half-life t_{1/2} = ln(2) / lambda = 0.693 / lambda; Mean life tau = 1 / lambda = t_{1/2} / 0.693 = 1.44 * t_{1/2}.
25
Nuclear Binding Energy Curve and Mass Defect
Mass defect Delta m = [Z m_p + (A - Z) m_n] - M_nucleus. Binding energy E_b = Delta m * c^2 (931.5 MeV/u). Peak occurs near 56Fe (~8.8 MeV/nucleon), driving fusion and fission.
26
Zener Diode as a Voltage Regulator
Operates under reverse breakdown bias at constant breakdown voltage V_Z. Regulates load voltage despite variations in unregulated input supply voltage or load current.

JEE Main in India

In India, JEE Main is part of: Engineering entrance.

Students on the same pathway also practise:

More JEE Main practice

JEE Main mock tests

All JEE Main practice →