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Home  ›  Mathematics  ›  Binomial Theorem Revision   StudyBeacon Binomial Theorem — Complete JEE Mains 2026 Revision Capsule This capsule collects every formula and identity you need for JEE Mains: finite binomial theorem, coefficients, combinatorial identities, Newton’s generalized binomial, approximations, problem patterns, and practice questions — all equations in LaTeX. 1. Finite Binomial Theorem (Standard)

  Motion in a Plane — Quiz 2 (Questions 11–20) Instructions MCQs — choose one radio option. Numeric answers — type values without units (dot for decimal). ±1% accepted (absolute 0.01 if correct value = 0). Each question has a separate Check (validates) and Show Solution (reveals explanation). Use Check All & Score to evaluate all answers at once. 11. A particle moves from point r₀ = (2 î + 4 ĵ) m at t = 0 with initial velocity v₀ = (5 î + 4 ĵ) m/s and constant acceleration a = (4 î − 4 ĵ) m/s². What is its distance from the origin at t = 2 s? [11 Jan 2019 — Shift-II] (a) 15 m (b) √416 m (≈ 20.396 m) (c) 5 m (d) 10√2 m Check Show Solution 12. Position coordinates: x = a cos(ωt), y = a sin(ωt), z = a ω t. The speed of the particle is: [09 Jan 2019 — Shift-I...

  Motion in a Plane — Quiz 1 (Questions 1–10) Attempt Questions 1–10. MCQs use radio buttons; numeric questions accept keyboard input. Numeric answers have ±1% tolerance. Click Check to reveal the correct answer and a compact stepwise solution for that question. Instructions MCQs — select one radio option. Numerical — type numeric value (no units). Use dot for decimals. ±1% accepted. Press Check below each question to reveal solution for that question. Use Check All & Score for full evaluation. 1. Position of an ant (S in metres) moving in Y–Z plane is given by S = (2 t) ŷ + (5 t^2) ẑ (here we interpret the pasted expression as S = 2t j + 5t² k). The magnitude and direction of velocity of the ant at t = 1 s will be: [27 Jan 2024 — Shift-I] (a) 16 m/s in y-direction (b) 4 m/s in x-direction (c) 9 m/s in z-direction (d) 4 m/s i...

Mole Concept — Interactive Quiz (25 Qs)    Instructions MCQs — choose one radio option. Numerical questions — type the numeric answer (no units). Use dot for decimals. ±1% accepted. Click "Check" for a question to reveal the solution for that question. Use "Check All & Score" to evaluate the whole quiz. 1. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 'A' × 10 12 Hz and that has a radiant intensity in that direction of 1/'B' watt per steradian. 'A' and 'B' are respectively. [09 April 2024 — Shift-II] (a) 540 and 1/683 (b) 540 and 683 (c) 450 and 1/683 (d) 450 and 683 Check 2. Which of the following have same number of significant figures? (A) 0.00253   (B) 1.0003   (C) 15.0   (D)...

Home  ›  Mathematics  ›  Sequence and Series Revision Sequence & Series — Complete JEE Mains 2026 Revision Capsule A compact but exhaustive capsule covering: AP, GP, HP, mixed series, telescoping, AGP, recurrence relations, inequalities, patterns, tricks, worked examples, and a practice set with answers. Memorize formulas, practice patterns, and use the quick-checks to score reliably. AP: $a_n = a + (n-1)d$ $S_n = \dfrac{n}{2}[2a+(n-1)d]$ GP: $a_n = ar^{n-1}$ $S_n = a\dfrac{r^n-1}{r-1}$, $S_\infty=\dfrac{a}{1-r}$ ($|r| HP / Means: $HM \le GM \le AM$ $HM=\dfrac{2ab}{a+b}$ 1. Basics & Notation Sequence: ordered list $\\{a_n\\}$, Series: sum $S_n=\\sum_{k=1}^n a_k$. General term often written $a_n$ or $T_n$. Use index shifts carefully. 2. Arithmetic Progression (AP) nth term: $a_n = a + (n-1)d$. ...