Tag: ai
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JEE MAIN 2025 (Online) 5th April Evening Shift
Question 1: Let α, β be the roots of the equation x² – x + p = 0 and γ, δ be the roots of the equation x² – 4x + q = 0; p, q ∈ Z. If α, β, γ, δ are in G.P., then |p + q| equals: (A) 16 (B) 32…
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JEE MAIN 2025 (Online) 5th April Morning Shift
Question 1: Let a, b ∈ C. Let α, β be the roots of the equation x² + ax + b = 0. If β – α = √11 and β² – α² = 3i√11, then (β³ – α³)² is equal to: (A) 160 (B) 176 (C) 194 (D) 187 ▶ Click here to Check…
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JEE MAIN 2025 (Online) 6th April Morning Shift
Question 1: Let [t] denote the greatest integer function. If the domain of the function f(x) = sin⁻¹((x + [x])/3) is [α, β), then α² + β² is equal to: (A) 2 (B) 5 (C) 10 (D) 13 ▶ Click here to Check Answer & View Solution Correct Answer: Detailed Verification: [Solution space] Question 2:…
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FORMULA LIBRARY : SEQUENCE AND SERIES
JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX SEQUENCE AND SERIES — JEE MATH APEX — JEE MATH APEX 1. Arithmetic Progression (AP) 📌 General Term & Sum of AP • General form: a, a+d, a+2d, a+3d, … •…
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FORMULA LIBRARY : COMPLEX NUMBERS
JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX JEE MATH APEX COMPLEX NUMBERS — JEE MATH APEX — JEE MATH APEX 1. Definition & Representation 📌 Complex Number Forms • Standard form: z = a + bi (where a, b ∈ R, i² = −1) • Real part: Re(z) = a…
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JEE MAIN 2025 (Online) 8th April Evening Shift
Question 1: Consider the relation R on the set {-2, -1, 0, 1, 2} defined by (a, b) ∈ R if and only if 1 + ab > 0. Then, among the statements: I. The number of elements in R is 17 II. R is an equivalence relation (A) Only I is true (B) Only…
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FORMULA LIBERARY : QUADRATIC EQUATIONS
JEE MATH APEX JEE MATH APEX JEE MATH APEX QUADRATIC EQUATIONS — JEE MATH APEX — JEE MATH APEX 1. General Form & Roots 📌 Standard Quadratic Equation & Quadratic Formula • General form: ax² + bx + c = 0 (where a ≠ 0) • Quadratic formula: x = [−b ± √(b² − 4ac)]…
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FORMULA LIBERARY : SETS
1. Basic Definitions & Representation 📌 Set Notations & Basic Concepts • Set-builder form: { x : P(x) } — the set of all x such that property P(x) holds. • Roster form: A = { 1, 2, 3, 4 } • Empty set: ∅ or { } — contains no element. • Singleton set:…
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FORMULA LIBRARY : SETS
1. Basic Definitions & Representation 📌 Set Notations & Basic Concepts • Set-builder form: { x : P(x) } — the set of all x such that property P(x) holds. • Roster form: A = { 1, 2, 3, 4 } • Empty set: ∅ or { } — contains no element. • Singleton set:…
