jee_main_2025_04_april_morning - Sets, Relations and Functions Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

QUESTION #51 Composition of Functions
Let f, g: (1, ∞) → R be defined as f(x) = (2x + 3)/(5x + 2) and g(x) = (2 - 3x)/(1 - x). If the range of the function f(g(x)) on the interval [2, 4] is [α, β], then (1)/(β - α) is equal to
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QUESTION #52 Number of Functions
Consider the sets: A = (x,y) in R × R : x² + y² = 25 B = (x,y) in R × R : (x²)/(144) + (y²)/(16) = 1 C = (x,y) in Z × Z : x² + y² ≤ 4 and D = A B. The total number of one-one functions from the set D to the set C is:
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QUESTION #60 Functional Equations and Series
Let f: R → R be a continuous function satisfying f(0) = 1 and f(2x) - f(x) = x for all x in R. If n → ∞ f(x) - f((x)/(2ⁿ)) = G(x), then Σr=1¹⁰ G(r²) is equal to
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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