25 verified questions · ~38 minutes · answer key checked against the official NTA final key across multiple sources. Text-only questions (diagram-based excluded until they can be shown properly).
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 fog: [2, 4] → ℝ is [α, β], then 1/(β − α) is equal to
Consider the sets A = {(x, y) ∈ ℝ × ℝ : x² + y² = 25}, B = {(x, y) ∈ ℝ × ℝ : x² + 9y² = 144}, C = {(x, y) ∈ 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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