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Assertion-1: The period of the function f(x) = sin(4π{ x }) + tan(π[x]), where [x] and {x} represent the greatest integer function and fractional part of x respectively, is 1. Assertion-2: A function f(x) is called periodic if there exists a positive constant T, independent of x, such that f(x+T)=f(x). The least such positive T is the period, or fundamental period.

1. Assertion-1 is false, Assertion-2 is true.
2. Assertion-1 is true, Assertion-2 is true, and Assertion-2 correctly explains Assertion-1.
3. Assertion-1 is true, Assertion-2 is true, but Assertion-2 does not correctly explain Assertion-1.
4. Assertion-1 is true, Assertion-2 is false.

Correct answer: Assertion-1 is true, Assertion-2 is true, and Assertion-2 correctly explains Assertion-1.

Solution

Assertion-1 is true because the function combines periodic components, resulting in a period of 1. Assertion-2 is true as it defines periodicity accurately, and since Assertion-1 is a specific case of this definition, it correctly explains why the function is periodic.

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