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Limits Continuity and Differentiability · 2020 · Shift 2

3 Mathematics questions from this JEE Advanced paper

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JEE Advanced
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2020 · Shift 2
Mathematics
Limits Continuity and Differentiability

Limits Continuity and Differentiability · 2020 · Shift 2

3 Mathematics questions from this JEE Advanced paper

Q23.Let the functions $f : (- 1, 1) \to R$ and $g : (- 1, 1) \to (- 1, 1)$ be defined by $f (x) = ∣2 x - 1∣ + ∣2 x + 1∣$ and $g (x) = x - [x]$ , where [x] denotes the greatest integer less than or equal to x. Let $f o g : (- 1, 1) \to R$ be the…
Mathematics · Limits Continuity and Differentiability · Numerical
Q24.The value of the limit $x \to \frac{π}{2} lim \frac{4 2 ( s i n 3 x + s i n x )}{( 2 s i n 2 x s i n \frac{3 x}{2} + c o s \frac{5 x}{2} ) - ( 2 + 2 c o s 2 x + c o s \frac{3 x}{2} )}$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q27.Let f : R $\to$ R and g : R $\to$ R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y $\in$ R. If $x \to 0 lim g (x) = 1$ , then which of the following statements is/are TRUE?
Mathematics · Limits Continuity and Differentiability · Multiple correct