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Definite Integration · 2021 · Shift 2

6 Mathematics questions from this JEE Advanced paper

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JEE Advanced
Papers
2021 · Shift 2
Mathematics
Definite Integration

Definite Integration · 2021 · Shift 2

6 Mathematics questions from this JEE Advanced paper

Q22.Let $f : [- \frac{π}{2}, \frac{π}{2}] \to R$ be a continuous function such that $f (0) = 1$ and $\int_{0}^{\frac{π}{3}} f (t) d t = 0$ . Then which of the following statements is(are) TRUE?
Mathematics · Definite Integration · Multiple correct
Q30.Let $g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2$ , and $f : [\frac{π}{8}, \frac{3 π}{8}] \to R$ be functions such that $g_{1} (x) = 1, g_{2} (x) = ∣4 x - π ∣$ and $f (x) = sin^{2} x$ , for all $x \in [\frac{π}{8}, \frac{3 π}{8}]$ …
Mathematics · Definite Integration · Numerical
Q31.Let $g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2$ , and $f : [\frac{π}{8}, \frac{3 π}{8}] \to R$ be functions such that $g_{1} (x) = 1, g_{2} (x) = ∣4 x - π ∣$ and $f (x) = sin^{2} x$ , for all $x \in [\frac{π}{8}, \frac{3 π}{8}]$ …
Mathematics · Definite Integration · Numerical
Q34.Let $ψ_{1} : [0, \infty) \to R$ , $ψ_{2} : [0, \infty) \to R$ , f : (0, $\infty$ ) $\to$ R and g : [0, $\infty$ ) $\to$ R be functions such that f(0) = g(0) = 0, $ψ_{1} (x) = e^{- x} + x, x \geq 0$ , $ψ_{2} (x) = x^{2} - 2 x - 2 e^{- x} + 2, x \geq 0$ …
Mathematics · Definite Integration · MCQ
Q35.Let $ψ_{1} : [0, \infty) \to R$ , $ψ_{2} : [0, \infty) \to R$ , f : (0, $\infty$ ) $\to$ R and g : [0, $\infty$ ) $\to$ R be functions such that f(0) = g(0) = 0, $ψ_{1} (x) = e^{- x} + x, x \geq 0$ , $ψ_{2} (x) = x^{2} - 2 x - 2 e^{- x} + 2, x \geq 0$ …
Mathematics · Definite Integration · MCQ
Q38.For any real number x, let [ x ] denote the largest integer less than or equal to x. If $I = 0 \int 10 [\frac{10 x}{x + 1}] d x$ , then the value of 9I is .
Mathematics · Definite Integration · Numerical