The area of the region : $R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $

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The area of the region : $R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $

Topic: JEE Main 2021 (24 February Evening Shift)

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A possible value of $\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)$ is :

Topic: JEE Main 2021 (24 February Evening Shift)

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The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their inters…

Topic: JEE Main 2021 (24 February Evening Shift)

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If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x $-$ 1, then the co-ordinates of…

Topic: JEE Main 2021 (24 February Evening Shift)

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$f:R \to R$ be defined as$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,…

Topic: JEE Main 2021 (24 February Evening Shift)

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Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $ \ne $ 0 for all x $ \in…

Topic: JEE Main 2021 (24 February Evening Shift)

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Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 $-$ x) for all x$ \in $ (0, 2), f(0) = 1…

Topic: JEE Main 2021 (24 February Evening Shift)

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For the system of linear equations: $x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$, consider the following statemen…

Topic: JEE Main 2021 (24 February Evening Shift)

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Let a, b$ \in $R. If the mirror image of the point P(a, 6, 9) with respect to the line ${{x - 3} \over 7} = {{y - 2} \o…

Topic: JEE Main 2021 (24 February Evening Shift)

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The value of the integral, $\int\limits_1^3 {[{x^2} - 2x - 2]dx} $, where [x] denotes the greatest integer less than or…

Topic: JEE Main 2021 (24 February Evening Shift)

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Let $f(x) = 3{\sin ^4}x + 10{\sin ^3}x + 6{\sin ^2}x - 3$, $x \in \left[ { - {\pi \over 6},{\pi \over 2}} \right]$. T…

Topic: JEE Main 2021 (24 February Evening Shift)

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Let Sn be the sum of the first n terms of an arithmetic progression. If S3n = 3S2n, then the value of ${{{S_{4n}}} \ove…

Topic: JEE Main 2021 (24 February Evening Shift)