Let f : R $ \to $ R be defined as f(x) = e^$-$xsinx. If F : [0, 1] $ \to $ R is a differentiable function with that F(x) = $\int_0^x {f(t)dt} $, then the value of $\int_0^1 {(F'(x) + f(x)){e^x}dx} $ lies in the interval

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Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurren…

Topic: JEE Main 2021 (17 March Evening Shift)

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If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of tri…

Topic: JEE Main 2021 (17 March Evening Shift)

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Let $S_1, S_2$ and $S_3$ be three sets defined as $S_1 = \{z \in C : |z - 1| \le \sqrt{2}\}$ ,$S_2 = \{z \in C : …

Topic: JEE Main 2021 (17 March Evening Shift)

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The number of solutions of the equation ${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^…

Topic: JEE Main 2021 (17 March Evening Shift)

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If the curve y = y(x) is the solution of the differential equation $2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})dx = {2x^…

Topic: JEE Main 2021 (17 March Evening Shift)

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Let O be the origin. Let $\overrightarrow{OP} = x\widehat i + y\widehat j - \widehat k$ and $\overrightarrow{OQ} = -\wi…

Topic: JEE Main 2021 (17 March Evening Shift)

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$ \text{If } \displaystyle \int_{0}^{10}\frac{[\sin 2\pi x]}{e^{,x-[x]}},dx ;=; \alpha e^{-1}+\beta e^{-1/2}+\gamma,\ \…

Topic: JEE Main 2021 (17 March Evening Shift)

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The value of the limit $\mathop {\lim }\limits_{\theta \to 0} {{\tan (\pi {{\cos }^2}\theta )} \over {\sin (2\pi {{\s…

Topic: JEE Main 2021 (17 March Evening Shift)

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Consider the function f : R $ \to $ R defined by $f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right…

Topic: JEE Main 2021 (17 March Evening Shift)

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The value of $\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}$, where r is a non-zero …

Topic: JEE Main 2021 (17 March Evening Shift)

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If x, y, z are in arithmetic progression with common difference d, x $\ne$ 3d, and the determinant of the matrix $\left…

Topic: JEE Main 2021 (17 March Evening Shift)

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Let y = y(x) be the solution of the differential equation $\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos…

Topic: JEE Main 2021 (17 March Evening Shift)