If $\int\limits_0^{100\pi } {{{{{\sin }^2}x} \over {{e^{\left( {{x \over \pi } - \left[ {{x \over \pi }} \right]} \right)}}}}dx = {{\alpha {\pi ^3}} \over {1 + 4{\pi ^2}}},\alpha \in R} $ where [x] is the greatest integer less than or equal to x, then the value of $\alpha$ is :
Previous 10 Questions — JEE Main 2021 (22 July Evening Shift)
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Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $\times$ 2 matrices. The prob…
Topic: JEE Main 2021 (22 July Evening Shift)
Let y = y(x) be the solution of the differential equation $\cos e{c^2}xdy + 2dx = (1 + y\cos 2x)\cos e{c^2}xdx$, with $…
Topic: JEE Main 2021 (22 July Evening Shift)
Let f : R $\to$ R be defined as $f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr …
Topic: JEE Main 2021 (22 July Evening Shift)
Let Sn denote the sum of first n-terms of an arithmetic progression. If S10 = 530, S5 = 140, then S20 $-$ S6 is equal t…
Topic: JEE Main 2021 (22 July Evening Shift)
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The values of $\lambda$ and $\mu$ such that the system of equations $x + y + z = 6$, $3x + 5y + 5z = 26$, $x + 2y + \la…
Topic: JEE Main 2021 (22 July Evening Shift)
If the shortest distance between the straight lines $3(x - 1) = 6(y - 2) = 2(z - 1)$ and $4(x - 2) = 2(y - \lambda ) = …
Topic: JEE Main 2021 (22 July Evening Shift)
Let A = [aij] be a real matrix of order 3 $\times$ 3, such that ai1 + ai2 + ai3 = 1, for i = 1, 2, 3. Then, the sum of …
Topic: JEE Main 2021 (22 July Evening Shift)
Let [x] denote the greatest integer less than or equal to x. Then, the values of x$\in$R satisfying the equation ${[{e^…
Topic: JEE Main 2021 (22 July Evening Shift)
Let the circle S : 36x2 + 36y2 $-$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate a…
Topic: JEE Main 2021 (22 July Evening Shift)
Let n denote the number of solutions of the equation z2 + 3$\overline z $ = 0, where z is a complex number. Then the va…
Topic: JEE Main 2021 (22 July Evening Shift)
If the domain of the function $f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{…
Topic: JEE Main 2021 (22 July Evening Shift)
Let f : R $\to$ R be defined as $f(x) = \left\{ {\matrix{ {{{{x^3}} \over {{{(1 - \cos 2x)}^2}}}{{\log }_e}\left( {{{…
Topic: JEE Main 2021 (22 July Evening Shift)
Let ${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$. Let E2 be another ellipse such that it touc…
Topic: JEE Main 2021 (22 July Evening Shift)
