If the value of the integral $\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta } $, where $\alpha$, $\beta$ $\in$ R, 5$\alpha$ + 6$\beta$ = 0, and [x] denotes the greatest integer less than or equal to x; then the value of ($\alpha$ + $\beta$)2 is equal to :
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The local maximum value of the function $f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$, x > 0, is
Topic: JEE Main 2021 (26 August Evening Shift)
Let $A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 1 \cr 1 & 0 & 0 \cr } } \right)$. T…
Topic: JEE Main 2021 (26 August Evening Shift)
Let [t] denote the greatest integer less than or equal to t. Let f(x) = x $-$ [x], g(x) = 1 $-$ x + [x], and h(x) = min…
Topic: JEE Main 2021 (26 August Evening Shift)
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Let y(x) be the solution of the differential equation 2x2 dy + (ey $-$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is …
Topic: JEE Main 2021 (26 August Evening Shift)
The domain of the function ${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$ is :
Topic: JEE Main 2021 (26 August Evening Shift)
A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probabil…
Topic: JEE Main 2021 (26 August Evening Shift)
If $\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $, then the value of tan p is :
Topic: JEE Main 2021 (26 August Evening Shift)
Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations, x + y…
Topic: JEE Main 2021 (26 August Evening Shift)
The locus of the mid points of the chords of the hyperbola x2 $-$ y2 = 4, which touch the parabola y2 = 8x, is :
Topic: JEE Main 2021 (26 August Evening Shift)
The value of $2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8…
Topic: JEE Main 2021 (26 August Evening Shift)
If ${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$, then p and q are roots of the equation :
Topic: JEE Main 2021 (26 August Evening Shift)
The value of $\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\left( {{{1 + {{\sin }^2}x} \over {1 + {\pi ^{\sin x}}}…
Topic: JEE Main 2021 (26 August Evening Shift)
A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two poi…
Topic: JEE Main 2021 (26 August Evening Shift)
