Let y = y(x) be the solution of the differential equation $x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( {{y \over x}} \right) - x} \right)dx$, $ - 1 \le x \le 1$, $y\left( {{1 \over 2}} \right) = {\pi \over 6}$. Then the area of the region bounded by the curves x = 0, $x = {1 \over {\sqrt 2 }}$ and y = y(x) in the upper half plane is :
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Let [ x ] denote the greatest integer $\le$ x, where x $\in$ R. If the domain of the real valued function $f(x) = \sqrt…
Topic: JEE Main 2021 (20 July Morning Shift)
If z and $\omega$ are two complex numbers such that $\left| {z\omega } \right| = 1$ and $\arg (z) - \arg (\omega ) = {{…
Topic: JEE Main 2021 (20 July Morning Shift)
Let $A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$, a$\in$R be written as P + Q where P is a sy…
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If $\alpha$ and $\beta$ are the distinct roots of the equation ${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$, then the value o…
Topic: JEE Main 2021 (20 July Morning Shift)
The value of the integral $\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $ is equal to:
Topic: JEE Main 2021 (20 July Morning Shift)
The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, t…
Topic: JEE Main 2021 (20 July Morning Shift)
Let a be a positive real number such that $\int_0^a {{e^{x - [x]}}} dx = 10e - 9$ where [ x ] is the greatest integer l…
Topic: JEE Main 2021 (20 July Morning Shift)
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Let $A = [{a_{ij}}]$ be a 3 $\times$ 3 matrix, where ${a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr …
Topic: JEE Main 2021 (20 July Morning Shift)
The number of real roots of the equation ${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi…
Topic: JEE Main 2021 (20 July Morning Shift)
Let y = y(x) be the solution of the differential equation ${e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy =…
Topic: JEE Main 2021 (20 July Morning Shift)
Let 'a' be a real number such that the function f(x) = ax2 + 6x $-$ 15, x $\in$ R is increasing in $\left( { - \infty ,…
Topic: JEE Main 2021 (20 July Morning Shift)
Let a function f : R $\to$ R be defined as $f(x) = \left\{ {\matrix{ {\sin x - {e^x}} & {if} & {x \le 0} \cr…
Topic: JEE Main 2021 (20 July Morning Shift)
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the …
Topic: JEE Main 2021 (20 July Morning Shift)
The probability of selecting integers a$\in$[$-$ 5, 30] such that x2 + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, i…
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