If $y = y(x)$ is the solution of the differential equation $x{{dy} \over {dx}} + 2y = x\,{e^x}$, $y(1) = 0$ then the local maximum value of the function $z(x) = {x^2}y(x) - {e^x},\,x \in R$ is :

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If $\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c} $, $g(1) = 0$, then $g\left( {{1 \over 2}} \right)$…

Topic: JEE Main 2022 (26 June Evening Shift)

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The area of the region bounded by y2 = 8x and y2 = 16(3 $-$ x) is equal to:

Topic: JEE Main 2022 (26 June Evening Shift)

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Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a co…

Topic: JEE Main 2022 (26 June Evening Shift)

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Let f(x) = min {1, 1 + x sin x}, 0 $\le$ x $\le$ 2$\pi $. If m is the number of points, where f is not differentiable a…

Topic: JEE Main 2022 (26 June Evening Shift)

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$\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}$ is equal to :

Topic: JEE Main 2022 (26 June Evening Shift)

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If the system of equations$\alpha$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $\beta$has infinitely many solutions, t…

Topic: JEE Main 2022 (26 June Evening Shift)

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Let f : R $\to$ R be defined as f (x) = x $-$ 1 and g : R $-$ {1, $-$1} $\to$ R be defined as $g(x) = {{{x^2}} \over {{…

Topic: JEE Main 2022 (26 June Evening Shift)

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f the solution of the differential equation ${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x}…

Topic: JEE Main 2022 (26 June Evening Shift)

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The locus of the mid point of the line segment joining the point (4, 3) and the points on the ellipse ${x^2} + 2{y^2} =…

Topic: JEE Main 2022 (26 June Evening Shift)

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Let $\overrightarrow a = \widehat i + \widehat j + 2\widehat k$, $\overrightarrow b = 2\widehat i - 3\widehat j + \wi…

Topic: JEE Main 2022 (26 June Evening Shift)

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The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observati…

Topic: JEE Main 2022 (26 June Evening Shift)

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$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$ is equal to :

Topic: JEE Main 2022 (26 June Evening Shift)

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If the inverse trigonometric functions take principal values then ${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\…

Topic: JEE Main 2022 (26 June Evening Shift)

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The area of the polygon, whose vertices are the non-real roots of the equation $\overline z = i{z^2}$ is :

Topic: JEE Main 2022 (26 June Evening Shift)

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Let the system of linear equations $x + 2y + z = 2$, $\alpha x + 3y - z = \alpha $, $ - \alpha x + y + 2z = - \alpha $…

Topic: JEE Main 2022 (26 June Evening Shift)

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$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} …

Topic: JEE Main 2022 (26 June Evening Shift)