Let $\lambda \ne 0$ be in R. If $\alpha $ and $\beta $ are the roots of the equation, x² - x + 2$\lambda $ = 0 and $\alpha $ and $\gamma $ are the roots of the equation, $3{x^2} - 10x + 27\lambda = 0$, then ${{\beta \gamma } \over \lambda }$ is equal to:

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Let $\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$ where each Xi contains 10 e…

Topic: JEE Main 4 September 2020 (Evening)

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Let a1, a2, ..., an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + .... + an. If a1 = 1, an =…

Topic: JEE Main 4 September 2020 (Evening)

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Suppose the vectors x1, x2 and x3 are the solutions of the system of linear equations, Ax = b when the vector b on the …

Topic: JEE Main 4 September 2020 (Evening)

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If a and b are real numbers such that ${\left( {2 + \alpha } \right)^4} = a + b\alpha$ where $\alpha = {{ - 1 + i\sq…

Topic: JEE Main 4 September 2020 (Evening)

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If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, t…

Topic: JEE Main 4 September 2020 (Evening)

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Let $f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)$ be a differentiable function such that f(1) = e and $…

Topic: JEE Main 4 September 2020 (Evening)

7

The minimum value of 2sinx + 2cosx is :

Topic: JEE Main 4 September 2020 (Evening)

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The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie…

Topic: JEE Main 4 September 2020 (Evening)

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In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on …

Topic: JEE Main 4 September 2020 (Evening)

10

The integral $\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2…

Topic: JEE Main 4 September 2020 (Evening)

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The solution of the differential equation${{dy} \over {dx}} - {{y + 3x} \over {{{\log }_e}\left( {y + 3x} \right)}} + 3…

Topic: JEE Main 4 September 2020 (Evening)

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The function $f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} {{1 \…

Topic: JEE Main 4 September 2020 (Evening)