The least value of |z| where z is complex number which satisfies the inequality $\exp \left( {{{(|z| + 3)(|z| - 1)} \over {||z| + 1|}}{{\log }_e}2} \right) \ge {\log _{\sqrt 2 }}|5\sqrt 7 + 9i|,i = \sqrt { - 1} $, is equal to :

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Let A = {2, 3, 4, 5, ....., 30} and '$ \simeq $' be an equivalence relation on A $\times$ A, defined by (a, b) $ \simeq…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $\int_0^1 {P(x)dx} $ = 1 and P(x) lea…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let C1 be the curve obtained by the solution of differential equation $2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0$…

Topic: JEE Main 2021 (16 March Evening Shift)

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Consider the integral $I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx} $, where [x] denotes the greatest int…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let f : S $ \to $ S where S = (0, $\infty $) be a twice differentiable function such that f(x + 1) = xf(x). If g : S $ …

Topic: JEE Main 2021 (16 March Evening Shift)

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Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Le…

Topic: JEE Main 2021 (16 March Evening Shift)

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If the foot of the perpendicular from point (4, 3, 8) on the line ${L_1}:{{x - a} \over l} = {{y - 2} \over 3} = {{z - …

Topic: JEE Main 2021 (16 March Evening Shift)

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Let $\overrightarrow{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\overrightarrow{b} = 2\hat{i} - 3\hat{j} + 5\hat{k}$. I…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let f be a real valued function, defined on R $-$ {$-$1, 1} and given by f(x) = 3 loge $\left| {{{x - 1} \over {x + 1}}…

Topic: JEE Main 2021 (16 March Evening Shift)

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If y = y(x) is the solution of the differential equation ${{dy} \over {dx}}$ + (tan x) y = sin x, $0 \le x \le {\pi \o…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let $\alpha$ $\in$ R be such that the function $f(x) = \left\{ {\matrix{ {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin…

Topic: JEE Main 2021 (16 March Evening Shift)

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Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which s…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2${\sq…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let A($-$1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at poin…

Topic: JEE Main 2021 (16 March Evening Shift)

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Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. The…

Topic: JEE Main 2021 (16 March Evening Shift)

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The maximum value of $f(x) = \left| {\matrix{ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr {1 + {{…

Topic: JEE Main 2021 (16 March Evening Shift)