Let the maximum area of the triangle that can be inscribed in the ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} = 1,\,a > 2$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt 3 $. Then the eccentricity of the ellipse is :
Previous 10 Questions — JEE Main 2022 (24 June Evening Shift)
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A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at th…
Topic: JEE Main 2022 (24 June Evening Shift)
The value of the integral $\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {(1 + {e^x})({{\sin }^6}x + {{\cos }^6}x)}}} $…
Topic: JEE Main 2022 (24 June Evening Shift)
Let $$f(x) = \left\{ {\matrix{ {{{\sin (x - [x])} \over {x - [x]}}} & {,\,x \in ( - 2, - 1)} \cr {\max \{ 2x,3[|x…
Topic: JEE Main 2022 (24 June Evening Shift)
Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is
Topic: JEE Main 2022 (24 June Evening Shift)
Let the system of linear equations
$x + y + \alpha z = 2$,
$3x + y + z = 4$,
$x + 2z = 1$
have a unique solution $(x^…
Topic: JEE Main 2022 (24 June Evening Shift)
The sum of all the real roots of the equation $({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$ is
Topic: JEE Main 2022 (24 June Evening Shift)
Let $x * y = {x^2} + {y^3}$ and $(x * 1) * 1 = x * (1 * 1)$.Then a value of $2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2…
Topic: JEE Main 2022 (24 June Evening Shift)
Next 10 Questions — JEE Main 2022 (24 June Evening Shift)
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Let the area of the triangle with vertices $A(1,\alpha)$, $B(\alpha,0)$ and $C(0,\alpha)$ be $4$ sq. units. If the poin…
Topic: JEE Main 2022 (24 June Evening Shift)
The number of distinct real roots of the equation x7 $-$ 7x $-$ 2 = 0 is
Topic: JEE Main 2022 (24 June Evening Shift)
A random variable X has the following probability distribution :The value of P(1 < X < 4 | X $\le$ 2) is equal to…
Topic: JEE Main 2022 (24 June Evening Shift)
If the shortest distance between the lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{\lambda}$ and $\dfrac{x-2}{1}…
Topic: JEE Main 2022 (24 June Evening Shift)
If the shortest distance between the lines $\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{\lambda}$ and $\dfrac{x-2}{1}…
Topic: JEE Main 2022 (24 June Evening Shift)
If $y = {\tan ^{ - 1}}\left( {\sec {x^3} - \tan {x^3}} \right),{\pi \over 2} < {x^3} < {{3\pi } \over 2}$, then
Topic: JEE Main 2022 (24 June Evening Shift)
Let $\lambda^*$ be the largest value of $\lambda$ for which the function $f_\lambda(x) = 4\lambda x^3 - 36\lambda x^2 +…
Topic: JEE Main 2022 (24 June Evening Shift)
