Let the eccentricity of an ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$, $a > b$, be ${1 \over 4}$. If this ellipse passes through the point $\left( { - 4\sqrt {{2 \over 5}} ,3} \right)$, then ${a^2} + {b^2}$ is equal to :
Previous 10 Questions — JEE Main 2022 (27 June Morning Shift)
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In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie…
Topic: JEE Main 2022 (27 June Morning Shift)
If ${{dy} \over {dx}} + {{{2^{x - y}}({2^y} - 1)} \over {{2^x} - 1}} = 0$, x, y > 0, y(1) = 1, then y(2) is equal to :
Topic: JEE Main 2022 (27 June Morning Shift)
The value of the integral $\int\limits_{ - 2}^2 {{{|{x^3} + x|} \over {({e^{x|x|}} + 1)}}dx} $ is equal to :
Topic: JEE Main 2022 (27 June Morning Shift)
If $\int {{{({x^2} + 1){e^x}} \over {{{(x + 1)}^2}}}dx = f(x){e^x} + C} $, where C is a constant, then ${{{d^3}f} \over…
Topic: JEE Main 2022 (27 June Morning Shift)
If ${\cos ^{ - 1}}\left( {{y \over 2}} \right) = {\log _e}{\left( {{x \over 5}} \right)^5},\,|y| < 2$, then :
Topic: JEE Main 2022 (27 June Morning Shift)
The number of distinct real roots of x4 $-$ 4x + 1 = 0 is :
Topic: JEE Main 2022 (27 June Morning Shift)
Let a be an integer such that $\mathop {\lim }\limits_{x \to 7} {{18 - [1 - x]} \over {[x - 3a]}}$ exists, where [t] is…
Topic: JEE Main 2022 (27 June Morning Shift)
Next 10 Questions — JEE Main 2022 (27 June Morning Shift)
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If two straight lines whose direction cosines are given by the relations $l + m - n = 0$, $3{l^2} + {m^2} + cnl = 0$ ar…
Topic: JEE Main 2022 (27 June Morning Shift)
Let $\overrightarrow a = \widehat i + \widehat j - \widehat k$ and $\overrightarrow c = 2\widehat i - 3\widehat j + 2…
Topic: JEE Main 2022 (27 June Morning Shift)
Five numbers ${x_1},{x_2},{x_3},{x_4},{x_5}$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arrang…
Topic: JEE Main 2022 (27 June Morning Shift)
The value of $\cos \left( {{{2\pi } \over 7}} \right) + \cos \left( {{{4\pi } \over 7}} \right) + \cos \left( {{{6\pi }…
Topic: JEE Main 2022 (27 June Morning Shift)
$\sin^{-1}\left(\sin \frac{2\pi}{3}\right) + \cos^{-1}\left(\cos \frac{7\pi}{6}\right) + \tan^{-1}\left(\tan \frac{3\pi…
Topic: JEE Main 2022 (27 June Morning Shift)
