Let the eccentricity of the ellipse ${x^2} + {a^2}{y^2} = 25{a^2}$ be b times the eccentricity of the hyperbola ${x^2} - {a^2}{y^2} = 5$, where a is the minimum distance between the curves y = e^x and y = log_ex. Then ${a^2} + {1 \over {{b^2}}}$ is equal to :

1

Let $\alpha_1, \alpha_2 ; (\alpha_1 < \alpha_2)$ be the values of $\alpha$ for the points $(\alpha, -3), (2, 0)$ and $(…

Topic: JEE Main 2022 (30 June Morning Shift)

2

Let m and M respectively be the minimum and the maximum values of $f(x) = {\sin ^{ - 1}}2x + \sin 2x + {\cos ^{ - 1}}2x…

Topic: JEE Main 2022 (30 June Morning Shift)

3

If xy4 attains maximum value at the point (x, y) on the line passing through the points (50 + $\alpha$, 0) and (0, 50 +…

Topic: JEE Main 2022 (30 June Morning Shift)

4

If xy4 attains maximum value at the point (x, y) on the line passing through the points (50 + $\alpha$, 0) and (0, 50 +…

Topic: JEE Main 2022 (30 June Morning Shift)

5

For two positive real numbers a and b such that ${1 \over {{a^2}}} + {1 \over {{b^3}}} = 4$, then minimum value of the …

Topic: JEE Main 2022 (30 June Morning Shift)

6

Let $A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right]$ and $B = \left[ {\matr…

Topic: JEE Main 2022 (30 June Morning Shift)

7

The real part of the complex number ${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$ …

Topic: JEE Main 2022 (30 June Morning Shift)

8

The real part of the complex number ${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$ …

Topic: JEE Main 2022 (30 June Morning Shift)

9

Let ${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$ and ${…

Topic: JEE Main 2022 (30 June Morning Shift)

1

$ \alpha = \tan\left(\frac{5\pi}{16} \sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right) $ $ \beta = \cos…

Topic: JEE Main 2022 (30 June Morning Shift)