Let $A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right]$ and $B = \left[ {\matrix{ 2 & \alpha \cr { - 1} & 2 \cr 4 & { - 5} \cr } } \right],\,\alpha \in C$. Then the absolute value of the sum of all values of $\alpha$ for which det(AB) = 0 is :
Previous 10 Questions — JEE Main 2022 (30 June Morning Shift)
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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)
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)
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)
Next 10 Questions — JEE Main 2022 (30 June Morning Shift)
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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)
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)
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)
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)
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)
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} …
Topic: JEE Main 2022 (30 June Morning Shift)
$ \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)
