If $A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \cr } } \right)$, $B = \left( {\matrix{ 1 & 0 \cr i & 1 \cr } } \right)$, $i = \sqrt { - 1} $, and Q = ATBA, then the inverse of the matrix A Q2021 AT is equal to :
Previous 10 Questions — JEE Main 2021 (26 August Morning Shift)
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The value of $\int\limits_{{{ - 1} \over {\sqrt 2 }}}^{{1 \over {\sqrt 2 }}} {{{\left( {{{\left( {{{x + 1} \over {x - 1…
Topic: JEE Main 2021 (26 August Morning Shift)
If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point ($-$30, 0) and is tangent to…
Topic: JEE Main 2021 (26 August Morning Shift)
The equation $\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$ represents a circle with :
Topic: JEE Main 2021 (26 August Morning Shift)
Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs…
Topic: JEE Main 2021 (26 August Morning Shift)
Let $f(x) = \cos \left( {2{{\tan }^{ - 1}}\sin \left( {{{\cot }^{ - 1}}\sqrt {{{1 - x} \over x}} } \right)} \right)$, 0…
Topic: JEE Main 2021 (26 August Morning Shift)
Let $\theta \in \left( {0,{\pi \over 2}} \right)$. If the system of linear equations $(1 + {\cos ^2}\theta )x + {\sin…
Topic: JEE Main 2021 (26 August Morning Shift)
Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A,…
Topic: JEE Main 2021 (26 August Morning Shift)
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mis…
Topic: JEE Main 2021 (26 August Morning Shift)
Let y = y(x) be a solution curve of the differential equation $(y + 1){\tan ^2}x\,dx + \tan x\,dy + y\,dx = 0$, $x \in …
Topic: JEE Main 2021 (26 August Morning Shift)
