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, B occurs) = ${5 \over 9}$, is :
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The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mis…
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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)
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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 $f(x) = \cos \left( {2{{\tan }^{ - 1}}\sin \left( {{{\cot }^{ - 1}}\sqrt {{{1 - x} \over x}} } \right)} \right)$, 0…
Topic: JEE Main 2021 (26 August Morning Shift)
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)
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)
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 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 = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} &…
Topic: JEE Main 2021 (26 August Morning Shift)
If the sum of an infinite GP a, ar, ar2, ar3, ....... is 15 and the sum of the squares of its each term is 150, then th…
Topic: JEE Main 2021 (26 August Morning Shift)
