Let $f(x) = \cos \left( {2{{\tan }^{ - 1}}\sin \left( {{{\cot }^{ - 1}}\sqrt {{{1 - x} \over x}} } \right)} \right)$, 0 < x < 1. Then :

1

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)

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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)

3

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)

4

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)

1

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)

2

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)

3

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)

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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)

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If $A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} &amp; {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} &amp…

Topic: JEE Main 2021 (26 August Morning Shift)

6

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)