1
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
Change Language
Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B) such that 1 $$ \le $$ |B| < |A|, equals .............
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2
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
Change Language
Suppose

det$$\left| {\matrix{ {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \cr {\sum\limits_{k = 0}^n {{}^n{C_k}.k} } & {\sum\limits_{k = 0}^n {{}^n{C_k}{3^k}} } \cr } } \right| = 0$$

holds for some positive integer n. Then $$\sum\limits_{k = 0}^n {{{{}^n{C_k}} \over {k + 1}}} $$ equals ..............
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3
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
Change Language
Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is ............
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4
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
Change Language
The value of the integral $$ \int\limits_0^{\pi /2} {{{3\sqrt {\cos \theta } } \over {{{(\sqrt {\cos \theta } + \sqrt {\sin \theta } )}^5}}}} d\theta $$ equals ..............
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