class 12

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JEE Advanced

A position is emitted from $_{11}Na$. The ratio of the atomic mass and atomic number of the resulting nuclide is

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Let $XandY$be two events that $P(X)=31 ,P(X|Y)=21 andP(Y|X)=52 $then:$P(Y)=154 $ (b) $P(X∪Y)=52 $$P(X_{prime}|Y)=21 $ (d) $P(X∩Y)=51 $

A pack contains $n$cards numbered from 1 to $n$. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of het numbers on the removed cards is $k,$then $k−20=$____________.

Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let $x$be the number of such words where no letter is repeated; and let $y$be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, $9xy =$

Let $P$be a matrix of order $3×3$such that all the entries in $P$are from the set ${−1,0,1}$. Then, the maximum possible value of the determinant of $P$is ______.

Let $f(x)=7tan_{8}x+7tan_{6}x−3tan_{4}x−3tan_{2}x$for all $x∈(−2π ,2π )$ . Then the correct expression (s) is (are) (a) $∫_{0}xf(x)dx=121 $ (b)$∫_{0}f(x)dx=0$(c)$∫_{0}xf(x)=61 $ (d) $∫_{0}f(x)dx=121 $

The largets value of non negative integer for which $x→1lim x+sin(x−1)−1(−ax+sin(x−1)+a]1−x }_{1−x1−x}=41 $

Let $S$be the set of all non-zero real numbers such that the quadratic equation $αx_{2}−x+α=0$has two distinct real roots $x_{1}andx_{2}$satisfying the inequality $∣x_{1}−x_{2}∣<1.$Which of the following intervals is (are) a subset (s) of $S?$$(21 ,5 1 )$b. $(5 1 ,0)$c. $(0,5 1 )$d. $(5 1 ,21 )$

Let $X$be the set consisting of the first 2018 terms of the arithmetic progression $1,6,11,,¨ $and $Y$be the set consisting of the first 2018 terms of the arithmetic progression $9,16,23,¨$. Then, the number of elements in the set $X∪Y$is _____.