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JEE Advanced

For the process $H_{2}(l)→H_{2}O(g)$ at $T=100_{∘}C$ and 1 atmosphere pressure, the correct choice is

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In the following reactions, the structure of the major product 'X' is

The coefficient of $x_{9}$ in the expansion of $(1+x)(1+x_{2})(1+x_{3})….(1+x_{100})$ is

Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

In a triangle PQR, P is the largest angle and $cosP=31 $. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of $nm $ is ____

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

Let a,b ,c be positive integers such that $ab $ is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of $a+1a_{2}+a−14 $ is

Let $V_{r}$ denote the sum of the first' ' terms of an arithmetic progression (A.P.) whose first term is'r and the common difference is $(2r−1)$. Let $T_{r}=V_{r+1}−V_{r}−2$ and $Q_{r}=T_{r+1}−T_{r}$ for $r=1,2,…….$ The sum $V_{1}+V_{2}+……+V_{n}$ is