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JEE Advanced

The wavelength of the first spectral line in the Balmer series of hydrogenatom is 6561 Å. The wavelength of the second spectral lie in the Balmer series of singly-ionized helium atom is

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Consider the cube in the first octant with sides OP,OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where $O(0,0,0)$ is the origin. Let $S(21 ,21 ,21 )$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If $p =SP,q =SQ ,r=SR$ and $t=ST$ then the value of $∣(p ×q )×(r×(t)∣is$

Let $MandN$ be two $3×3$ matrices such that $MN=NM˙$ Further, if $M=N_{2}andM_{2}=N_{4},$ then Determinant of $(M_{2}+MN_{2})$ is 0 There is a $3×3$ non-zeero matrix $U$ such tht $(M_{2}+MN_{2})U$ is the zero matrix Determinant of $(M_{2}+MN_{2})≥1$For a $3×3$ matrix $U,if(M_{2}+MN_{2})U$ equal the zero mattix then $U$ is the zero matrix

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 ____

Consider the set of eight vector $V={ai^+bj^ +ck^;a,bc∈{−1,1}}˙$Three non-coplanar vectors can be chosen from $V$is $2_{p}$ways. Then $p$is_______.

Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her, is (A) $21 $ (B) $31 $ (C) $32 $ (D) $43 $

Let $z_{k}=cos(2k10π )+isin(2k10π );k=1,2,34,…,9$ (A) For each $z_{k}$ there exists a $z_{j}$ such that $z_{k}.z_{j}=1$ (ii) there exists a $k∈{1,2,3,…,9}$ such that $z_{1}z=z_{k}$

Let w = ($3 +2ι )$ and $P={w_{n}:n=1,2,3,…..},$ Further $H_{1}={z∈C:Re(z)>21 }andH_{2}={z∈c:Re(z)<−21 }$ Where C is set of all complex numbers. If $z_{1}∈P∩H_{1},z_{2}∈P∩H_{2}$ and O represent the origin, then $∠Z_{1}OZ_{2}$ =

Let $−61 <θ<−12π $ Suppose $α_{1}andβ_{1}$, are the roots of the equation $x_{2}−2xsecθ+1=0$ and $α_{2}andβ_{2}$ are the roots of the equation $x_{2}+2xtanθ−1=0$. If $α_{1}>β_{1}$ and $α_{2}>β_{2}$, then $α_{1}+β_{2}$ equals