Arrange the following wavelenghts `(lamda)`of given emission lines of H atoms in increasing order Choose the correct option (1) `lamda_(4)ltlamda_(3)ltlamda_(2)ltlamda_(1)` (2)`lamda_(4)ltlamda_(2)ltlamda_(3)ltlamda_(1)` (3) `lamda_(1)ltlamda_(2)ltlamda_(3)ltlamda_(4)` (4) `lamda_(1)ltlamda_(3)ltlamda_(2)ltlamda_(4)`

If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(lamda-3, lamda+4, 3lamda)|=plamda^(4)+qlamda^(3)+rlamda^(3)+slamda+t ,then t=

If plamda^(4)+qlamda^3+rlamda^2+slamda+t =|(lamda^3+3lamda,lamda-1,lamda+3),(lamda+1,2-lamda,lamda-3),(lamda-3,lamda+4,3lamda)| then t is equal to :

Due to transitions among its first three energy levels, hydrogenic atom emits radiation at three discrete wavelengths lamda_(1), lamda_(2), " and " lamda_(3) (lamda_(1) lt lamda_(2) lt lamda_(3)) . Then

The matrix A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:} is idempotent if lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k where lamda_(1),lamda_(2),lamda_(3) are non-zero real numbers. Then the value of (10+k)^(2) is . . .

The matrix A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:} is idempotent if lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k where lamda_(1),lamda_(2),lamda_(3) are non-zero real numbers. Then the value of (10+k)^(2) is . . .

If p lamda ^(4) + q lamda ^(3) + r lamda ^(2) + s lamda +t = |{:(lamda ^(2) + 3 lamda, lamda -1, lamda +3), ( lamda +1, 2 - lamda , lamda -4), ( lamda -3, lamda+4, 3lamda):}|. then the value of t is

Let plamda^(4)+qlamda^(3)+rlamda^(2)+slamda+t =|(lamda^(2)+3lamda,lamda-1,lamda-3),(lamda-1,-2lamda,lamda-4),(lamda-3,lamda+4,3lamda)| where p,q,r,s, and t are constant. Then value of t is

If |a_(i)|lt1lamda_(i)ge0 for i=1,2,3,.......nandlamda_(1)+lamda_(2)+.......+lamda_(n)=1 then the value of |lamda_(1)a_(1)+lamda_(2)a_(2)+.......+lamda_(n)a_(n)| is :

If |a_(i)|lt1lamda_(i)ge0 for i=1,2,3,.......nandlamda_(1)+lamda_(2)+.......+lamda_(n)=1 then the value of |lamda_(1)a_(1)+lamda_(2)a_(2)+.......+lamda_(n)a_(n)| is :