Two parabolas `y^(2)=4a(x-lamda_(1))andx^(2)=4a(y-lamda_(2))` always touch each other (`lamda_(1),lamda_(2)` being variable parameters). Then their point of contact lies on a

lamda_1, lamda_2, lamda_3 are the first 3 lines of balmer series. Find lamda_1//lamda_3

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 (x+y)^(2)=2(x^(2)+y^(2))and(x-y+lamda)^(2)=4,lamdagt0, then lamda is equal to :

If line (2x-4)/(lamda)=(lamda-1)/(2)=(z-3)/(1) and (x-1)/(1)=(3y-1)/(lamda)=(z-2)/(1) are perpendicular to each then lamda= . . .

If the lines (x-4)/1=(y-2)/1=(z-lamda)/3 and x/1=(y+2)/2=z/4 intersect each other, then lamda lies in the interval

For two sound waves lamda_(1) = 100 cm, lamda_(2) = 110 cm and velocity of sound is 330 m/s. When lamda_(1) and lamda_(2) super impose, the number of beats produced per second is