A variable plane moves so that the sum of reciprocals of its intercepts on the three coordinate axes is constant `lambda` . It passes through a fixed point whose coordinate are (a) `(lambda,lambda,lambda)` (b) `((-1)/lambda,(-1)/lambda,(-1)/lambda)` (c) `(1/lambda,1/lambda,1/lambda)` (d) `(-lambda,-lambda,-lambda)dot`

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-1, lambda+3] , [lambda^2+1, 2-lambda, lambda-3] , [lambda^2-3, lambda+4, 3lambda]| then t=

If the points A(lambda, 2lambda), B(3lambda,3lambda) and C(3,1) are collinear, then lambda=

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. lambda_(1), lambda_(2) and lambda_(3) . Which one of the following equations correctly ralates lambda_(1), lambda_(2) and lambda_(3) ? lambda_(1)=lambda_(2)-lambda_(3) lambda_(1)=lambda_(3)-lambda_(2) (1)/(lambda_(1))=(1)/(lambda_(2))+(1)/(lambda_(3)) (1)/(lambda_(2))=(1)/(lambda_(3))+(1)/(lambda_(1))

Show that the area of the triangle with vertices (lambda, lambda-2), (lambda+3, lambda) and (lambda+2, lambda+2) is independent of lambda .

The system of homogeneous equation lambdax+(lambda+1)y +(lambda-1)z=0, (lambda+1)x+lambday+(lambda+2)z=0, (lambda-1)x+(lambda+2)y + lambdaz=0 has non-trivial solution for :

Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+5=0,lambda being arbitrary, pass through a fixed point. Also find the fixed point.

If a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

Two particle are moving perpendicular to each with de-Broglie wave length lambda_(1) and lambda_(2) . If they collide and stick then the de-Broglie wave length of system after collision is : (A) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (B) lambda = (lambda_(1))/(sqrt(lambda_(1)^(2) + lambda_(2)^(2))) (C) lambda = (sqrt(lambda_(1)^(2) + lambda_(2)^(2)))/(lambda_(2)) (D) lambda = (lambda_(1) lambda_(2))/(sqrt(lambda_(1) + lambda_(2)))

If vec a is a nonzero vector of magnitude a and lambda a nonzero scalar, then lambda vec a is unit vector if (A) lambda = 1 (B) lambda= -1 (C) a = |lambda| (D) a = 1/(|lambda|)