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

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))

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

If veca satisfies vec axx( hat i+2 hat j+ hat k)= hat i- hat k , then vec a is equal to a. lambda hat i+(2lambda-1) hat j+lambda hat k ,lambda in R b. lambda hat i+(1-2lambda) hat j+lambda hat k ,lambda inR c. lambda hat i+(2lambda+1) hat j+lambda hat k ,lambda inR d. lambda hat i-(1+2lambda) hat j+lambda hat k ,lambda inR

If the circumcentre of the triangle whose vertices are (3, 2, -5) , (-3, 8, -5) and (-3, 2, 1) is (-1, lambda, -3) the integer lambda must be equal to……

10 different vectors are lying on a plane out of which four are parallel with respect to each other. Probability that three vectors chosen from them will satisfy the equation lambda_1a+lambda_2b+lambda_3c=0, where lambda_1, lambda_2 and lambda_3ne=0 is

If the direction ratios of two lines are (1, lambda, 2) and (lambda, lambda + 1, lambda) and the angle between the lines is 90^(@) then the modulus of sum of all values of lambda is ________

The charge per unit length of the four quadrant of the ring is 2 lambda, -2lambda, lambda and -lambda respectively. The electric field at the centre is:

A certain radioactive material can undergo three constant lambda,2lambda and 3 lambda . Then, the effective decay constant lambda_(eff) is equal to n lambda . What is the value of n?

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