`tan^(-1)3 + tan^(-1) lambda = tan^(-1) {(3+ lamda)/(1- 3 lamda)}` is valid for what values of `lambda` ?
A) `lambda in (-1/3,1/3)`
B) `lambda gt (1/3)`
C) `lambda lt (1/3)`
D) all real values of `lambda`

lambda cos x - 3 sinx=lambda +1 is solvabel for which value of λ .

If the equation (x^(2))/( 3 - lambda) + (y^(2))/(lambda - 8) + 1 = 0 represents an ellipse, then (i) lambda lt 8 (ii) lambda gt 3 (iii) 3 lt lambda lt 8 (iv) lambda lt 3" or "lambda gt 8

The vectors 2hati-lamdahatj+3lamdahatk and (1+lamda)hati-2lamdahatj+hatk include an acute angle for (A) all values of lambda (B) lamda lt -2 and lamdagt-1/2 (C) lambda=-1/2 (D) lamdaepsilon [-2,-1/2]

lim_(lamda to 0)(int_(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal to

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))

int (dx)/sqrt(1-tan^2 x)=1/lambda sin^-1 (lambdasinx)+C ,then lambda=

Find the value of lambda . If the points A(-1,3,2), B(-4,2,-2) and C(5,lambda,10) are collinear.

If alpha, beta be the roots of 4x^2-17x+lambda=0, lambda in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 then the number of integral values of lambda is

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

The values of lambda for which the function f(x)=lambdax^3-2lambdax^2+(lambda+1)x+3lambda is increasing through out number line (a) lambda in (-3,3) (b) lambda in (-3,0) (c) lambda in (0,3) (d) lambda in (1,3)