Value of lambda for which`(lambda,lambda^2)` lies between the lines `|x+2y|=3` is
(a)`( -1/2,2)` (b) `(-3/2,2)`
(c) `(-3/2,1)` (d) `(-1,3/2)`

the value of lambda for which the line 2x-8/3lambday=-3 is a normal to the conic x^2+y^2/4=1 is:

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)

Number of integral values of lambda for which (lim)_(x to 1)sec^(-1)((lambda^2)/((log)_e x)-(lambda^2)/(x-1)) does not exist is a. 1 b. 2 c. 3 d. 4

Let veca = 2hati+lambda_1 hatj+3hatk , vec(b)=4hati+(3-lambda_2) hatj+6hatk and vec(c)=3hati+6hatj+(lambda_3-1)hatk be three vectors such that vec(b)=2 vec(a) and vec(a) is perpendicular to vec(c) then a possible value of ((lambda)_1,(lambda)_2,(lambda)_3) is: (a) (1,3,1) (b) ((-1/2),4,0) (c) (1,5,1) (d) ((1/2), 4, -2)

The value of lambda for which the sum of squares of roots of the equation x^2+(3-lambda)x+2=lambda is minimum, then lambda is equal to (a) 2 (b) -1 (c) -3 (d) -2

The value value of lambda so that the line y=2x+lambda may touch the ellipse 3x^(2)+5y^(2)=15

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

The equation 2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0 has exactly three roots in (0,2pi) , then lambda can be equal to (a) 0 (b) 2 (c) 1 (d) -1

Find all values of lambda for which the (lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0 possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

If the matrix A = [[lambda_(1)^(2), lambda_(1)lambda_(2), lambda_(1) lambda_(3)],[lambda_(2)lambda_(1),lambda_(2)^(2),lambda_(2)lambda_(3)],[lambda_(3)lambda_(1),lambda_(3)lambda_(2),lambda_(3)^(2)]] is idempotent, the value of lambda_(1)^(2) + lambda_(2)^(2) + lambda _(3)^(2) is