If the equation `|x^(2)-5x+6|-lambda x+7 lambda=0` has exactly three solutions,then `lambda` is equal to

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If the equation x^(3)-6x^(2)+9x+lambda=0 has exactly one root in (1, 3), then lambda belongs to the interval

If the equation sin^(-1)(x^2+x +1)+cos^(-1)(lambda x+1)=pi/2 has exactly two solutions, then the value of lambda is

If the equation sin^(-1)(x^2+x+1)+cos^(-1)(lambda x+1)=pi/2 has exactly two solutions for lambda in [a , b] , then the value of a+b is

If the equation 2 cos x + cos 2 lambda x=3 has only one solution , then lambda is

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

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 0 (b) 2 (c) 1 (d) -1

If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negative roots, then the least value of lambda equals__________.

If the equation 3x^2 + 3y^2 + 6lambdax + 2lambda = 0 represents a circle, then the value of lambda . lies in

If one root of the equation 3x^(2)-5x+lambda=0 is the reciprocal of the other, then the value of lambda is