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

If "sin" x = lambda has exactly one solution in [0, 9 pi//4] then the number of values of lambda , is

The equation "sin"^(6) x + "cos"^(6) x = lambda , has a solution if

If the equation cos (lambda "sin" theta) = "sin" (lambda "cos" theta) has a solution in [0, 2pi] , then the smallest value of lambda , is

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

Prove that for lambda gt 1 , the equation xlog x +x =lambda has least one solution in [1 , lambda] .

The equation 2cos^(-1)x+sin^(-1)x=(11pi)/6 has a. no solution b. only one solution c. two solutions d. three solutions

Let the number of solutions of the equations sinx =x^(2) - 4x +5 be lambda . The general solution of the equation 1+tan((lambda^(2) - 2lambda + 1)theta) + 2/(1-tan((lambda^(2) + 2lambda+1)theta)=0 is