Function `f(x)=cosx-2\ lambda\ x` is monotonic decreasing when (a) `lambda>1//2` (b) `lambda<1//2` (c) `lambda<2` (d) `lambda>2`

The function f(x)=(lambdasinx+2cosx)/(sinx+cosx) is increasing, if (a) lambda 1 (c) lambda 2

In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) monotonically increasing (b) monotonically decreasing (c) not monotonic (d) constant

If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x in the largest possible interval (-2,-2/3)dot Then (a ) lambda=4 (b) lambda=2 (c) lambda=-1 (d) lambda has no real value

If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x in the largest possible interval (-2,-2/3)dot Then (a) lambda=4 (b) lambda=2 lambda=-1 (d) lambda has no real value

If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x in the largest possible interval (-2,-2/3)dot Then lambda=4 (b) lambda=2 lambda=-1 (d) lambda has no real value

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)

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if (a) lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

Let a,b,c be the sides of a triangle. No two of them are equal and lambda in R If the roots of the equation x^2+2(a+b+c)x+3lambda(ab+bc+ca)=0 are real, then (a) lambda 5/3 (c) lambda in (1/5,5/3) (d) lambda in (4/3,5/3)

If f:[-pi//2,pi//2] cupR given by f(x)=cosx+sin[(x+1)/(lambda)] is an even function. Then the set of values of lambda(lambda gt0) is Here, [*] denotes the greatest integer function.