41.

The range of the function ^7-xP_x-3 is

• {1, 2, 3}

• {1, 2, 3, 4, 5}

• {1, 2, 3, 4}

• {1, 2, 3, 4}

Let A  The only correct statement about the matrix A is

• A is a zero matrix

• A² = I

• A⁻¹ does not exist

• A⁻¹ does not exist

Let .If B is the inverse of matrix A, then α is

• -2

• 5

• -2

• -2

If f : R S, defined by  , is onto, then the interval of S is

• [0, 3]

• [-1, 1]

• [0, 1]

• [0, 1]

let  . If f(x) is continuous in  then f (π/4) is

• 1

• -1/2

• -1

• -1

If 

• x /x+1

• x-1/x

• 1/x

• 1/x

A function y = f(x) has a second order derivative f″(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is

• (x-1)²

• (x-1)³

• (x+1)³

• (x+1)³

The normal to the curve x = a(1 + cosθ), y = asinθ at ‘θ’ always passes through the fixed point

• (a, 0)

• (0, a)No

• (0,0)

• (0,0)

The differential equation for the family of curves,x² +y² -2ay = 0  where a is an arbitrary constant is

• 2(x²-y²)y' = xy

• (x²+y²)y' = xy

• 2(x²+y²)y' = xy

• 2(x²+y²)y' = xy

The solution of the differential equation ydx + (x + x²y) dy = 0 is

• -1/ XY  =C

• -1/XY + log y = C

• 1/XY + log y = C

• 1/XY + log y = C