If , then

Matrix A is such that , where I is the identity matrix The for

Statement‐I:: If is increasing function with concavity upwards, then concavity of is also upwards
Statement‐II:: If is decreasing function with concavity upwards, then concavity of is also upwards.

Statement‐I:: , where is Napiersconstant.
Statement‐II:: If f and is positive , then increases with concavity up and any chord lies above the curve.

The beds of two rivers (within a certain region) are a parabola and a straight line y=x-2 These rivers are to be connected by a straight canal The coordinates of the ends of the shortest canal can be:

If f(x) is twice differentiable function f((1)=1, f(2)=4, f(3)=9

If f(x) , then f(x)

The set of value (s) of ’for which the function possess anegative point of inflection‐

The greatest, the least values of the function, are respectively

Hence the final answer is (2,0)

Suppose that is differentiable for allx and that for all x If and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

dxthenfis‐

The tangent to the curve at (1,1) meets the curve again at the point‐

The final answer is option B

If the number of images that are formed between two mirrors are 6, then the angle between them is:

 in the above fig, .

The image of a real object on a plane mirror is ...

When light propagates in Vacuum, there are electric and magnetic fields. These fields