A flag staff stands vertically on a pillar The height of the flag staff being double the height of the pillar Aman on the ground at a distance finds both pillar and the flag staff subtends equal angle at his eye then

Assertion A : The radius of the circle inscribed in the triangle obtained by joining the middle points of the sides of ABC is equal to half the radius of incircle of ABC.
Reasons R : In ABC, D, E, F be midpoints of the sides of ABC, ',2s' denote area and perimeter of ΔDEF then ' =  / 4 and s' = s / 2

Let ABC be a triangle such the ,then equal to

In this question, we have to find the sum of the series. Separate the series in even and odd series, and replace with Log ( 1 – x²) and Log ( 1 + x / 1-x ) .

If  and principal value be considered then value of z is-

The conditional  is

If p and q are simple propositions, then is true when

Using Simpson’s rule, the value of for the following data, is

A curve passes through the points given by the following table :

By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is

With the help of trapezoidal rule for numerical integration and the following table

the value of is

A river is 80 metre wide. Its depth d metre and corresponding distance x metre from one bank is given below in table

Then approximate area of cross-section of river by Trapezoidal rule, is

A curve passes through

Then area bounded by x=1 and x=4 by Trapezoidal rule, is

A curve passes through the points given by the following table :

By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is

From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47,  x=7.52, is

In the group (G={0,1,2,3,4},+5) the inverse of  is