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

If (G,×) is a group such that for all then G is

In any group the number of improper subgroups is