Mathematics Tes...

If \(z_{1}=2-i\) and \(z_{2}=1+i\), then \(\left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+1}\right|\) is:

Suppose \(\sin 2 \theta=\cos 3 \theta\), here \(0<\theta<\frac{\pi}{2}\) then what is the value of \(\cos 2 \theta\)?

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m (see Fig). Find its length and breadth.

Evaluate the following definite integrals:

\(\int_{0}^{1} \frac{1-x}{1+x} d x\)

If there are 76 persons in a party and if they shake hands with each other, how many handshakes are possible

What is \(\left[\begin{array}{lll}\mathrm{x} & \mathrm{y} & \mathrm{z}\end{array}\right]\left[\begin{array}{lll}\mathrm{a} & \mathrm{h} & \mathrm{g} \\ \mathrm{h} & \mathrm{b} & \mathrm{f} \\ \mathrm{g} & \mathrm{f} & \mathrm{c}\end{array}\right]\) equal to?

For the differential equation find the general solution:

\(\left(e^{x}+e^{-x}\right) d y-\left(e^{x}-e^{-x}\right) d x=0\)

The complex numbers \(z=x+ iy\) which satisfy the equation \(\frac{|z-5 i|}{|z+5 i|}=1\), lie on:

For a set of five true or false questions, no student has written the all correct answers and no students have given the same sequence of answers. What is the maximum number of students in the class for this to be possible?

Find \(M_{13} \times C_{21}+C_{33} \times C_{31}\) for the given matrix \(A=\left[\begin{array}{ccc}2 & -3 & 4 \\ 1 & 0 & -1 \\ 3 & 1 & -2\end{array}\right]\), where \(M_{i j}\) and \(C_{i j}\) are the respective minor and co-factor of the element \(a_{i j}\)?