Mathematics Tes...

If \((1+i)(1+2 i)(1+3 i) \ldots(1+n i)=\alpha+i \beta\) then \(2.5 .10 \ldots\left(1+n^{2}\right)\):

Which of the following is true?

If \(\alpha, \beta\) are the roots of \(x^2+p x+q=0\), and \(x^{2 n}+p^n x^n+q^n=0\) and \(\frac{\alpha}{\beta}\) is a root of \(x^n+1+(x+1)^n=0, \alpha^n \neq \beta^n\), the \(n\) must be:

Find the area bounded by the curve \(x^{2}=4 y\) and the line \(x=4 y-2\).

What is the value of\(1-2+3-4+5 \ldots 101\)?

If the matrix \(\left[\begin{array}{lll}x & 1 & 2 \\ 1 & x & 2 \\ 1 & 1 & x\end{array}\right]\) is singular, then the value of \(x\) is:

For the given differential equation, find the general solution:

\(\cos ^{2} x \frac{d y}{d x}+y=\tan x \left(0 \leq x<\frac{\pi}{2}\right)\)

How many different words can be formed by taking four letters out of the letters of the word ‘AGAIN’ if each word has to start with A?

If the system of equation \(2 x+3 y+5=0, x+k y+5=0, k x-12 y-14=0\) be consistent, then the values of \(k\) are: