Mathematics Tes...

If \(2(3 x-4)-2<4 x-2 \geq 2 x-4 ;\) then the possible value of \(x\) can be:

If \(\cos ^{-1}\left(\frac{p}{a}\right)+\cos ^{-1}\left(\frac{q}{b}\right)=\alpha\), then \(\frac{p^{2}}{a^{2}}+k \cos \alpha+\frac{q^{2}}{b^{2}}=\sin ^{2} \alpha\) where \(\mathrm{k}\) is equal to:

Weather Forecast Company makes a forecast of raining at \(70 \%\). Company's forecast are only correct \(60 \%\) of the time. Find the probability of it correctly forecasting rain?

A set containing \(n\) elements, has exactly ___________ subsets.

Let $m\in N$ , and suppose three numbers are chosen at random from the numbers $1, 2, 3, ..., m$.

Statement - 1: If $m = 2n$ for some $n\in N$ , then the chosen numbers are in A.P. with probability $\frac{3}{2(2n-1)}$ 

Statement - 2: If $m = 2n + 1$ for some $n\in N$, then the chosen numbers are in A.P. with probability $\frac{3n}{4n^2-1}$

What is \(\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)\) equal to?

If $\left|z_1\right|=2, |z_2-1|=4$,

If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda }{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$ , then the sum of all possible values of λ is:

Find the general solution: \(\sec ^{2} x \tan y\ d x+\sec ^{2} y \tan x\ d y=0\)

What is the value of the determinant \(\left|\begin{array}{ccc}{i} & {i}^{2} & {i}^{3} \\ {i}^{4} & {i}^{6} & {i}^{8} \\ {i}^{9} & {i}^{12} & {i}^{15}\end{array}\right|\) where \({i}=\sqrt{-1}\) ?