Mathematics Tes...

Find the angle between two vectors \((\vec{a}=2 \hat{i}+\hat{j}-3 \hat{k})\) and \((\vec{b}=3 \hat{i}-2 \hat{j}-\hat{k})\).

Let \(S\) be the set of all real roots of the equation, \(3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right|\). Then \(s\) :

If f(x) = log x then AM of f(xy) and f(x/y) is ?

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?

What is the value of \(m\) if the vectors \(2 \hat{ i }-\hat{ j }+\hat{ k }, \hat{ i }+2 \hat{ j }-3 \hat{ k }\) and \(3 \hat{ i }+ m \hat{ j }+5 \hat{ k }\) are coplanar?

If \(\mathrm{f}(\mathrm{x}), \mathrm{g}(\mathrm{x})\) be twice differential functions on \([0,~2]\) satisfying \(\mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{g}^{\prime \prime}(\mathrm{x}), \mathrm{f}^{\prime}(1)\) \(=2 g^{\prime}(1)=4\) and \(f(2)=3 g(2)=9,\) then:

If \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) are two vectors such that \(|\overrightarrow{\mathrm{a}}|=\frac{1}{\sqrt{3}},|\overrightarrow{\mathrm{b}}|=2\) and \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\) is a unit vector, then find the angle between \(\vec{a}\) and \(\vec{b}\)

\(\operatorname{lim}_{x \rightarrow 0} \frac{1+\sin x-\cos x+\ln (1-x)}{x \cdot \tan ^{2} x}\) is equal to:

The plane x - 3y + 5z - 8 = 0 makes an angle sin^-1 (∝) with Z -axis. The value of ∝ is equal to

If \(\log 2=03.301\) and \(\log 3=0.4771\), find the value of \(\log _372^5\):