Mathematics Tes...

Find the Area of the region (in square unit) bounded by the curve \(y=x-2\) and \(x=0\) to \(x=4\).

If \({}^{12} \mathrm{P}_r=1320\) then \(\mathrm{r}\) is:

If \(\left|\begin{array}{ccc}1+a x & 1+b x & 1+c x \\ 1+a_{1} x & 1+b_{1} x & 1+c_{1} x \\ 1+a_{2} x & 1+b_{2} x & 1+c_{2} x\end{array}\right|=A_{0}+A_{1} x+A_{2} x^{2}+A_{3} x^{3},\) then \(A_{0}\) is equal to ______.

If \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{k}}\) are three vectors such that \(\overrightarrow{\mathrm{a}}+\lambda \overrightarrow{\mathrm{b}}\) is perpendicular to \(\overrightarrow{\mathrm{c}},\) then find the value of \(\lambda ?\)

\(\forall \mathrm{n} \in \mathrm{N} ; 3 \mathrm{n}^{5}+5 \mathrm{n}^{3}+7 \mathrm{n}\) is divisible by:

Find the length of latus rectum of hyperbola \(25 y^{2}-24 x^{2}=600\).

Find the 5th term form the end in the expansion of \(\left(x-\frac{1}{x}\right)^{12} ?\)

The angle between the straight lines \(\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}\) and \(\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}\) is-

The value of \(\left|\begin{array}{ccc}\sin ^{2} x & \cos ^{2} x & 1 \\ \cos ^{2} x & \sin ^{2} x & 1 \\ 12 & -10 & 2\end{array}\right|\):

If \(f: R \rightarrow R\) is a function defined by \(f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi\). where, [.] denotes the greatest integer function, then \(f\) is: