Mathematics Tes...

Integrate the function: \(\frac{1}{x-\sqrt{x}}\)

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

If the coefficient of \(x^{7}\) in \(\left[a x^{2}+\frac{1}{b x}\right]^{11}\) equals the coefficient of \(x^{-7}\) in \(\left[a x-\left(\frac{1}{b x^{2}}\right)\right]^{11},\) then a and b satisfy the relation.

In the given figure, \(O\) is the centre of the circle of radius \(5 \mathrm{~cm}\). If \(O M=4 \mathrm{~cm}\), find the length of \(P N\):

The degree of the differential equation:

\(\frac{d^{2} y}{d x^{2}}+3\left(\frac{d y}{d x}\right)^{2}=x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right)\)

Suppose f : R → R is defined by \(f(x)=\frac{x^{2}}{1+x^{2}}\). What is the range of the function?

If cot 35° = m, then sec 55° =?

What is the value of the following determinant?

\(\left|\begin{array}{ccc}\cos C & \tan A & 0 \\ \sin B & 0 & -\tan A \\ 0 & \sin B & \cos C \end{array}\right|\)

The position vectors of the points \(A, B\) and \(C\) are respectively \(\vec{a}, \vec{b}\) and \(\vec{c}\). If \(P\) divides \(\overrightarrow{A B}\) in the ratio \(3: 4\) and \(Q\) divides \(\overrightarrow{B C}\) in the ratio \(2: 1\) both externally, then \(\overrightarrow{P Q}\) is: