Mathematics Tes...

Find the general solution of given differential equation \(\frac{x d y}{d x}+3 y=4 x^3 ?\)

Find the distance between the planes 2x - 3y + 6z - 5 = 0 and 6x - 9y + 18z + 20 = 0.

The region represented by \(\{\mathrm{z}=\mathrm{x}+\mathrm{iy} \in \mathrm{C}:|\mathrm{z}|-\operatorname{Re}(\mathrm{z}) \leq 1\}\) is also given by the inequality:

Let \(y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1

If \(n \in N,\) then \(121^{n}-25^{n}+1900^{n}-(-4)^{n}\) is divisible by which one of the following?

Given the sets \(A =\{2,3,4,5,6,7\}, B =\{6,7,8\}\) and \(C =\{1,5,8,9\}\) then find \(A \cap(B \cup C)\) and number of elements in \(A \cap(B \cup C)\)

Let \(\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=12 \vec{a}+4 \vec{b}\) and \(\overrightarrow{O C}=\vec{b}\), where \(O\) is the origin. If \(S\) is the parallelogram with adjacent sides \(\mathrm{OA}\) and \(\mathrm{OC}\), then \(\frac{\text { area of the quadrilateral } O A B C}{f S}\) is equal to:

If \(\sec ^{2} \theta+\tan ^{2} \theta=7\) then, find the value of \(\sec \theta\):

If the position vectors of the vertices \(A, B\) and \(C\) of a \(\triangle A B C\) are respectively \(4 \hat{i}+7 \hat{j}+8 \hat{k}, 2 \hat{i}+3 \hat{j}+4 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+7 \hat{k}\), then the position vector of the point, where the bisector of \(\angle \mathrm{A}\) meets \(\mathrm{BC}\) is: