Mathematics Tes...

Solve: \(\frac{-1}{(|x|-2)} \geq 1\) where x ∈ R, x ≠ ±2

What is the area of the rectangle having vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\) with position vectors \(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) and \(-\hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\)?

Evaluate the integral \(\int_{2}^{3} \frac{\cos x-\sin x}{4} dx\).

If \(2 \sin ^{2} A+3 \cos ^{2} A=2\), find the value of \((\tan A-\cot A)^{2}\) where, \(\sin A>0\)

A sequence \(a_{1}, a_{2}, a_{3} \ldots\) is defined by letting \(a_{1}=3\) and \(a_{k}=7 a_{k-1}\) for all natural numbers \(k \geq 2\). Show that a_n \(=3.7^{\mathrm{n}-1}\) for all:

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:

Find the value of \(\lim _{x \rightarrow 0} \frac{\sqrt[p]{1+x}-1}{x}\), where \(p\) is a positive integer.

If \(\frac{e^{x}}{1-x}=B_{0}+B_{1} x+B_{2} x^{2}+\ldots+B_{n} x^{n}+\ldots\), then the value of \(B_{n}-B_{n-1}\) is:

Find the equation of the line which makes an angle of \(30^{\circ}\) with the positive direction of the \(x\) -axis and cuts off an intercept of 4 units with the negative direction of the \(y\) axis?

If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0}\), then \(|\vec{a} \times \vec{c}|\) is equal to: