Mathematics Tes...

Consider the two sets :

$A=\{m\in R$ : both the roots of $x^2-(m+1)x+m+4=0$ are real $\}$ and $B=(-3,5)$ Which of the following is not true?

The condition of being one root of the equations $a{x}^2+bx+c=0$ and $a^{\prime }{x}^2+b^{\prime }x+c^{\prime }=0$ common is:

For the given curve: $y=2x-x^2$, when $x$ increases at the rate of 3 units/sec, then how the slope of curve changes?

Let $\overrightarrow{\alpha }=3\hat{i}+\hat{j}$ and $\overrightarrow{\beta }=2\hat{i}-\hat{j}+3\hat{k}$. If $\overrightarrow{\beta }={\overrightarrow{\beta }}_1-{\overrightarrow{\beta }}_2$, where ${\overrightarrow{\beta }}_1$ is parallel to $\overrightarrow{\alpha }$ and ${\overrightarrow{\beta }}_2$ is perpendicular to $\overrightarrow{\alpha }$, then ${\overrightarrow{\beta }}_1\times {\overrightarrow{\beta }}_2$ is equal to:

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^2\sin \theta -x(\sin \theta \cos \theta +1)+\cos \theta =0(0<\theta <{45}^{\circ })$, and $\alpha <\beta$. Then $\sum _{n=0}^{\mathrm{\infty }}({\alpha }^n+\frac{(-1{)}^n}{{\beta }^n})$ is equal to :

Let $PQ$ be a focal chord of the parabola $y^2=4x$ such that it subtends an angle of $\frac{\pi }{2}$ at the point $(3,0)$. Let the line segment PQ be also a focal chord of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a^2>b^2$. If $e$ is the eccentricity of the ellipse $E$, then the value of $\frac{1}{e^2}$ is equal to:

The degree of the differential equation:

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

Find the 8^th term in the following sequence whose nth term is$a_n=\frac{n^2}{2^n}$.

What is ${\int }_0^a\frac{f(a-x)}{f(x)+f(a-x)}dx$ equal to?