List of top Mathematics Questions

The value of $\frac{d}{dx}{x}^{2x}=$

Consider the following statements:1. If $y=\ln (\sec x+\tan x)$, then $\frac{dy}{dx}=\sec x$.2. If $y=\ln (\mathrm{cosec}x-\cot x)$, then $\frac{dy}{dx}=\mathrm{cosec}x$.Which of the above is / are correct?

If $\int \frac{x^2+1}{x(x+1{)}^2}dx=A\ln |x|+\frac{B}{1+x}+C$, where C is the constant of integration, then $A+B$ $=$

What is the area of the parabola $x^2=y$ bounded by the line $y=1$?

If $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$, then $\overrightarrow{BA}$ is:

The integrating factor of the differential equation $2y\frac{dx}{dy}+x=5y^2$ is, $(y\ne 0)$:

If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.

If $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}$, $\overrightarrow{\mathrm{b}}=3\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then the angle between $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}$ is:

The point which does not belong to the feasible region of the LPP:Minimize: $\mathrm{Z}=60\mathrm{x}+10\mathrm{y}$subject to $3\mathrm{x}+\mathrm{y}\ge 18$$2x+2y\ge 12$$x+2y\ge 10$$\mathrm{x},\mathrm{y}\ge 0$ is:

If ${\cos }^{-1}\left(\frac{p}{a}\right)+{\cos }^{-1}\left(\frac{q}{b}\right)=\alpha$, then $\frac{p^2}{a^2}+k\cos \alpha +\frac{q^2}{b^2}={\sin }^2\alpha$ where $\mathrm{k}$ is equal to:

A circle with center $(4,-5)$ is tangent to the $y$ -axis in the standard $(x,y)$ coordinate plane. What is the radius of this circle?

The solution of differential equation $dy=(4+y^2)dx$ is:

Find the value of $\sqrt{(5+12i)}$, where $i=\sqrt{-1}$.

Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k},\overrightarrow{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ be three non-zero vectors such that $\overrightarrow{c}$ is a vector perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$ then $\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=?$

Form the differential equation of $y=a{e}^{3x}\cos (x+b)$ Where $y^{\prime }=\frac{dy}{dx}$ and $y^n=\frac{d^{2}y}{d{x}^2}$?

Graphic location of mode is done with reference to:

If $2x^3-3y^2=7$, what is $\frac{dy}{dx}$ equal to $(y\ne 0)$:

If $\sin (\alpha +\beta )=6\sin (\alpha -\beta )$ and $k=\frac{\tan \alpha }{\tan \beta }$, then, what is the value of $k$ ?

The maximum value of $\frac{\ln x}{x}$ is:

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is:

What is the area of the region bounded by the curve $f(x)=1-\frac{x^2}{4},x\in [-2,2]$ and the $x$-axis?

The integral of \( \sec^{2/3}x \csc^{4/3}x \, dx \) from \( \pi/6 \) to \( \pi/3 \) is equal to:

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

Find the equation of tangent to the curve $y=\sqrt{5x-3}-2$, which is parallel to the line $4x-2y+3=0$?