List of top Mathematics Questions

The differential equation \(\left|\frac{dy}{dx}\right|+|y|+3=0\) admits

Solution of the differential equation \(xdy-ydx-\sqrt{x^2+y^2}\,dx=0\) is

Area enclosed by the curve \(\pi\left[4(x-\sqrt{2})^2+y^2\right]=8\) is

Let P, Q, R and S be statements and suppose that \(P\to Q \to R \to P\); if \(\sim S \to R\), then

The value of \(\int_{0}^{a}\sqrt{\frac{a-x}{x}}\,dx\) is

The directrix of the parabola \(y^2 + 4x + 3 = 0\) is

The length of the parabola \(y^2=12x\) cut off by the latus-rectum is

Let \([\,]\) denote the greatest integer function and \(f(x)=[\tan^2 x]\). Then

A spherical balloon is expanding. If the radius is increasing at the rate of 2 centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 centimeters is

If \(g(x)\) is a polynomial satisfying \(g(x)g(y)=g(x)+g(y)+g(xy)-2\) for all real \(x\) and \(y\) and \(g(2)=5\), then \(\lim_{x\to 3} g(x)\) is

The value of \(f(0)\) so that \(\frac{-e^x+2^x}{x}\) may be continuous at \(x=0\) is

If \(I=\int \frac{x^5}{\sqrt{1+x^3}}\,dx\), then \(I\) is equal to

The shortest distance between the straight lines through the points \(A_1=(6,2,2)\) and \(A_2=(-4,0,-1)\), in the directions of \((1,-2,2)\) and \((3,-2,-2)\) is

The center and radius of the sphere \(x^2+y^2+z^2-3x-4z+1=0\) are

In a triangle ABC, the sides \(b\) and \(c\) are the roots of the equation \(x^2-61x+820=0\) and \(A=\tan^{-1}\left(\frac{4}{3}\right)\), then \(a^2\) is equal to

Let A and B are two fixed points in a plane then locus of another point C on the same plane then CA+CB = constant, \(>AB\) is

If \(\left|\frac{z-25}{z-1}\right|=5\), the value of \(|z|\)

Argument of the complex number \(\left(\frac{-1-3i}{2+i}\right)\) is

The equation \(r^2 - 2\vec{r}\cdot\vec{c} + h = 0,\ |\vec{c}|>\sqrt{h}\), represents

The simplified expression of \(\sin(\tan^{-1}x)\), for any real number \(x\) is given by

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y -11 = 0$ is

A person travels 285 km in 6 hrs in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hr. In the second part of the journey, he travels by train at the speed of 55 km per hr. How much distance did he travel by train?