List of top Mathematics Questions asked in VITEEE

Let \(y\) be the number of people in a village at time \(t\). Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time \(t\) is given by

The differential equation of all straight lines touching the circle \(x^2+y^2=a^2\) is

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

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

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

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 \(I=\int \frac{x^5}{\sqrt{1+x^3}}\,dx\), 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

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

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

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

Let $y$ be the number of people in a village at time $t$. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time $t$ is given by

The value of $\int^{^a}_{0}\sqrt{\frac{a-x}{x}}dx$ is

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 $5$ centimetres is

The directrix of the parabola y$^2$ + 4x + 3 = 0 is