List of top Mathematics Questions asked in VITEEE

Evaluate $\int \frac{x^{2}+4}{x^{4}+16}dx.$

In an equilateral triangle, the inradius, circumradius and one of the exradii are in the ratio

Evaluate $\int\limits^{3\pi/4}_{\pi/4} \frac{1}{1+cos\,x}dx$

Find the value of $(7.995)^{1/3}$ correct to four decimal places.

The sum of the coefficients of $(6\,a-5\,b)^n$, where $n$ is a positive integer, is

In how many ways 6 letters be posted in 5 different letter boxes?

If $D$ is the set of all real $x$ such that $1-e^{\left(1/ x\right)-1}$ is positive, then $D$ is equal to

The number of ways of painting the faces of a cube of six different colours is

If one $AM 'A'$ and two $GM$ $p$ and $q$ are inserted between two given numbers, then find the value of $\frac{p^{2}}{q}+\frac{q^{2}}{p}$

If the roots of the equation $x^2 + ax + b = 0$ are $c$ and $d$, then one of the roots of the equation $x^{2}+\left(2c+a\right)x+c^{2}+ac+b=0$ is

The numerically greatest term in the expansion of \((3-5x)^{11}\) when \(x=\dfrac{1}{5}\), is

If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is

The principal value of \(\sin^{-1}\left\{\sin\left(\frac{5\pi}{6}\right)\right\}\) is

The distance between the line \(\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda(\hat{i}-\hat{j}+4\hat{k})\) and the plane \(\vec{r}\cdot(\hat{i}+5\hat{j}+\hat{k})=5\), is

The equation of sphere concentric with the sphere \(x^2+y^2+z^2-4x-6y-8z-5=0\) and which passes through the origin, is

If the lines \(\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-1}{4}\) and \(\dfrac{x-3}{1}=\dfrac{y-k}{2}=\dfrac{z}{1}\) intersect, then the value of \(k\) is

The two curves \(y=3^x\) and \(y=5^x\) intersect at an angle

The equation \(\lambda x^2+4xy+y^2+\lambda x+3y+2=0\) represents a parabola, if \(\lambda\) is

If two circles \(2x^2+2y^2-3x+6y+k=0\) and \(x^2+y^2-4x+10y+16=0\) cut orthogonally, then the value of \(k\) is

If \(A(-2,1)\), \(B(2,3)\) and \(C(-2,-4)\) are three points. Then, the angle between \(BA\) and \(BC\) is

If \(x=\sec\theta-\cos\theta,\ y=\sec^n\theta-\cos^n\theta\), then \((x^2+4)\left(\dfrac{dy}{dx}\right)\) is equal to

If \(y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\cdots}}}}\), then \(\dfrac{dy}{dx}\) is equal to

The area bounded by the curve \(y=|\sin x|\), \(x\)-axis and the lines \(x=\pi\), is

If \(\displaystyle \int_{1}^{x}\frac{dt}{t\sqrt{t^2-1}}=\frac{\pi}{6}\), then \(x\) can be equal to

The degree of differential equation of all curves having normal of constant length \(c\) is