List of top Mathematics Questions asked in VITEEE

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

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

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

If \(\vec{a}=2\hat{i}+2\hat{j}+3\hat{k}\), \(\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\) and \(\vec{c}=3\hat{i}+\hat{j}\), then \(\vec{a}+\vec{b}\) is perpendicular to \(\vec{c}\), if \(t\) is equal to

The condition that the line \(lx+my=1\) may be normal to the curve \(y^2=4ax\), is

If the equation of an ellipse is \(3x^2+2y^2+6x-8y+5=0\), then which of the following are true?

The equation of the common tangents to the two hyperbolas \(\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\) and \(\dfrac{y^2}{a^2}-\dfrac{x^2}{b^2}=1\), are

\(\displaystyle \int \sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx\) is equal to

If \(\{f(x)\dx=f(x)\), then \(\int \{f(x)\}^2 dx\) is equal to}

Domain of the function \(f(x)=\log_x(\cos x)\), is

Range of the function \(y=\sin^{-1}\left(\dfrac{x^2}{1+x^2}\right)\), is

A rod of length \(l\) slides with its ends on two perpendicular lines. Then, the locus of its mid point is

The equation of straight line through the intersection of the lines \(2x+y=1\) and \(3x+2y=5\) and passing through the origin is

The line joining \((5,0)\) to \((10\cos\theta,10\sin\theta)\) is divided internally in the ratio \(2:3\) at \(P\). If \(\theta\) varies, then the locus of \(P\) is

If \(2x+y+k=0\) is a normal to the parabola \(y^2=-8x\), then the value of \(k\) is