List of top Mathematics Questions asked in VITEEE

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

For what values of m can the expression $2x^2 + mxy + 3y^2 - 5y - 2$ be expressed as the product of two linear factors

If $B$ is a non-singular matrix and $A$ is a square matrix, then det $(B^{-1} AB)$ is equal to

If $\int\limits^x_1 \frac{dt}{|t\, \sqrt{t^2 - 1}} = \frac{\pi}{6}$ , then $x$ can be equal to

\(\cos^{-1}\left(-\frac{1}{2}\right)-2\sin^{-1}\left(\frac{1}{2}\right)+3\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)-4\tan^{-1}(-1)\) equals

If \(f:\mathbb{R}\rightarrow \mathbb{R}\) is defined by
\[ f(x)= \begin{cases} \dfrac{2\sin x-\sin 2x}{2x\cos x}, & x\neq 0 \\ a, & x=0 \end{cases} \] then the value of \(a\) so that \(f\) is continuous at \(0\) is

The solution of the differential equation
\[ \frac{dy}{dx}=\sin(x+y)\tan(x+y)-1 \] is

If \(p\Rightarrow(\sim p\vee q)\) is false, then the truth value of \(p\) and \(q\) are respectively

The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x\), \(y=\cos x\) and x-axis \((0\leq x\leq \frac{\pi}{2})\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1:A_2\) equals

The function \(f(x)=x^3+ax^2+bx+c\), \(a^2\leq 3b\) has

If
\[ x=\cos^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), \quad y=\sin^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right), \] then \(\frac{dy}{dx}\) is equal to

If
\[ \frac{d}{dx}\left[a\tan^{-1}x+b\log\left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1} \] then \(a-2b\) is equal to

If
\[ y=e^{a\sin^{-1}x}=(1-x^2)y_{n+2}-(2n+1)xy_{n+1} \] is equal to

If \(I_n=\int \sin^n x\,dx\), then \(I_n-nI_{n-2}\) equals

If
\[ \int \left(\frac{2-\sin2x}{1-\cos2x}\right)e^x\,dx \] is equal to

The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

If a line in the space makes angles \(\alpha,\beta,\gamma\) with the coordinate axes, then
\[ \cos2\alpha+\cos2\beta+\cos2\gamma+\sin^2\alpha+\sin^2\beta+\sin^2\gamma \] equals

The radius of the sphere
\[ x^2+y^2+z^2=12x+4y+3z \] is

The number of normals drawn to the parabola \(y^2=4x\) from the point \((1,0)\) is

If the circle \(x^2+y^2=a^2\) intersects the hyperbola \(xy=c^2\) in four points \((x_1,y_1)\) for \(i=1,2,3,4\), then \(y_1+y_2+y_3+y_4\) equals

The mid point of the chord \(4x-3y=5\) of the hyperbola \(2x^2-3y^2=12\) is

Evaluate
\[ \lim_{x\to 0}\left(\frac{x+5}{x+2}\right)^{x+3} \]

The area (in square unit) of the circle which touches the lines \(4x+3y=15\) and \(4x+3y=5\) is

The area (in square unit) of a triangle formed by \(x+y+1=0\) and the pair of straight lines \(x^2-3xy+2y^2=0\) is

The pairs of straight lines \(x-3y+2y^2=0\) and \(x^2-3xy+2y^2-x-2=0\) form a