List of top Mathematics Questions asked in VITEEE

The solution of the differential equation \[ \frac{dy}{dx} = \frac{y}{f(x)} - y^2 \] is

The solution of the differential equation $\frac{dy}{dx}=\frac{yf '\left(x\right)-y^{2}}{f \left(x\right)}$ is

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b=0$ and if $\alpha^{n}+\beta^{n}=V_{_n},$ then

The sum of the series $ \displaystyle\sum_{r = 0}^{n}\left(-1\right)^{r}\, ^{n}C_{r}\left(\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+...m \text{terms}\right)$ is

If a tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^{2}}{18}+\frac{y^{2}}{34}=1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to (O is the centre of the ellipse)

The value of the determinant $\begin{vmatrix}1&cos \left(\alpha-\beta\right)&cos \alpha\\ cos \left(\alpha -\beta \right)&1&cos \beta\\ cos \alpha &cos \beta &1\end{vmatrix}$ is

The value of $2 \,tan^{-1} (cosec \,tan^{-1} x - tan \,cot^{-1} x))$ is

The value of the integral $\int\limits ^{1/2}_{-1/2}\left[\left(\frac{x+1}{x-1}\right)^{^2}+\left(\frac{x+1}{x-1}\right)^{^2}-2\right]^{^{1/2}}\:\:dx$ is

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of $15^{\circ}$. The equation of the line in the now position,is

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

The angle of intersection of the circles $x^{2}+y^{2}-x+y-8=0$ and $x^{2}+y^{2}+2 x+2 y-11=0$ is

The line $2x+\sqrt{6y}=2$ is a tangent to the curve $x^{2}-2y^{2}=4$. The point of contact is

If the points ($x_1$, $y_1$), ($x_2$, $y_2$) and ($x_3$, $y_3$) are collinear, then the rank of the matrix $\begin{bmatrix}x_{_1}&y_{_1}&1\\ x_{_2}&y_{_2}&1\\ x_{_3}&y_{_3}&1\end{bmatrix}$will always be less than

The number of integral values of $K$, for which the equation $7\, \cos \,x + 5\, \sin\, x = 2K + 1$ has a solution, is

If | $x^2 - x - 6 | = x + 2$, then the values of $x$ are

If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{for } x \leq \frac{\pi}{2}, \\ \sin x + n, & \text{for } x>\frac{\pi}{2}, \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then:

The value of the determinant \[ \begin{vmatrix} \cos \alpha & -\sin \alpha & 1 \\ \sin \alpha & \cos \alpha & 1 \\ \cos(\alpha + \beta) & -\sin(\alpha + \beta) & 1 \end{vmatrix} \] is:

The relation \( R \) defined on the set of natural numbers as \( (a, b) : a \) differs from \( b \) by 3 is given by:

The general solution of the differential equation \[ (1 + y^2) \, dx + (1 + x^2) \, dy = 0 \] is:

The order and degree of the differential equation \[ \rho = \frac{\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2}}{\frac{d^2y}{dx^2}}, \] are respectively:

The domain of the function \[ f(x) = \frac{\sqrt{4 - x^2}}{\sin^{-1}(2 - x)} \] is:

If a plane meets the coordinate axes at \( A \), \( B \), and \( C \) in such a way that the centroid of \( \triangle ABC \) is at the point \( (1, 2, 3) \), then the equation of the plane is:

The sum of the series \[ 1 + \frac{1^2 + 2^2}{2!} + \frac{1^2 + 2^2 + 3^2}{3!} + \frac{1^2 + 2^2 + 3^2 + 4^2}{4!} + \dots \] is:

The value of \[ \lim_{x \to \infty} \left( \frac{\pi}{2} - \tan^{-1} x \right)^{1/x} \] is:

The area lying in the first quadrant and bounded by the circle \( x^2 + y^2 = 4 \), the line \( x = \sqrt{3}y \), and the \( x \)-axis is: