List of top Mathematics Questions asked in VITEEE

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 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 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 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

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

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

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

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

If $A = \begin{bmatrix}1&-5&7\\ 0&7&9\\ 11&8&9\end{bmatrix}$, then trace of matrix $A$ is

The value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ is

$\int \frac{dx}{\sin x - \cos x + \sqrt{2}} $ equals to

The equation of straight line through the intersection of the lines $x - 2y = 1 $ and $x + 3y = 2$ and parallel $3x + 4y = 0$ is

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A, its equation is

The tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at

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

There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

The coefficient of $x^n$ in the expansion of $\log_a (1 + x)$ is

The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is

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

If $(-3, 2)$ lies on the circle $x^2 + y^2 + 2gx + 2fy + c = 0$, which is concentric with the circle $x^2 + y^2 + 6x + 8y - 5 = 0,$ then c is equal to

If $\vec {a} = \hat {i} + \hat{j} + \hat{k}$, $\vec {b} = \vec {i} + 3\vec {j} + 5\hat{k}$ and $\vec {c} = 7\hat{i} + 9\hat {j} + 11 \hat{k}$, then the area of Parallelogram having diagonals $\vec{a} +\vec{b}$ and $\vec{b} +\vec{c}$ is

If one root is square of the other root of the equation $x^2 + px + q = 0$, then the relations between p and q is

If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \left(a > b\right)$ and $x^{2} - y^{2} = c^{2}$ cut at right angles, then

A dice is rolled twice and the sum of the numbers appearing on them is observed to be $7$. What is the conditional probability that the number $2$ has appeared at least once ?