List of top Mathematics Questions asked in VITEEE

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 $A = \begin{bmatrix}1&-5&7\\ 0&7&9\\ 11&8&9\end{bmatrix}$, then trace of matrix $A$ 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 value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ 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

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 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

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

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

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

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

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

If $\frac{x^{2}+2x+7}{2x+3} < 6, x\,\in\,R, $ then

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

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

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

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 ?

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 $X$ is a poisson variate such that $P(X = 1) = P(X = 2)$, then $P(X=4)$ is equal to

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