List of top Mathematics Questions asked in VITEEE

If the complex numbers \( z_1, z_2, z_3 \) are in AP, then they lie on a:

If \( 3p \) and \( 4p \) are resultant of a force \( 5p \), then the angle between \( 3p \) and \( 5p \) is:

The solution of the differential equation \[ \frac{dy}{dx} + \frac{2yx}{1 + x^2} = \frac{1}{(1 + x^2)^2} \] is

If \( x, y, z \) are all distinct and \[ \begin{vmatrix} x^2 & 1 + x^3 \\ y^2 & 1 + y^3 \\ z^2 & 1 + z^3 \end{vmatrix} = 0, \] then the value of \( xyz \) is:

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then \( P(A) + P(B) \) is:

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

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

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

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

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

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

If \[ \mathbf{I} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \] then \( B \) is equal to:

The solution of the differential equation \[ \frac{dy}{dx} = (4x + y + 1)^2 \] is:

The order and degree of the differential equation \[ \left( 1 + 4 \frac{dy}{dx} \right)^{2/3} = 4 \frac{d^2 y}{dx^2} \] are respectively:

If \( X \) is a Poisson variate such that \( P(X = 1) = P(X = 2) \), then \( P(X = 4) \) is equal to:

The system of equations \[ 2x + y - 5 = 0, \quad x - 2y + 1 = 0, \quad 2x - 14y - a = 0 \] is consistent. Then, \( a \) is equal to: