List of top Mathematics Questions asked in VITEEE

$\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 area enclosed by \( y = 3x - 5 \), \( y = 0 \), \( x = 3 \), and \( x = 5 \) 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:

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

Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):

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:

In how many ways 6 letters can be posted in 5 different letter boxes?

The locus of the mid-points of the focal chord of the parabola \( y^2 = 4ax \) is:

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

If \( A \) and \( B \) are two sets such that \( A \times B \) consists of 6 elements, find \( B \times A \):

Let \( p \) and \( q \) be two statements. Then, \( p \vee q \) is false if:

Find the value of \[ \sin 12^\circ \sin 48^\circ \sin 54^\circ \]

A die 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?

Which of the following is correct?

In a group \( (G^*) \), the equation \( x * a = b \) has a:

If \( \alpha, \beta, \gamma \) are the roots of \( x^3 + ax^2 + b = 0 \), then the value of \[ \frac{\alpha \beta}{\gamma}, \quad \frac{\beta \gamma}{\alpha}, \quad \frac{\gamma \alpha}{\beta} \]

If the axes are shifted to the point \( (1, 2) \) without solution, then the equation \[ 2x^2 + 2y^2 - 4x + 4y = 0 \] becomes: