List of top Mathematics Questions asked in VITEEE

The region of the Argand plane defined by \( |z - 1| + |z + 1| \leq 4 \) is:

The value of the sum \( \sum_{n=1}^{13} (i^n + i^{n+1}) \), where \( i = \sqrt{-1} \), equals:

If \( \mathbf{a} = i + 2j + 3k \), \( \mathbf{b} = i + 2j + k \), and \( \mathbf{c} = 3i + j \), then \( \mathbf{a} + \mathbf{b} \) is at right angle to \( \mathbf{c} \), then \( a + b \) and \( t \) are equal to:

If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the value of \( \alpha^3 + \beta^3 \) is:

Consider an infinite geometric series with the first term and common ratio. If its sum is 4 and the second term is \( \frac{3}{4} \), then:

The volume of the tetrahedron with vertices \( P(1, 2, 0), Q(2, 1, -3), R(1, 0, 1) \), and \( S(3, -2, 3) \) is:

An equation of the plane passing through the line of intersection of the planes \( x + y + z = 6 \) and \( 2x + 3y + 4z = 5 \), and passing through \( (1, 1, 1) \) is:

The length of the shortest distance between the lines \( \mathbf{r} = 3i + 5j + 7k + \lambda(2i - 2j + 3k) \) and \( \mathbf{r} = -i - j + k + \mu(7i - 6j + k) \) is:

If \( e^x = y + \sqrt{1 + y^2} \), then the value of y is:

The non-integer roots of \( x^4 - 3x^3 - 2x^2 + 3x + 1 = 0 \) are:

The value of \( x \), for which the matrix \( A \) is singular, is: \[ A = \begin{pmatrix} 2 & x & -1 & 2 \\ 1 & x & 2x^2 \\ 1 & \frac{1}{x} & 2 \end{pmatrix} \]

The values of \( \alpha \) for which the system of equation \( x + y + z = 1 \), \( x + 2y + 4z = \alpha \), \( x + 4y + 10z = \alpha^2 \) is consistent are given by:

What is the least value of k such that the function x$^2$ + kx + 1 is strictly increasing on (1,2)

In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ?

if $e^x \, =\, y+ \sqrt{1+y^2},$ then the value of y is

The volume of the tetrahedron with vertices P (-1, 2, 0), Q ( 2, 1, -3), R (1, 0, 1) and S (3, -2, 3) is

$If \, \, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}, \, \vec{b}= \, -\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c} \, = \, 3\hat{i}+\hat{j}$ then t such that $\vec{a}+t\vec{b}$ is at right angle to $\vec{c}$ will be equal to

Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist

If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is

An equilateral triangle is inscribed in the parabola y$^2$ = 4x one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and passing through (1, 1, 1) is

The length of the shortest distance between the lines $\vec{r}=3\hat{i}+5\hat{j}+7\hat{k}+\lambda(\hat{i}-2\hat{j}+\hat{k})$ and $\vec{r} = -\hat{i}-\hat{j}-\hat{k}+\mu (7\hat{i}-6\hat{j}+\hat{k})$ is

If x = -9 is a root of A = $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{vmatrix}$ = 0, then other two root are

The values of $\alpha$ for which the system of equation x + y + z = 1, x + 2y + 4z = $\alpha$, x + 4y + 10z = $\alpha^2$ is consistent are given by