List of top Mathematics Questions asked in VITEEE

If a tangent having slope \( \frac{-4}{3} \) to the ellipse \[ \frac{x^2}{18} + \frac{y^2}{32} = 1 \] intersects the major and minor axes in points A and B respectively, then the area of \( \triangle OAB \) is equal to

If \( P \) is a double ordinate of hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] such that \( OPQ \) is an equilateral triangle, \( O \) being the centre of the hyperbola, then the eccentricity \( e \) of the hyperbola satisfies

The vector \( \mathbf{r} = 3\hat{i} + 4\hat{k} \) can be written as the sum of a vector \( \mathbf{v} \), parallel to \( \hat{i} + \hat{k} \), and a vector \( \mathbf{u} \), perpendicular to \( \hat{i} + \hat{k} \). Then, the value of \( \mathbf{v} \) is

The number of integral values of \( K \), for which the equation \( 7 \cos x + 5 \sin x = 2K + 1 \) has a solution, is

The number of integral points (integral point means both the coordinates should be integers) exactly in the interior of the triangle with vertices \( (0, 0), (0, 21), (21, 0) \) is

The value of the determinant \[ \begin{vmatrix} \cos(\alpha - \beta) & \cos \alpha & \cos \beta
\cos(\alpha - \beta) & 1 & \cos \beta
\cos \alpha & \cos \beta & 1 \end{vmatrix} \]

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 new position is

The line \( 2x + \sqrt{6}y = 2 \) is tangent to the curve \( x^2 - 2y^2 = 4 \). The point of contact is

If the points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are collinear, then the rank of the matrix \[ \begin{bmatrix} x_1 & y_1 & 1
x_2 & y_2 & 1
x_3 & y_3 & 1 \end{bmatrix} \]

A tower \( A \) leans towards west making an angle \( \theta \) with the vertical. The angular elevation of \( B \), the topmost point of the tower is \( \beta \) as observed from a point \( C \) at a distance \( d' \) from \( B \). If the angular elevation of \( B \) from point \( D \) due east of \( C \) is the same and \( 2d \) from \( C \), then \( \theta \) can be given as

If \( a_1, a_2, a_3 \) be any positive real numbers, then which of the following statement is true?

The angle of intersection of the circles \( x^2 + y^2 - 8x - 9 = 0 \) and \( x^2 + y^2 + 2x - 4y - 11 = 0 \) is

If \( x^2 + 2x - 5 = 0 \), then the values of \( x \) are

\( \theta \) and \( \gamma \) are the roots of the equation \( x^2 - \alpha x + \beta = 0 \) and if \( \theta + \gamma = \alpha \), then what is the value of \( \theta^2 + \gamma^2 \)?

The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is

A complex number \( z \) is such that \( \arg \left( \frac{-2}{3} + \frac{2i}{3} \right) = \frac{\pi}{3} \). The points representing this complex number will lie on

Which of the following is the correct expansion of the series \[ \sum_{n=0}^{\infty} \left( \binom{C}{n} \right) \left( \frac{3}{5} \right)^n \left( \frac{2}{5} \right)^{n+1} \]

The value of \( 2 \tan^{-1} x - \left( \text{cosec} \, \tan^{-1} x - \tan \, \cot \, x \right) \)

If two events A and B. If odds against A are 2:1 and those in favour of \( A \cup B \) are 3:1, then

If \( N \) denote the set of all natural numbers and \( R \) the relation on \( N \times N \) defined by \( (a, b) R (c, d) \), if \( a(b + c) = b(a + d) \), then \( R \) is

The proposition \( \neg (p \iff q) \) is equivalent to

If truth values of \( p \) be F and \( q \) be T, then truth value of \( \neg(p \vee q) \) is

The rate of change of the surface area of a sphere of radius \( r \), when the radius is increasing at the rate of \( 2 \, \text{cm/s} \), is proportional to

The relation \( R \) defined on set \( A = \{x : |x|<3, x \in \mathbb{R} \} \) by \( R = \{(x, y): y = |x|\} \) is

If \( a \), \( b \), and \( c \) are in AP, then determinant \[ \begin{vmatrix} x+2 & x+3 & x+4
x+4 & x+5 & x+6
x+7 & x+8 & x+9 \end{vmatrix} \]