List of top Mathematics Questions asked in VITEEE

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

The eccentricity of the ellipse, which meets the straight line \( \frac{x}{7} + \frac{y}{2} = 1 \) on the axis of \( x \) and the straight line \( \frac{x}{3} - \frac{y}{5} = 1 \) on the axis of \( y \), and whose axes lie along the axes of coordinates, is:

If \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a>b) \] and \[ x^2 - y^2 = c^2 \] cut at right angles, then:

The equation of the conic with focus at \( (1, -1) \), directrix along \( x - y + 1 = 0 \), and eccentricity \( \sqrt{2} \) is:

The value of the integral \[ I = \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \] is:

\[ \int \frac{dx}{\sin x - \cos x + \sqrt{2}} = ? \]

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelopes is:

The value of the integral \[ I = \int_0^1 \left| x - \frac{1}{2} \right| \, dx \] 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 tangent at \( (1, 7) \) to the curve \( x^2 = y - 6 \) touches the circle \( x^2 + y^2 + 16x + 12y + c = 0 \) at:

The equation of the straight line through the intersection of the lines \( x - 2y = 1 \) and \( x + 3y = 2 \) and parallel to \( 3x + 4y = 0 \) is:

If \[ A = \begin{pmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{pmatrix}, \] then the trace of matrix \( A \) is:

The maximum value of \( 4 \sin^2 x - 12 \sin x + 7 \) is:

If \( \mathbf{a} = \mathbf{i} + \mathbf{j} + \mathbf{k}, \mathbf{b} = \mathbf{i} + 3\mathbf{j} + 5\mathbf{k}, \) and \( \mathbf{c} = 7\mathbf{i} + 9\mathbf{j} + 11\mathbf{k} \), then the area of the parallelogram having diagonals \( \mathbf{a} + \mathbf{b} \) and \( \mathbf{b} + \mathbf{c} \) is:

The lines \( 2x - 3y - 5 = 0 \) and \( 3x - 4y - 7 = 0 \) are diameters of a circle of area 154 square units, then the equation of the circle 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 angle of depression of the top and the foot of a chimney as seen from the top of a second chimney, which is 150 m high and standing on the same level as the first, are \( \theta \) and \( \phi \) respectively. Then the distance between their tops when \( \tan \theta = \frac{4}{3} \) and \( \tan \phi = \frac{5}{2} \) is:

The number of real solutions of the equation \[ \left( \frac{9}{10} \right) = -3 + x - x^2 \] 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:

Let \( a, b, c \) be in AP and \( |a|<1, |b|<1, |c|<1 \). If \[ x = 1 + a + a^2 + a^3 + \dots \quad \text{to} \quad \infty, \] \[ y = 1 + b + b^2 + b^3 + \dots \quad \text{to} \quad \infty, \] \[ z = 1 + c + c^2 + c^3 + \dots \quad \text{to} \quad \infty, \] then \( x, y, z \) are in:

The coefficient of \( x^{53} \) in the following expansion \[ \sum_{m=0}^{100} \binom{100}{m} (x - 3)^{100 - m} 2^m \] is:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \[ f(x) = (x - 1)(x - 2)(x - 3) \] is:

Dual of \( (x + y)(x + 1) = x + x \cdot y + y \) is:

Let \( a \) be any element in a Boolean algebra \( B \). If \( a + x = 1 \) and \( ax = 0 \), then:

If \( 2 \tan^{-1} (\cos x) = \tan^{-1} (2 \csc x) \), then the value of \( x \) is: