List of top Mathematics Questions asked in VITEEE

Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]
The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2, respectively. Find \( P(X = 1) \).
If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:
The lines \[ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 \] are perpendicular to a common line for:
If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:
In \( \triangle ABC \), the midpoints of the sides \( AB, BC, \) and \( CA \) are respectively \( (1, 0, 0) \), \( (0, m, 0) \), and \( (0, 0, n) \). Then, \[ \frac{AB^2 + BC^2 + CA^2}{1^2 + m^2 + n^2} \text{ is equal to:} \]
If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:

Eccentricity of ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] if it passes through point (9, 5) and (12, 4) is: 

If the vertex of a parabola is \( (2, -1) \) and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:

For what value of \( k \), does the equation \[ 9x^2 + y^2 = k(x^2 - y^2 - 2x) \] represent the equation of a circle?

The point \( (t^2 + 2t + 5, 2t^2 + t - 2) \) { lies on the line} \( x + y = 2 \) { for:}

The principal value of \(\sin^{-1} \left( \sin \frac{5\pi}{3} \right)\) is:

A parabola has the origin as its focus and the line \( x = 2 \)  as the directrix. Then the vertex of the parabola is at:

For the parabola \( y^2 = -12x \), the equation of the directrix is  \( x = a \). The value of  \( a \) is:

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity \( \sqrt{\frac{2}{5}} \) is:

The following determinant is equal to:

\[ \begin{vmatrix} \sin^2 x & \cos^2 x & 1 \\ \cos^2 x & \sin^2 x & 1 \\ -10 & 12 & 2 \end{vmatrix} \]

The value of the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \] is:

The equation of the hyperbola with vertices at

\[ (0, \pm 6) \quad \text{and} \quad e = \frac{5}{3} \]

is:

If \[ \frac{n + 2C8}{n - 2P4} = \frac{57}{16}, { then the value of } n { is:} \]
The point diametrically opposite to the point \( P(1, 0) \) { on the circle} \[ x^2 + y^2 + 2x + 4y - 3 = 0 { is:} \]
To fill 12 vacancies, there are 25 candidates of which five are from the scheduled caste. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made is:
The total number of 3-digit numbers, the sum of whose digits is even, is equal to:
The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^2 + x \) is:
Coin is tossed till heads is obtained what is expectation of no. of coin tosses
The area enclosed between the graph of \( y = x^3 \) { and the lines} \[ x = 0, \, y = 1, \, y = 8 { is:} \]