List of top Mathematics Questions asked in VITEEE

If the function \[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \] is continuous at \( x = 2 \) and \( x = 4 \), then the values of \( a \) and \( b \) are:

The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] 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:

The determinant of the matrix:

is:

If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:

Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]

Consider a curve \( y = y(x) \) in the first quadrant as shown in the figure. Let the area \( A_1 \) be twice the area \( A_2 \). The normal to the curve perpendicular to the line \[ 2x - 12y = 15 \] does NOT pass through which point?

The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is:

The minimum value of the function \[ y = x^4 - 2x^2 + 1 \] in the interval \( \left[\frac{1}{2}, 2 \right] \) is:

If \[ \frac{n + 2C8}{n - 2P4} = \frac{57}{16}, { then the value of } n { is:} \]

The modulus of \( (1 + i\sqrt{3})(2 + 2i) \) / \( (\sqrt{3} - i) \) is:

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

If \( 12\cot^2 \theta - 31\csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:

The middle term in the expansion of \[ (10x + x^{10})^{10} \] {is:}

A class has 175 students. The following data shows the number of students opting for one or more subjects. Maths = 100, Physics = 70, Chemistry = 40, Maths and Physics = 30, Maths and Chemistry = 28, Physics and Chemistry = 23, Maths, Physics, and Chemistry = 18.
How many have offered Maths alone?

Let \( R \) be a relation on the set \( \mathbb{N} \) defined by \[ \{(x, y) \mid x, y \in \mathbb{N}, \, 2x + y = 41\}. \] {Then, \( R \) is:}

The solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]

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 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:

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:

Find the probability of getting the sum as a perfect square number when two dice are thrown together.

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

What was the ratio between the ages of P and Q four years ago? I. The ratio between the present ages of P and Q is 3 : 4. II. The ratio between the present ages of Q and R is 4 : 5.