List of top Mathematics Questions asked in VITEEE

The equations of the lines which cut off an intercept 1 from the y-axis and are equally inclined to the axes are:

The function \( f(x) \) is given by:

\[ f(x) = \begin{cases} x \sin \left( \frac{1}{x} \right), & \text{for } x \neq 0 \\ 0, & \text{for } x = 0 \end{cases} \]

Two statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements: 1. All utensils are spoons.
2. All bowls are spoons.
Conclusions: I. No utensil is a bowl. II. Some utensils are bowls. III. No spoon is a utensil.

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

The value of the definite integral

\[ \int_0^{\frac{\pi}{2}} \log(\tan x) \, dx \]

is:

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

If the system of linear equations \[ x + ky + 3z = 0, \quad 3x + ky - 2z = 0, \quad 2x + 4y - 3z = 0 \] has a non-zero solution \( (x, y, z) \), then \( \frac{xz}{y^2} \) is equal to:

The variance of the data \( 2, 4, 6, 8, 10 \) is:

If \( \alpha, \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then \[ \frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b} = \]

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

The fourth, seventh, and tenth terms of a G.P. are \( p, q, r \) respectively, then:

The relationship between \( a \) and \( b \) so that the function \( f(x) \) defined by

\[ f(x) = \begin{cases} ax + 1, & \text{if } x \leq 3 \\ bx + 3, & \text{if } x > 3 \end{cases} \]

is continuous at \( x = 3 \), 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:

The area enclosed between the graph of \( y = x^3 \) { and the lines} \[ x = 0, \, y = 1, \, y = 8 { is:} \]

The distance between the parallel lines \[ 3x - 4y + 7 = 0 \quad {and} \quad 3x - 4y + 5 = 0 { is } \frac{a}{b}. { Value of } a + b { is:} \]

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:

What is the average marks obtained by these seven students in History? (rounded off to two digits)