List of top 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 middle term in the expansion of \[ (10x + x^{10})^{10} \] {is:}
The distance between the parallel lines \[ 3x - 4y + 7 = 0 \quad {and} \quad 3x - 4y + 5 = 0 { is } \frac{a}{b}. { Value of } a + b { is:} \]
The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^2 + x \) 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:
Find the probability of getting the sum as a perfect square number when two dice are thrown together.
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 solution set of the inequality \[ 37 - (3x + 5) \geq 9x - 8(x - 3) { is:} \]

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

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

\[ f(x) = \begin{cases} x \sin \left( \frac{1}{x} \right), & \text{for } x \neq 0 \\ 0, & \text{for } x = 0 \end{cases} \]
The modulus of \( (1 + i\sqrt{3})(2 + 2i) \) / \( (\sqrt{3} - i) \) is:

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

The local minimum value of the function \[ f(x) = 3 + |x|, \quad x \in \mathbb{R} \] 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 fourth, seventh, and tenth terms of a G.P. are \( p, q, r \) respectively, then:

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:

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

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

is:

If \[ \frac{1}{q + r}, \quad \frac{1}{r + p}, \quad \frac{1}{p + q} \] {are in A.P., then:}
If \( 12\cot^2 \theta - 31\csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:
The point diametrically opposite to the point \( P(1, 0) \) { on the circle} \[ x^2 + y^2 + 2x + 4y - 3 = 0 { is:} \]
The locus of a point that is equidistant from the lines \[ x + y - 2\sqrt{2} = 0 \quad {and} \quad x + y - \sqrt{2} = 0 { is:} \]

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