List of top Mathematics Questions asked in VITEEE

The local minimum value of the function \[ f(x) = 3 + |x|, \quad x \in \mathbb{R} \] is:

The coordinates of the point which divides the line segment joining the points $ (2, -1, 3) $ and $ (4, 3, 1) $ internally in the ratio $ 3:4 $ are:

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

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

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 function $ f(x) $ is given by:

\[ f(x) = \begin{cases} x \lfloor x \rfloor & \text{if } 0 \leq x < 2 \\ (x - 1)x & \text{if } 2 \leq x < 3 \end{cases} \]

The function is:

The principal value of $\sin^{-1} \left( \sin \frac{5\pi}{3} \right)$ 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 definite integral

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

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 equation of the hyperbola with vertices at

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

is:

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

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

In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

An accurate clock shows 8 O'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 20:00 (8 O'clock in the evening)?

The eccentricity of the curve $ 2x^2 + y^2 - 8x - 2y + 1 = 0 $ is:

The equation of the plane which bisects the angle between the planes $$ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 3z - 3 = 0 \quad \text{which contains the origin is:} $$

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

If \[ \frac{1}{q + r}, \quad \frac{1}{r + p}, \quad \frac{1}{p + q} \] {are in A.P., then:}

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

The point diametrically opposite to the point $ P(1, 0) $ { on the circle} \[ x^2 + y^2 + 2x + 4y - 3 = 0 { is:} \]

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

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

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: