List of top Questions asked in VITEEE

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

The number of distinct real roots of the equation: \[ x^7 - 7x - 2 = 0 \] is:

Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]

For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?

The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:

If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then \( \frac{dy}{dx} \) is:

The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:

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

Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]

The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] 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:

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 limiting molar conductivities of \( HCl \), \( CH_3COONa \), and \( NaCl \) are respectively 425, 90, and 125 mho cm\(^2\) mol\(^{-1}\) at 25°C. The molar conductivity of 0.1M \( CH_3COOH \) solution is 7.8 mho cm\(^2\) mol\(^{-1}\) at the same temperature. The degree of dissociation of 0.1M acetic acid solution at the same temperature is:

In the given figure, two equal positive point charges \( q_1 = q_2 = 2.0 \mu C \) interact with a third point charge \( Q = 4.0 \mu C \). The magnitude and direction of the net force on \( Q \) is:
\includegraphics[width=0.5\linewidth]{35.png}

Arrange the following in increasing order of ionic radii: \( C^{4-}, N^{3-}, F^{-}, O^{2-} \).

The compounds \( CH_3CH=CHCH_3 \) and \( CH_3CH_2CH=CH_2 \):

An element X has a body-centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm\(^{-3}\). The number of atoms present in 300g of the element X is:
Given: Avogadro Constant, \( N_A = 6.0 \times 10^{23} \) mol\(^{-1} \).

The bond dissociation energies of \( X_2, Y_2, \) and \( XY \) are in the ratio of 1:0.5:1. If \( \Delta H \) for the formation of \( XY \) is -200 kJ mol\(^{-1}\), what is the bond dissociation energy of \( X_2 \)?