List of top Questions asked in VITEEE

The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

The statement $(p \Rightarrow q ) \Leftrightarrow ( \sim p \Lambda q)$ is a

$2.76\, g$ of silver carbonate on being strongly heated yields a residue weighing

An installation consisting of an electric motor driving a water pump left $75\, L$ of water per second to a height of $4.7\, m$. If the motor consumes a power of $5\, kW$, then the efficiency of the installation is

The amplification factor of a triode is $50$. If the grid potential is decreased by $0.20\, V$. What increase,in plate potential will keep the plate current unchanged?

If the integers $m$ and $n$ are chosen at random from $1$ to $100$ , then the probability that a number of the form $7^{n}+7^{m}$ is divisible by $5$ , equals to

Which of these ions is expected to be coloured in aqueous solution?

Which of the following ligands is tetradentate?

What is the EAN of \( [\text{Al}(\text{C}_4\text{O}_4)_3]^{3-} \)?

The solution of the differential equation \[ (1 + y^2) \, \frac{dy}{dx} = e^{-(x - y)} \] is

If the gradient of the tangent at any point \( (x, y) \) of a curve passing through the point \( (1, \frac{\pi}{4}) \) is \[ \left| \frac{dy}{dx} \right| = \frac{1}{x} \cdot \left| \log \left( \frac{y}{x} \right) \right| \] then the equation of the curve is

In the expansion of \( a + bx \), the coefficient of \( x^r \) is

If \( n = 1999 \), then \( \sum_{i=1}^{1999} \log x_i \) is equal to

\( P \) is a fixed point \( (a, a, a) \) on a line through the origin equally inclined to the axes, then any plane through \( P \) perpendicular to \( OP \), makes intercepts on the axes, the sum of whose reciprocals is equal to

For which of the following values of \( m \), the area of the region bounded by the curve \( y = x - x^2 \) and the line \( y = mx \) equals 5?

If \( R \to R \) be such that \( f(1) = 3 \) and \( f'(1) = 6 \), then \( f(x) \) is equal to

If \( f(x) = \left\{ \begin{array}{ll} 1 + \left| \sin x \right|, & \text{for } -\pi \leq x<0
e^{x/2}, & \text{for } 0 \leq x<\pi
\end{array} \right. \) then the value of \( a \) and \( b \), if \( f \) is continuous at \( x = 0 \), are respectively

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

\( \int (x + 1)(x - x^2) e^x \, dx \) is equal to

If \( f(x) = x - \lfloor x \rfloor \), for every real number \( x \), where \( \lfloor x \rfloor \) is the integral part of \( x \), then \[ \int f(x) \, dx \] is equal to

The value of the integral \[ \int_1^\infty \frac{x+1}{|x-1|} \left( \frac{x-1}{x+1} \right)^{1/2} \, dx \] is

If a tangent having slope \( \frac{-4}{3} \) to the ellipse \[ \frac{x^2}{18} + \frac{y^2}{32} = 1 \] intersects the major and minor axes in points A and B respectively, then the area of \( \triangle OAB \) is equal to

The locus of mid points of tangents intercepted between the axes of ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] is

If \( P \) is a double ordinate of hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] such that \( OPQ \) is an equilateral triangle, \( O \) being the centre of the hyperbola, then the eccentricity \( e \) of the hyperbola satisfies

The sides \( AB \), \( BC \), and \( CA \) of a triangle \( \triangle ABC \) have respectively 3, 4, and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is