List of top Questions asked in VITEEE- 2013

A current of $2.0\, A$ passed for $5$ hours through a molten metal salt deposits $22.2\, g$ of metal (At wt. = $177$). The oxidation state of the metal in the metal salt is

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

Which of the following ligands is tetradentate?

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

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

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

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

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

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

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

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

The number of integral points (integral point means both the coordinates should be integers) exactly in the interior of the triangle with vertices \( (0, 0), (0, 21), (21, 0) \) is

The line \( 2x + \sqrt{6}y = 2 \) is tangent to the curve \( x^2 - 2y^2 = 4 \). The point of contact is

The value of the determinant \[ \begin{vmatrix} \cos(\alpha - \beta) & \cos \alpha & \cos \beta
\cos(\alpha - \beta) & 1 & \cos \beta
\cos \alpha & \cos \beta & 1 \end{vmatrix} \]

The line joining two points \( A(2,0) \), \( B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an angle of \( 15^\circ \). The equation of the line in the new position is

If the points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are collinear, then the rank of the matrix \[ \begin{bmatrix} x_1 & y_1 & 1
x_2 & y_2 & 1
x_3 & y_3 & 1 \end{bmatrix} \]