List of top Questions asked in VITEEE

The solution of the differential equation \[ \frac{dy}{dx}(x - y^3) = 0 \] is

The number of positive integral solutions of the equation \( x_1 + x_2 + x_3 + x_4 = 1050 \) is

Let \( A = \{ 1, 2, 3, \dots, n \} \) and \( B = \{ a, b, c, \dots \} \), then the number of functions from A to B that are onto is

If \( (x + y) \sin u = x^2 y^2 \), then \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is

The angle between the tangents at those points on the curve \( x = t^2 + 1 \) and \( y = t^2 - t - 6 \) where it meets the x-axis is

The value of \( \int_{1}^{4} |x - 3| \, dx \) is equal to

The area of the region bounded by the straight lines \( x = 0 \) and \( x = 2 \) and the curves \( y = 2x^2 \) and \( y = 2x - x^2 \) is equal to

If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( \cos^{-1} x + \cos^{-1} y \) is equal to

The equation of a directrix of the ellipse \( \frac{x^2}{16} + \frac{y^2}{25} = 1 \) is

If the normal at \( (a^2, 2a^2) \) on the parabola \( y^2 = 4ax \), meets the parabola again at \( (a^2, 2a^2) \), then

The length of the straight line \( x - 3y = 1 \) intercepted by the hyperbola \( x^2 - 4y^2 = 1 \) is

The curve described parametrically by \[ x = t^2 + 2t - 1, \quad y = 3t + 5 \] represents

If the normal to the curve \( y = f(x) \) at \( (3, 4) \) makes an angle \( \frac{3\pi}{4} \) with the positive x-axis, then \( f'(3) \) is equal to

Aldol condensation is given by

Give the IUPAC name for \[ \text{H}_3\text{C} - \text{CH}_2 - \text{C} - \text{CH}_2 - \text{C} - \text{OCH}_3 \]

In which of the below reactions do we find \( \alpha, \beta \)-unsaturated carbonyl compounds undergoing a ring closure reaction with conjugated dienes?

Let the pairs \( \mathbf{a}, \mathbf{b} \) and \( \mathbf{c}, \mathbf{d} \) each determine a plane. Then the planes are parallel if

The area of a parallelogram with \( 3\hat{i} + \hat{j} - 2\hat{k} \) and \( \hat{i} - 3\hat{j} + 4\hat{k} \) as diagonals is

If \( \cos x + \cos 2x = 1 \), then the value of \( \sin^{12}x + 3\sin^{10}x + 3\sin^8x + \sin^6x - 1 \) is equal to

For strong electrolytes the plot of molar conductance vs \( \sqrt{C} \) is

If the molar conductance values of \( \text{Ca}^{2+} \) and \( \text{Cl}^- \) at infinite dilution are respectively \( 18.88 \times 10^{-4} \, \text{m}^2 \, \text{mol}^{-1} \) and \( 77.33 \times 10^{-4} \, \text{m}^2 \, \text{mol}^{-1} \), then that of \( \text{CaCl}_2 \) is (in \( \text{m}^2 \, \text{mol}^{-1} \))

The standard reduction potentials at 298K for the following half reactions are given: \[ \text{Zn}^{2+}(aq) + 2e^- \rightarrow \text{Zn}(s) \quad E_0 = -0.762 \, \text{V} \] \[ \text{Cr}^{3+}(aq) + 3e^- \rightarrow \text{Cr}(s) \quad E_0 = -0.740 \, \text{V} \] \[ 2H^+(aq) + 2e^- \rightarrow H_2(g) \quad E_0 = 0.00 \, \text{V} \] \[ \text{Fe}^{3+}(aq) + e^- \rightarrow \text{Fe}^{2+}(aq) \quad E_0 = +0.762 \, \text{V} \] The strongest reducing agent is

The epoxide ring consists of which of the following?

In the Grignard reaction, which metal forms an organometallic bond?

Phenol is less acidic than