List of top Questions asked in VITEEE- 2012

The number of real solutions of the equation \[ \left( \frac{9}{10} \right) = -3 + x - x^2 \] is:

The lines \( 2x - 3y - 5 = 0 \) and \( 3x - 4y - 7 = 0 \) are diameters of a circle of area 154 square units, then the equation of the circle is:

The angle of depression of the top and the foot of a chimney as seen from the top of a second chimney, which is 150 m high and standing on the same level as the first, are \( \theta \) and \( \phi \) respectively. Then the distance between their tops when \( \tan \theta = \frac{4}{3} \) and \( \tan \phi = \frac{5}{2} \) is:

If one root is square of the other root of the equation \( x^2 + px + q = 0 \), then the relations between \( p \) and \( q \) is:

The coefficient of \( x^{53} \) in the following expansion \[ \sum_{m=0}^{100} \binom{100}{m} (x - 3)^{100 - m} 2^m \] is:

If \( (-3, 2) \) lies on the circle \( x^2 + y^2 + 2gx + 2fy + c = 0 \), which is concentric with the circle \( x^2 + y^2 + 6x + 8y - 5 = 0 \), then \( c \) is equal to:

If \( 3p \) and \( 4p \) are resultant of a force \( 5p \), then the angle between \( 3p \) and \( 5p \) is:

If \( 2 \tan^{-1} (\cos x) = \tan^{-1} (2 \csc x) \), then the value of \( x \) is:

Let \( a \) be any element in a Boolean algebra \( B \). If \( a + x = 1 \) and \( ax = 0 \), then:

Dual of \( (x + y)(x + 1) = x + x \cdot y + y \) is:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \[ f(x) = (x - 1)(x - 2)(x - 3) \] is:

If the complex numbers \( z_1, z_2, z_3 \) are in AP, then they lie on a:

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

If \( x, y, z \) are all distinct and \[ \begin{vmatrix} x^2 & 1 + x^3 \\ y^2 & 1 + y^3 \\ z^2 & 1 + z^3 \end{vmatrix} = 0, \] then the value of \( xyz \) is:

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then \( P(A) + P(B) \) is:

Which one of the following complexes is not expected to exhibit isomerism?

A 0.1 molal aqueous solution of a weak acid is 30% ionised. If Kf for water is \( 1.86^\circ C/\text{mol} \), the freezing point of the solution will be

Which of the following compound is the most basic?

Which of the following structures is the most preferred and hence of lowest energy for \( \text{SO}_3 \)?

What is the value of electron gain enthalpy of \( \text{Na} \), if \( \text{IE}_\text{Na} = 5.1 \, \text{eV} \)?

The unit of rate constant for a zero order reaction is

Which of the following compounds undergoes nucleophilic substitution reaction most easily?

Which of the following carbonyls will have the strongest C—O bond?

The order of reactivity of phenyl magnesium bromide (\( \text{PhMgBr} \)) with the following compounds is:

A solid compound XY has NaCl structure. If the radius of the cation is 100 pm, the radius of the anion \( Y^{1-} \) will be