List of top Questions asked in VITEEE

If \( a \), \( b \), and \( c \) are in A.P., then the value of: \[ |x + 1| + |x + 2| + |x + 3| + |x + b| + |x + c| \]

The solution of \( \sin x = \frac{-\sqrt{3}}{2} \) is:

The equation \( y^2 + 3 = 2(2x + y) \) represents a parabola with the vertex at:

If \( \omega = \frac{-1 + \sqrt{3}i}{2} \), then \( (3 + \omega + 3\omega^2) \) is:

If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are tangents to a circle, then radius of the circle is:

The position vector of A and B are: \[ 2\hat{i} + 2\hat{j} + \hat{k} \quad \text{and} \quad 2\hat{i} + 4\hat{j} + 4\hat{k} \] The length of the internal bisector of \( \triangle AOB \) is:

If \[ A = \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \end{bmatrix}, \quad B = \begin{bmatrix} a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2 \end{bmatrix}, \] then \( AB \) is equal to:

A circle has radius 3 and its center lies on the line \( y = x - 1 \). The equation of the circle, if it passes through (7, 3), is:

A coordination complex compound of cobalt has the molecular formula containing five ammonia molecules, one nitro group and two chlorine atoms for one cobalt atom. One mole of this compound produces three mole ions in an aqueous solution; on reacting with excess of \( \text{AgNO}_3 \), \( \text{AgCl} \) is precipitated. The ionic formula for this complex would be:

An endothermic reaction with high activation energy for the forward reaction is given by the diagram:

The volume of a closed reaction vessel in which the following equilibrium reaction occurs is halved: \[ 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) \] \text{As a result,}

If \( \tan \theta = \sqrt{n} \) for some non-square natural number \( n \), then sec \( 2\theta \) is:

If \( z = x + iy \), \( z^{1/3} = a - ib \), then \( \frac{x}{a} = \frac{y}{b} = k \) is equal to:

If the coordinates at one end of a diameter of the circle \( x^2 + y^2 - 8x - 4y + c = 0 \) are \( (-3, -2) \), then the coordinates at the other end are:

The system of linear equations: \[ x + y + z = 0, \quad 2x + y - z = 0, \quad 3x + 2y = 0 \] \text{has:}

In a hydrogen-oxygen fuel cell, combustion of hydrogen occurs to:

Among the following molecules, those having the same number of lone pairs on Xe are: (i) \( XeO_3 \) (ii) \( XeOF_4 \) (iii) \( XeF_6 \)

An alkene of molecular formula \( C_9H_{18} \) on ozonolysis gives \( 2 \)-dimethylpropanal and \( 2 \)-butanone, then the alkene is:

Glucose when heated with \( CH_3OH \) in presence of dry HCl gas gives \( \alpha \)- and \( \beta \)-methyl glucosides because it contains:

When acetylene is passed into methanol at 160-200°C in the presence of a small amount of potassium methoxide under pressure, the following is formed:

Which compound can exist in a dipolar (zwitter) state?

The rate constant is doubled when temperature increases from 27°C to 37°C. Activation energy in kJ is:

In the reaction, \( C_6H_5OH + NaOH \rightarrow \) (B) \( \rightarrow (C) \), the compound (C) is:

Calculate the energy needed to convert three moles of sodium atoms in the gaseous state to sodium ions. The ionization energy of sodium is 495 kJ/mol:

The uncertainty in position and velocity of a particle are \( 10^{-10} \, \text{m} \) and \( 5.27 \times 10^{-24} \, \text{ms}^{-1} \) respectively. Calculate the mass of the particle is (h = \( 6.625 \times 10^{-34} \, \text{Js} \)):