VITEEE 2006 Question Paper is available for download here. VITEEE 2006 Question Paper includes 40 questions from Mathematics/Biology, 35 questions from Physics, 35 questions from Chemistry, 5 questions from English, 10 questions from Aptitude to be attempted in 150 minutes. Candidates can download the VITEEE 2006 Question Paper with Solution PDF using the link below.
VITEEE 2006 Question Paper with Solution PDF
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A potential difference of 300 V is applied to a combination of 2.0µF and 8.0µF capacitors connected in series. The charge on the 2.0µF capacitor is:
Two point charges \( +4 \mu C \) and \( -2 \mu C \) are separated by a distance of 1 m. Then, the distance of the point on the line joining the charges, where the resultant electric field is zero, is (in metre):
Figure shows a triangular array of three point charges. The electric potential \( V \) of these source charges at the midpoint \( P \) of the base of the triangle is:
A current of 5A is passing through a metallic wire of cross-sectional area \( 4 \times 10^{-6} \, m^2 \). If the density of the charge carriers in the wire is \( 5 \times 10^{22} \, m^{-3} \), the drift speed of the electrons will be:
The series combination of two capacitors shown in the figure is connected across 1000V. The magnitude of the charges on the capacitors will be:
Three resistances of values 2Ω, 3Ω, and 6Ω are to be connected to produce an effective resistance of 4Ω. This can be done by connecting:
The resistance of a field cold measures 50Ω at 20°C and 53Ω at 70°C. The temperature coefficient of resistance is:
The electrolyte used in Leclanché cell is:
A galvanometer has a resistance of 50Ω. If a resistance of 12Ω is connected across its terminals, the total current flow through the galvanometer is:
In a tangent galvanometer, a current of 1A is required to produce a deflection of 60° is:
In the presence of magnetic field \( B \) and electric field \( E \), the total force on a moving charged particle is:
A circular coil of radius 40 cm consists of 250 turns of wire in which the current is 20mA. The magnetic field in the center of the coil is:
The RMS value of AC is:
The LCR circuit becomes extremely sharp in resonance when:
In the case of a current carrying coil, the induced EMF is maximum when the coil's plane is:
The frequency of AC supply is determined by the:
Our eyes respond to wavelengths ranging from:
A ray of light strikes a piece of glass at an angle of incidence of 60° and the reflected beam is completely plane polarised. The refractive index of glass is:
In an experiment on Newton's rings, the diameter of the 20th dark ring was found to be 5.82mm and that of the 10th dark ring was 3.16mm. The wavelength of light used is:
The refractive index of a material is 1.5. The angle of incidence for which the angle of refraction is 30° is:
In the angular momentum equation for the hydrogen atom, the principal quantum number is:
The transition of an electron from \( n = 5 \) to \( n = 6 \) corresponds to:
The wavelength of a spectral line in the second order of the hydrogen spectrum is 2.82 Å. The wavelength of the spectral line in the first order is:
The inductance of an inductor becomes equal to capacitance when:
Which is the incorrect statement of the following?
The de Broglie wavelength associated with a steel ball of mass 100 g moving at a speed of 1 m/s is:
The velocity, \( v \), at which the mass of a particle is double its rest mass is:
How much energy is produced, if 2 kg of a substance is fully converted into energy?
The difference between the rest mass of the nucleus and the sum of the masses of the nucleons composing a nucleus is known as:
The half-life period of Radium is 3 minutes. Its decay constant is:
'Pair production' involves conversion of a photon into:
The neutrino has mass and neutron fall under the group of:
When the conductivity of a semiconductor is due only to the breaking up of the covalent bonds, the semiconductor is known as:
In a P-type semiconductor, the acceptor impurity is:
An amplifier with proper negative feedback network circuits:
Which of the following gates can perform perfect binary addition?
An FM transmitter without signal input is called:
The frequency of an FM transmitter without signal input is:
Vidicon works on the principle of:
The maximum range, \( d_{max} \), of radar is:
The equivalent weight of potassium permanganate when it acts as oxidizing agent in ferrous ion estimation is:
The magnetic moment of lanthanide ions is determined from which one of the following relation?
Which one of the following has maximum number of unpaired electrons?
Excess of NaOH reacts with Zn to form:
How many isomers does \( Co(C_6H_6)_3 \) have?
NH\(_3\), group in a coordination compound is named as:
Name the complex Ni(\(PF_6\))\(_2\):
The purple colour of KMnO\(_4\) is due to:
How many lattice points belong to a face-centered cubic unit cell?
Schottky defect in solids is due to:
Which one of the following is amorphous?
The metal that crystallizes in simple cubic system is:
When ideal gas expands in vacuum, the work done by the gas is equal to:
For a closed system consisting of a reaction, N\(_2\)O\(_4\) \( (g) \) \( \rightleftharpoons \) 2NO\(_2\) \( (g) \), the pressure:
6 moles of an ideal gas expand isothermally and reversibly from a volume of 1 litre to a volume of 10 liters at 27°C. What is the maximum work done?
The reaction, Zn(s) + CuSO\(_4\)(aq) \( \rightleftharpoons \) ZnSO\(_4\)(aq) + Cu(s) is an example of a:
For the reaction, H\(_2\)(g) + I\(_2\)(g) \( \rightleftharpoons \) 2HI(g), \( K_p \) = 0, what happens if the pressure on ice is increased at a constant temperature?
The order of the reaction: N\(_2\)O\(_4\)(g) \( \rightleftharpoons \) 2NO\(_2\)(g) is:
The order of the reaction N\(_2\)O\(_3\) \( \rightleftharpoons \) N\(_2\)O\(_4\) is:
The reactions with low activation energy are always:
For a cell reaction to be spontaneous, the standard free energy change of the reaction must be:
Equivalent conductance of an electrolyte containing NaF at infinite dilution is 90.1 Ohm\(^{-1}\) cm\(^{2}\). If NaF is replaced by KF, what is the value of equivalent conductance?
The tendencies of the electrodes made up of Cu, Zn and Ag to release electrons when dipped in their respective salt solutions decrease in the order:
The electrode reaction that takes place at the anode of CH\(_3\)OH - O\(_2\) fuel cell is:
What is the hybridization of the oxygen atom in an alcohol molecule?
R–OH + LiAlH\(_4\) \( \rightarrow \) ?
Which one of the following is correct?
Which one of the following products is obtained when diethyl ether is boiled with water in the presence of dilute acid?
Identify the product for the following reaction:
What is the reaction of acetaldehyde with concentrated sulphuric acid?
Calcium Acetate on heating under distillation gives:
Identify the correct statement.
The O–H stretching vibration of alcohols absorbs in the region 3700–3500 cm\(^{-1}\). The O–H stretching of carboxylic acids absorbs in the region:
Which among the following reduces Fehling’s solution?
Which one of the following is an ingredient of Phthalic acid manufacture by catalytic oxidation?
On comparison with H–C–H bond angle of methane, the C–N–C bond angle of trimethylamine is:
The transition of acylazide (RCON\(_3\)) with acidic or alkaline medium gives:
The sequence of basic strength of alkyl amines follows the order:
Activation of benzene ring in aniline can be decreased by treating with:
The value of \( x \), for which the matrix \( A \) is singular, is:
\[ A = \begin{pmatrix} 2 & x & -1 & 2
1 & x & 2x^2
1 & \frac{1}{x} & 2 \end{pmatrix} \]
If \( x = -9 \) is a root of \( \begin{pmatrix} 2 & 3
7 & 6 \end{pmatrix} \times \begin{pmatrix} x \end{pmatrix} = 0 \), then other two roots are:
The values of \( \alpha \) for which the system of equation \( x + y + z = 1 \), \( x + 2y + 4z = \alpha \), \( x + 4y + 10z = \alpha^2 \) is consistent are given by:
Let \( A = \begin{pmatrix} 1 & 3 & 2
4 & 2 & 5
7 & -t & -6 \end{pmatrix} \), then the values of \( t \) for which inverse of \( A \) does not exist are:
The non-integer roots of \( x^4 - 3x^3 - 2x^2 + 3x + 1 = 0 \) are:
If \( e^x = y + \sqrt{1 + y^2} \), then the value of y is:
Consider an infinite geometric series with the first term and common ratio. If its sum is 4 and the second term is \( \frac{3}{4} \), then:
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the value of \( \alpha^3 + \beta^3 \) is:
The volume of the tetrahedron with vertices \( P(1, 2, 0), Q(2, 1, -3), R(1, 0, 1) \), and \( S(3, -2, 3) \) is:
If \( \mathbf{a} = i + 2j + 3k \), \( \mathbf{b} = i + 2j + k \), and \( \mathbf{c} = 3i + j \), then \( \mathbf{a} + \mathbf{b} \) is at right angle to \( \mathbf{c} \), then \( a + b \) and \( t \) are equal to:
An equation of the plane passing through the line of intersection of the planes \( x + y + z = 6 \) and \( 2x + 3y + 4z = 5 \), and passing through \( (1, 1, 1) \) is:
The length of the shortest distance between the lines \( \mathbf{r} = 3i + 5j + 7k + \lambda(2i - 2j + 3k) \) and \( \mathbf{r} = -i - j + k + \mu(7i - 6j + k) \) is:
The region of the Argand plane defined by \( |z - 1| + |z + 1| \leq 4 \) is:
The value of the sum \( \sum_{n=1}^{13} (i^n + i^{n+1}) \), where \( i = \sqrt{-1} \), equals:
If \( \sin \theta, \cos \theta, \tan \theta \) are in G.P., then \( \cos^2 \theta + \cos \theta + 3 \cos \theta - 1 \) is equal to:
In a triangle ABC, \( 5 \cos C + 6 \cos B = 4 \) and \( 6 \cos A + 4 \cos C = 5 \), then:
In a model, it is shown that an arc of a bridge is semielliptical with major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from horizontal, the best approximation of the height of the arch, 2m from the center of the base is:
The number of real tangents through \( (3, 5) \) that can be drawn to the ellipses \( 3x^2 + 5y^2 = 32 \) and \( 25x^2 + 9y^2 = 450 \) is:
If the normal to the rectangular hyperbola \( xy = c^2 \) at the point \( (ct, c/t) \) meets the curve again at \( (ct', c/t') \), then:
An equilateral triangle is inscribed in the parabola \( y^2 = 4ax \), one of whose vertices is at the vertex of the parabola, the length of each side of the triangle is:
If \( f(2) = 4 \) and \( f'(2) = 1 \), then \[ \lim_{x \to 2} \frac{x f(2) - 2f(x)}{x - 2} is equal to: \]
What is the least value of \( k \) such that the function \( x^2 + kx + 1 \) is strictly increasing on \( (1, 2) \)?
The maximum value of \( \left| \frac{1}{x} \right| \) is:
If \( u = \tan^{-1} \left( \frac{x^3 + y^2}{x + y} \right) \), then \( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} \) is:
If \( f'(x) = \frac{x}{\sqrt{1 + x^2}} \) and \( f(0) = 0 \), then \( f(x) = \):
The value of the integral \( \int_0^{\frac{\pi}{2}} \log (\tan x) \, dx \) is:
What is the area of a loop of the curve \( r = a \sin 30^\circ \)?
The value of the integral \( \int_1^4 \sqrt{t} \, dt \) is:
The differential equation that represents all parabolas each of which has a latus rectum \( 4a \) and whose axes are parallel to the x-axis is:
The solution of \( x \sec \left( \frac{x}{y} \right) - y \, dx + x \, dy = 0 \) is:
The particular integral of \( \frac{d^2 y}{dx^2} + 2y = x^2 \) is:
The solution of \( D^2 + 16y = \cos 4x \) is:
Determine which one of the following relations on \( X = \{1, 2, 3, 4\} \) is not transitive.
Find the number of ways in which five large books, four medium-size books, and three small books can be placed on a shelf so that all books of the same size are together.
Consider the set \( Q \) of rational numbers. Let \( * \) be the operation \( a * b = a + b - ab \). The identity element under \( * \) is:
The statement \( p \to q \) is equivalent to:
In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6?
Team A has probability \( \frac{2}{3} \) of winning whenever it plays. Suppose A plays four games. What is the probability that A wins more than half of its games?
An unprepared student takes five questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?
The probability density \( f(x) \) of a continuous random variable is given by \( f(x) = K e^{-|x|} \) for \( -\infty < x < \infty \). Then the value of \( K \) is:
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