VITEEE 2007 Question Paper is available for download here. VITEEE 2007 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 2007 Question Paper with Solution PDF using the link below.
VITEEE 2007 Question Paper with Solution PDF
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The magnetic moment of the ground state of an atom whose open sub-shell is half-filled with five electrons is
Indicate which one of the following statements is NOT CORRECT?
Identify the graph which correctly represents Moseley's law.
Assuming \( f \) to be the frequency of the first line in Balmer series, the frequency of the immediate next (i.e., second) line is
The velocity of a particle at which the kinetic energy is equal to its rest energy is
One electron and one proton are accelerated by equal potential. Ratio in their deBroglie wavelength is
Two electrons moving in opposite direction with speeds 0.8c and 0.4c where \( c \) is the speed of light in vacuum. Then the relative speed is about
A photo-sensitive material would emit electrons if excited by photons beyond a threshold. To overcome the threshold, one would increase
The radius of nucleus is
Radio carbon dating is done by estimating in specimen
Ionization power and penetration range of radioactive radiation increases in the order
The half-life of a radioactive element is 3.8 days. The fraction left after 19 days will be
Two identical P-N junctions are connected in series in three different ways as shown below to a battery. The potential drop across the P-N junctions are equal in
The temperature coefficient of a zener mechanism is
Identify the logic gate from the following TRUTH table
In Boolean algebra, \( A \cdot B \) is equal to
Radar waves are sent towards a moving airplane and the reflected waves are received. When the airplane is moving towards the radar, the wavelength of the wave
The transmission of high frequencies in a coaxial cable is determined by
The output stage of a television transmitter is most likely to be a
The antenna current of an AM transmitter is 8A when only the carrier is sent, but it increases to 8.93A when the carrier is modulated by a single sine wave. Find the percentage modulation.
Two point like charges Q1 and Q2 of whose strength are equal in absolute value are placed at a certain distance from each other. Assuming the field strength to be positive in the positive direction of x-axis the signs of the charges Q1 and Q2 for the graphs (field strength versus distance) shown in Figures 1, 2, 3, and 4 are
ABCD is a rectangle. At corners B, C, and D of the rectangle are placed charges \( +10 \times 10^{-12}C \), \( -20 \times 10^{-12}C \), and \( +10 \times 10^{-12}C \) respectively. Calculate the potential at the fourth corner. The side AB = 4 cm and BC = 3 cm
A parallel plate capacitor of capacitance 100 pF is to be constructed by using paper sheets of 1 mm thickness as dielectric. If the dielectric constant of paper is 4, the number of circular metal foils of diameter 2 cm each required for the purpose is
The electric field intensity \( E \), due to an electric dipole of moment \( p \), at a point on the equatorial line is
Twelve wires of each resistance 6 ohms are connected to form a cube as shown in the figure. The current enters at a corner A and leaves at the diagonally opposite corner G. The joint resistance across the corners A and G are
A conductor and a semi-conductor are connected in parallel as shown in the figure. At a certain voltage both ammeters register the same current. If the voltage of the DC source is increased then
A uniform copper wire of length 1m and cross-sectional area \(5 \times 10^{-7} \, m^2\) carries a current of 1A. Assuming that there are \(8 \times 10^{28} \, free electrons/m^3\) in copper, how long will an electron take to drift from one end of the wire to the other?
The temperature coefficient of resistance of a wire is \( 0.00125 \, K^{-1} \). At 300K its resistance is 1 ohm. The resistance of the wire will be 2 ohms at
A rectangular coil ABCD which is rotated at a constant angular velocity about a horizontal axis as shown in the figure. The axis of rotation of the coil as well as the magnetic field \( B \) are horizontal. Maximum current will flow in the circuit when the plane of the coil is
If the total emf in a thermocouple is a parabolic function expressed as \( E = at + \frac{1}{2}bt^2 \), which of the following relations does not hold good
The proton of energy 1 MeV describes a circular path in plane at right angles to a uniform magnetic field of \( 6.28 \times 10^{-4} \, T \). The mass of the proton is \( 1.7 \times 10^{-27} \, Kg \). The cyclotron frequency of the proton is very nearly equal to
A wire AB, in the shape of two semicircular segments of radius \( R \) each and carrying a current \( I \), is placed in a uniform magnetic field \( B \) directed into the page (see figure). The magnitude of the force due to the field on the wire AB is
There are two solenoids of same length and inductance \( L \) but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series. 1) They are connected in series with separated by large distance 2) they connected in series with one inside the other and senses of the turns coinciding 3) they are connected in series with one inside the other with senses of the turns opposite as depicted in figures 1, 2 and 3 respectively. The total inductance of the solenoids in each of the case 1, 2 and 3 are respectively
From the figure shown below, a series LCR circuit connected to a variable frequency 200V source. \( L = 5H, C = 80 \mu F, R = 40 \Omega \). Then the source frequency which drives the circuit at resonance is
If the coefficient of mutual induction of the primary and secondary coils of an induction coil is 5H and a current of 10A is cut off in \( 5 \times 10^{-4} \) seconds, the emf induced (in volt) in the secondary coil is
A voltage of peak value 283V and varying frequency is applied to a series L, C, R combination in which \( R = 3 \, \Omega \), \( L = 25 \, mH \) and \( C = 400 \, \mu F \). The frequency (in Hz) of the source at which maximum power is dissipated in the above is
Four independent waves are represented by equations \[ X_1 = a_1 \sin \omega t, \, X_2 = a_2 \sin 2 \omega t, \, X_3 = a_3 \sin \omega t, \, X_4 = a_4 \sin (\omega t + \delta) \]
Interference is possible between waves represented by equations
Following diffraction pattern was obtained using a diffraction grating using two different wavelengths \( \lambda_1 \) and \( \lambda_2 \). With the help of the figure identify which is the longer wavelength and their ratios.
In Young's double slit experiment, the interference pattern is found to have an intensity ratio between bright and dark fringes is 9. This implies the
Rising and setting sun appears to be reddish because
The catalyst used in Rosenmund reaction is
(CH₃CO)₂O + RMgX \(\xrightarrow{H_2O}\) ?
Identify, which of the below does not possess any element of symmetry?
The weakest acid amongst the following is
HOOC–(CH₂)₄–COOH + 2C₂H₅OH \(\xrightarrow{H_2SO_4}\) C₂H₅COOC–CH₂–COOC₂H₅
The purpose of using toluene here is
Transesterification is the process of
The correct sequence of base strengths in aqueous solution is
When aqueous solution of benzene diazonium chloride is boiled, the product formed is
The carbamylation reaction is given by aliphatic
C₆H₅CHO + NH₃ \(\xrightarrow{H_2, Ni}\) ?
In TeCl₆, the central atom tellurium involves
The purple colour of KMnO₄ is due to the transition
A nuclear reaction of \( ^{235}_{92}U \) with a neutron produces \( ^{90}_{37}Kr \) and two neutrons. Other element produced in this reaction is
AgCl dissolves in a solution of NH₃, but not in water because
Which of the following is hexadentate ligand?
A coordinate bond is a dative covalent bond. Which of the below is true?
Which of the following complex has zero magnetic moment (spin only)?
The IUPAC name of \( [Ni(PPh₃)_2Cl₂]^{2+} \) is
Among the following, the compound that is both paramagnetic and coloured is
On an X-ray diffraction photograph, the intensity of the spots depends on
An ion leaves its regular site occupy a position in the space between the lattice sites is called
The 8:8 type of packing is present in
When a solid melts reversibly
Enthalpy is equal to
Condition for spontaneity in an isothermal process is
Given: 2C(s) + O₂(g) \(\rightarrow\) 2CO₂(g); \[ \Delta H = -787 \, kJ \]
H₂(g) + \( \frac{1}{2} \)O₂(g) \(\rightarrow\) H₂O(l); \[ \Delta H = -286 \, kJ \]
C₂H₂(g) + \( \frac{5}{2} \)O₂(g) \(\rightarrow\) 2CO₂(g) + H₂O(l); \[ \Delta H = -1310 \, kJ \]
The heat of formation of acetylene is
Given the equilibrium system: \[ NH₄Cl(s) \rightleftharpoons NH₃(aq) + Cl⁻(aq) \quad \Delta H = +3.5 \, Kcal/mol \]
What change will shift the equilibrium to the right?
According to Arrhenius equation, the rate constant (k) is related to temperature (T) as
Equivalent amounts of H₂ and I₂ are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to HI, the \( K_c \) at this temperature is
For the reaction \( H_2(g) + I_2(g) \rightleftharpoons 2HI(g) \), the equilibrium constant \( K_p \) changes with
How long (in hours) must a current of 5.0 amperes be maintained to electroplate 60g of calcium from molten CaCl₂?
For strong electrolytes the plot of molar conductance vs \( \sqrt{C} \) is
If the molar conductance values of \( Ca^{2+} \) and \( Cl^- \) at infinite dilution are respectively \( 18.88 \times 10^{-4} \, m^2 \, mol^{-1} \) and \( 77.33 \times 10^{-4} \, m^2 \, mol^{-1} \), then that of \( CaCl_2 \) is (in \( m^2 \, mol^{-1} \))
The standard reduction potentials at 298K for the following half reactions are given: \[ Zn^{2+}(aq) + 2e^- \rightarrow Zn(s) \quad E_0 = -0.762 \, V \] \[ Cr^{3+}(aq) + 3e^- \rightarrow Cr(s) \quad E_0 = -0.740 \, V \] \[ 2H^+(aq) + 2e^- \rightarrow H_2(g) \quad E_0 = 0.00 \, V \] \[ Fe^{3+}(aq) + e^- \rightarrow Fe^{2+}(aq) \quad E_0 = +0.762 \, V \]
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
Aldol condensation is given by
Give the IUPAC name for \[ H_3C - CH_2 - C - CH_2 - C - OCH_3 \]
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
The product of all values of \( \cos(\alpha) + i \sin(\alpha) )^{3/5} \) is equal to
The imaginary part of \( \frac{(1+i)^2}{i(2i-1)} \) is
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
The function \( f(x) = x^2 e^{-x} \), \( x > 0 \). Then the maximum value of \( f(x) \) 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
The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to
The value of the integral \[ \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx \]
is
If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is
The differential equation of the system of all circles of radius r in the XY plane is
The general solution of the differential equation \[ \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 2e^{3x} \]
is given by
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
Everybody in a room shakes hands with everybody else. The total number of handshakes in the room is
If \( G^{*} \) is a group and the order of an element \( a \in G \) is 10, then the order of the inverse of \( a \) is
A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even} or {even, odd} is
If \( P(A) = \frac{1}{2}, P(B) = \frac{5}{12} \) and \( P(B/A) = \frac{1}{15} \), then \[ P(A \cup B) \]
is equal to
If the probability density function of a random variable \( X \) is \( f(x) = \frac{x}{2} \) for \( 0 \leq x \leq 2 \), then \[ P(X > 1.5 \mid X > 1) \]
is equal to
If \( X \) is a Poisson variate such that \[ 2P(X = 0) + P(X = 2) = 2P(X = 1), then E(X) \]
is equal to
If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta
\end{matrix} \right] \) and \( AB = 1 \), then \[ (\cos \theta)B \]
is equal to
If \( x = -5 \) is a root of the equation \[ \begin{vmatrix} 2x+1 & 4 & 8
2 & 2x & 2
7 & 6 & 2x \end{vmatrix} = 0 \]
then the other roots are
The simultaneous equations \( Kx + 2y = 1 \), \( K(1 - y) - 2x = 2 \) and \( K + 2y = 3 \) have only one solution when
If the rank of the matrix \[ \begin{pmatrix} -1 & 2 & 5
2 & -4 & -4
1 & -2 & a + 1 \end{pmatrix} \]
is 1, then the value of \( a \) is
If \( b^2 \geq 4ac \) for the equation \( ax^4 + bx^2 + c = 0 \), then all the roots of the equation will be real if
If \( x > 0 \) and \( \log x + \log \left( \log x \right) + \log \left( \log \log x \right) + \dots = 4 \), then \[ x equals \]
The number of real roots of the equation \[ \left( x + \frac{1}{x} \right)^3 + \frac{1}{x} = 0 \]
is
If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of \[ \frac{H}{P} + \frac{H}{Q} \]
is
If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \]
is parallel to the vector
If \( \theta \) is the angle between the lines \( AB \) and \( AC \) where A, B, and C are the three points with coordinates \( (1, 2, -1) \), \( (2, 0, 3) \), \( (3, -1, 2) \) respectively, then \[ \sqrt{62} \cos \theta \]
is equal to
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