VITEEE 2012 Question Paper is available for download here. VITEEE 2012 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 2012 Question Paper with Solution PDF using the link below.
VITEEE 2012 Question Paper with Solution PDF
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A square loop, carrying a steady current \( I \), is placed in a horizontal plane near a long straight conductor carrying a steady current \( I_1 \), at a distance of \( d \) from the conductor as shown in figure. The loop will experience
The threshold frequency for a photo-sensitive metal is \( 3.3 \times 10^{14} \, Hz \). If light of frequency \( 8.2 \times 10^{14} \, Hz \) is incident on this metal, the cut-off voltage for the photo-electric emission is nearly
For the given circuit of a p-n junction diode, which of the following is correct?
If the binding energy per nucleon in \( Li^7 \) and \( He^4 \) nuclei are respectively \( 5.60 \, MeV \) and \( 7.06 \, MeV \), then the energy of the reactor
\[ Li^7 + p \to He^4 + 2e \]
is
The graph between the square root of the frequency of a specific line of the characteristic spectrum of X-ray and the atomic number of the target will be
A resistor \( R \), an inductor \( L \), and a capacitor \( C \) are connected in series to an oscillator of frequency \( n \). If the resonant frequency is \( n_r \), then the current lags behind voltage when
A parallel plate capacitor has capacitance \( C \). If it is equally filled the parallel layers of materials of dielectric constant \( K_1 \) and \( K_2 \), its capacity becomes \( C_T \). The ratio of \( C_T \) and \( C \) is
The potential of the electric field produced by a point charge at any point \( (x, y, z) \) is given by \( V = x^2 + 5y^2 \), where \( x \), \( y \) are in meters and \( V \) is in volts. The intensity of the electric field at \( (-2, 1, 0) \) is
The potential of a large liquid drop when eight liquid drops are combined is 20V. Then the potential of each single drop was
A and B are two metals with threshold frequencies \( 1.8 \times 10^{14} \, Hz \) and \( 2.2 \times 10^{14} \, Hz \). Two identical photons of energy \( 0.825 \, eV \) each are incident on them. Then photoelectrons are emitted by (Take \( h = 6.6 \times 10^{-34} \, J.s \)):
In the Wheatstone's network given, \( P = 100 \, \Omega \), \( Q = 200 \, \Omega \), \( R = 150 \, \Omega \), \( S = 300 \, \Omega \), the current passing through the battery (of negligible internal resistance) is
Three resistors \( 10 \, \Omega \), \( 20 \, \Omega \), and \( 30 \, \Omega \) are connected to form a triangle. Across \( 30 \, \Omega \) resistor a 3V battery is connected. The current through \( 30 \, \Omega \) resistor is
In a common emitter amplifier the input signal is applied across
The kinetic energy of an electron get tripled then the de-Broglie wavelength associated with it changes by a factor
A radioactive substance contains 10000 nuclei and its half-life period is 20 days. The number of nuclei present at the end of 10 days is
A direct X-ray photograph of the intensities is not generally taken by radiologists because
Charge passing through a conductor of crosssection area \( A = 0.3 \, m^2 \) is given by \( q = 3t^2 + 5t + 2 \, C \), where \( t \) is in seconds. What is the value of drift velocity at \( t = 2 \) seconds?
Two capacitors of capacitance \( 1 \mu F \) and \( 2 \mu F \) are connected in series and the combination is charged to a potential difference of 120 V. If the charge on the combination is 80 μC, the energy stored in the capacitor of capacitance \( C_1 \) is
A hollow conducting sphere is placed in an electric field produced by a point charge at \( P \) as shown in figure. Let \( V_A \), \( V_B \), \( V_C \) be the potentials at points A, B, and C respectively. Then
In a hydrogen discharged tube it is observed that through a given cross-section \( 3.13 \times 10^{15} \) electrons are moving from right to left and \( 3.12 \times 10^{15} \) protons are moving from left to right. What is the electric current in the discharge tube and what is its direction?
In CuSO₄ solution when electric current equal to 2.5 Faraday is passed, the gram equivalent deposited on the cathode is
In hydrogen atom, an electron is revolving in the orbit of radius 0.53 Å with \( 6.6 \times 10^{15} \) radiations. Magnetic field produced at the centre of the orbit is
The dipole moment of the short bar magnet is \( 12.5 \, A \cdot m^2 \). The magnetic field on its axis at a distance of \( 0.5 \, m \) from the centre of the magnet is
The turn ratio of transformers is given as 2:3. If the current through the primary coil is 3A, thus calculate the current through load resistance.
In an AC circuit, the potential across an inductance and resistance joined in series are respectively 16V and 20V. The total potential difference across the circuit is
If hydrogen atom is its ground state absorbs \( 10.2 \, eV \) of energy. The orbital angular momentum increases by
Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radius of nucleus to that of Helium nucleus is (14)³. The atomic number of nucleus will be
Each resistance shown in figure is \( 2 \, \Omega \). The equivalent resistance between A and B is
If a triode value amplification factor is 20 and plate resistance is \( 10 \, k\Omega \), then its mutual conductance is
The output wave form of full-wave rectifier is
Calculate the energy released when three \( \alpha \)-particles combined to form a \( C^{12} \) nucleus, the mass defect is
In the figure shown, the magnetic field induction as the point \( O \) will be
In photoelectric emission process from a metal of work function 1.8 eV, the kinetic energy of most energetic electrons is 0.5 eV. The corresponding stopping potential is
The current in a coil varies with time as shown in the figure. The variation of induced emf with time would be
In photoelectric emission, the current varies with time as shown. The variation of induced emf with time would be
A transistor is operated in common emitter configuration at \( V_C = 2V \) such that a change in the base current from 100 μA to 300 μA produces a change in the collector current from 10 mA to 20 mA. The current gain is
A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
Charge \( q \) is uniformly spread on a thin ring of radius \( R \). The ring rotates about its axis with a uniform frequency \( f \). The magnitude of magnetic induction at the centre of the ring is
A galvanometer of resistance \( G \) is shunted by a resistance \( S \, \Omega \). To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is
Three charges, each \( +q \), are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid-points of BC and CA. The work done in taking a charge \( Q \) from D to E is
A bubble of air is underwater at temperature 15°C and the pressure 1.5 bar. If the bubble rises to the surface where the temperature is 25°C and the pressure is 1.0 bar, what will happen to the volume of the bubble?
Match List-I with List-II for the compositions of substances and select the correct answer using the codes given below the lists.
The pairs of species of oxygen and their magnetic behaviours are noted below. Which of the following presents the correct description?
Consider the reactions
The mechanisms of reactions (i) and (ii) are respectively
The following reactions take place in the blast furnace in the preparation of impure iron. Identify the reaction corresponding to the formation of the slag.
Among the elements Ca, Mg, P and Cl, the order of increasing atomic radii is
The following reaction is a reversible reaction that exhibits high temperature behaviour:
Two charges, each \( +q \), are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid-points of BC and CA. The work done in taking a charge \( Q \) from D to E is
Which of the following expressions correctly represents the equivalent conductance at infinite dilution of \( Al_2(SO_4)_3 \)? Given that \( \Lambda^\circ_{Al^{3+}} \) and \( \Lambda^\circ_{SO_4^{2-}} \) are the equivalent conductances at infinite dilution of the respective ions?
The pressure exerted by 6.0g of methane gas in a 0.03m³ vessel at 129°C is (Atomic masses: C = 12.01, H = 1.01 and R = 8.314JK⁻mol⁻)
Match List-I with List-II for the equations and select the correct option.
Among the following, which one has the highest cation to anion size ratio?
Which of the following species is not electrophilic in nature?
Match List-I (Substances) with List-II (Processes employed in the manufacture of the substances) and select the correct option.
When glycerol is treated with excess of HI, it produces
Some statements about heavy water are given below. Which of the following statements are true?
Which of the following compounds will be most readily dehydrated?
Which one of the following complexes is not expected to exhibit isomerism?
Which of the following conformers for ethylene glycol is most stable?
The IUPAC name of the compound \( CH_3CH= CHCH_2\) is
Some of the properties of the two species, \( NO_3^- \) and \( H_2O \), are described below. Which one of them is correct?
Which of the following is not a fat-soluble vitamin?
Which of the above compounds on being warmed with iodine solution and NaOH will give iodoform?
Fructose reduces Tollen's reagent due to
In the following reaction,
Which of the following is not a fat-soluble vitamin?
Which of the statements about 'Denaturation' given below are correct?
(a) Denaturation of proteins causes loss of secondary and tertiary structures of the protein.
(b) Denaturation leads to the conversion of double strand of DNA into single strand.
(c) Denaturation affects the primary structure which gets destroyed.
Which has the maximum number of molecules among the following?
Which of the following compounds undergoes nucleophilic substitution reaction most easily?
A 0.1 molal aqueous solution of a weak acid is 30% ionised. If Kf for water is \( 1.86^\circ C/mol \), the freezing point of the solution will be
Which of the following carbonyls will have the strongest C—O bond?
The order of reactivity of phenyl magnesium bromide (\( PhMgBr \)) 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
Consider the following processes \[ \Delta H (kJ/mol) = \frac{1}{2} B + 150 \]
For \( B + D \rightarrow E + 2C \), \( \Delta H \) will be
Match the compounds given in List-I with List-II and select the suitable option using the codes given below:
Which of the following compound is the most basic?
Which of the following structures is the most preferred and hence of lowest energy for \( SO_3 \)?
What is the value of electron gain enthalpy of \( Na \), if \( IE_Na = 5.1 \, eV \)?
The unit of rate constant for a zero order reaction is
The solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy}{(1+x^2)^2} \]
is
If \( x, y, z \) are all distinct and \[ \begin{vmatrix} x^2 & 1+x^2 & 3
y^2 & 1+y^2 & 4
z^2 & 1+z^2 & 5 \end{vmatrix} = 0 \]
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
If \( 3p \) and \( 4p \) are resultant of a force \( 5p \), then the angle between \( 3p \) and \( 5p \) is
If \( \tan^{-1}(\cos x) = \tan^{-1}(2 \csc x) \), then the value of \( x \) is
Let \( a \) be any element in a Boolean algebra \( B \), if \( a + 1 = 1 \) and \( a \times 0 = 0 \), then
View Solution
In Boolean algebra, the operations follow certain laws. If \( a + 1 = 1 \) and \( a \times 0 = 0 \), then \( x \) must be equal to \( a \).
Step 2: Conclusion.
The correct answer is \( x = a \), corresponding to option (c).
Quick Tip: In Boolean algebra, \( a + 1 = 1 \) and \( a \times 0 = 0 \) are fundamental properties.
The function \( f : R \to R \) 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
View Solution
If three complex numbers are in arithmetic progression (AP), their corresponding points lie on a straight line. This is a geometric property of complex numbers.
Step 2: Conclusion.
The correct answer is that they lie on a line, corresponding to option (c).
Quick Tip: Three complex numbers in arithmetic progression lie on a straight line in the complex plane.
Let \( a, b \) and \( c \) be in AP and \( |a| < 1, |b| < 1, |c| < 1 \). If \[ x = a + b + c + \ldots, \, y = b + b^2 + c^2, \, z = c + b + c^2, \]
then \( x, y, z \) are in
If the complex numbers \( z_1, z_2, z_3 \) are in AP, then they lie on a
View Solution
For three complex numbers to be in Arithmetic Progression (AP), the points representing these numbers must lie on a straight line in the complex plane. This is a well-known geometric property of complex numbers in AP.
Step 2: Conclusion.
Therefore, the complex numbers \( z_1, z_2, z_3 \) lie on a line, corresponding to option (c).
Quick Tip: If three complex numbers are in arithmetic progression, they must lie on a straight line.
The number of real solutions of the equation \[ \frac{(2)^{10}}{10} = -3 + x^2 \]
is
The lines \( 2x - 3y = 5 \) and \( 3x + 4y = 7 \) are diameters of a circle of area 154 sq units, then the equation of the circle is
The angle of depressions 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 \[ \tan \theta = \frac{4}{3} \quad and \quad \tan \phi = \frac{5}{2} \]
is
The maximum value of \( 4\sin \alpha - 12 \sin x + 7 \) is
The coefficient of \( x^3 \) in the following expansion \[ 100 \sum_{m=0}^{\infty} \cos(x - 3)10^{-m} \]
is
The function \( f : R \to R \) defined by \( f(x) = (x-1)(x-2)(x-3) \) is
The order of reactivity of phenyl magnesium bromide (PhMgBr) with the following compounds
\[ H_3CCl, \, H_3CCOOH, \, PhCl, \, C_6H_5COOH \]
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
The value of the determinant \[ \begin{vmatrix} \cos \alpha & -\sin \alpha
\sin \alpha & \cos \alpha \end{vmatrix} \]
is
The value of the integral \[ \int \sin x - \cos x + \sqrt{2} \]
is
The value of the integral \[ \int \sqrt{x^2 + 1} \, dx \]
is
The tangent of the curve \( x^2 + 4y^2 = 25 \) at the point \( (3, 4) \) is
The equation of straight line through the intersection of the lines \( x - 2y = 1 \) and \( x + 3y = 2 \) and parallel to \( 3x + 4y = 5 \) is
\[ \int \sin x - \cos x + \sqrt{2} \, dx \]
equals to
The value of the integral \[ \int \frac{1}{|x|} \, dx \]
is
The value of \[ \int \frac{1}{\sqrt{1 - x^2}} \, dx \]
is
The eccentricity of the ellipse, which meets the straight line \( \frac{x}{7} = \frac{y}{12} \) on the axis of \( x \) and the straight line \( \frac{x}{3} = \frac{y}{5} \) on the axis of \( y \), is
View Solution
The eccentricity of an ellipse is calculated using the relationship between the axes. We calculate the eccentricity for this particular ellipse and find it to be \( \frac{\sqrt{6}}{7} \).
Step 2: Conclusion.
The eccentricity of the ellipse is \( \frac{\sqrt{6}}{7} \), corresponding to option (b).
Quick Tip: To find the eccentricity of an ellipse, use the formula \( e = \sqrt{1 - \frac{b^2}{a^2}} \), where \( a \) is the semi-major axis and \( b \) is the semi-minor axis.
The equation of the conic with focus at \( (1, -1) \) directrix along \( x - y + 1 = 0 \) and with eccentricity \( \sqrt{2} \) is
The sum of the series \[ 1^2 + 2^2 + 3^2 + 4^2 + \ldots + 10^2 \]
is
The value of the determinant \[ \begin{vmatrix} \cos \alpha & -\sin \alpha
\sin \alpha & \cos \alpha \end{vmatrix} \]
is
The value of the integral \[ \int \left( \frac{1}{|x|} \right) dx \]
is
The coefficient of \( x^3 \) in the expansion of \( \log(1+x) \) is
If a plane meets the coordinates at \( A \), \( B \), and \( C \) in such a way that the area of the plane is given by
\[ A = \frac{1}{3} \left| \vec{AB} \times \vec{AC} \right| \]
then the area of Parallelogram having diagonals \( a + b \) and \( a - b \) is
The area lying in the first quadrant and bounded by the circle \( x^2 + y^2 = 4 \), the line \( x = \sqrt{3}y \) and x-axis is
The value of \[ \lim_{x \to 1} \left( \frac{1}{1 + x} \right) \]
is
If \( f(x) = \sin x + n \), then the domain of the function is
The general solution of the differential equation \[ (1 + y)^2 \left( \frac{d}{dx} \right) y = \left( 3x + 4y + 25 \right) \]
is
The domain of the function \[ f(x) = \frac{1}{\sqrt{1 - x^2}} \]
is
The order and degree of the differential equation \[ \left( \frac{dy}{dx} \right)^2 + \left( \frac{dy}{dx} \right) y = 5 \]
are, respectively,
If the gradient of the tangent at any point \( (x, y) \) of a curve is given by \[ \frac{dy}{dx} = \frac{1 + x^2}{y^2} \]
then the equation of the curve is
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