VITEEE 2013 Question Paper is available for download here. VITEEE 2013 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 2013 Question Paper with Solution PDF using the link below.
VITEEE 2013 Question Paper with Solution PDF
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The amplitude of an electromagnetic wave in vacuum is doubled with no other changes made to the wave. As a result of this doubling of the amplitude, which of the following statement is correct?
An element with atomic number \( Z = 11 \) emits \( K_{\alpha} \)-X-ray of wavelength \( \lambda \). The atomic number which emits \( K_{\alpha} \)-X-ray of wavelength \( 4\lambda \) is
Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are \( 0.36 \, m^2 \, V^{-1} \, s^{-1} \) and \( 0.17 \, m^2 \, V^{-1} \, s^{-1} \), respectively. The electron and hole densities are each equal to \( 2.5 \times 10^{19} \, m^{-3} \). The electrical conductivity of germanium is
If a radio-receiver amplifies all the signal frequencies equally well, it is said to have high
If a progressive wave is represented as \[ y = 2 \sin \left( \pi \left( \frac{t}{2} - \frac{x}{4} \right) \right) \]
where \( x \) is in meters and \( t \) is in seconds, then the distance traveled by the wave in 5 s is
The gravitational potential at a place varies inversely with \( x^2 \) (i.e., \( V = kx^2 \)), the gravitational field at that place is
A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm, are connected end to end. When stretched by a force, the elongation in length 0.50 m is produced in the copper wire. The stretching force is ( \( Y_{cu} = 1.1 \times 10^{11} \, N/m^2, Y_{steel} = 2.0 \times 10^{11} \, N/m^2 \))
If \( v_p, v_{rms}, v_p \) represent the mean speed, root mean square speed, and most probable speed of the molecules in an ideal monoatomic gas at temperature \( T \) and \( m \) is the mass of the molecule, then
Two balls of equal masses are thrown upwards along the same vertical direction at an interval of 2 s, with the same initial velocity of 39.2 m/s. The two balls will collide at a height of
The dimensional formula of magnetic flux is
The time dependence of a physical quantity \( P \) is given by \( P = P_0 e^{\alpha (-\alpha t^2)} \), where \( \alpha \) is a constant and \( t \) is time. The constant \( \alpha \) has dimensions of
If the potential energy of a gas molecule is \[ U = \frac{M}{r} - \frac{N}{r^2} \]
where \( M \) and \( N \) are positive constants, then the potential energy at equilibrium must be
A table fan rotating at a speed of 2400 rpm is switched off and the resulting variation of revolution per minute with time is shown in figure. The total number of revolutions of the fan before it comes to rest is
In the adjoining figure, the position-time graph of a particle of mass 0.1 kg is shown. The impulse at \( t = 2 \) s is
The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are 4% and 2%, then the maximum error in the measurement of pressure is
The centre of a wheel rolling on a plane surface moves with a speed \( v_0 \). A particle on the rim of the wheel at the same level as the centre will be moving at speed
A body of mass \( 5 \, m \) initially at rest explodes into 3 fragments with mass ratio 3:1:1. Two of the fragments each of mass \( m \) are found to move with a speed of \( 60 \, m/s \) in mutually perpendicular directions. The velocity of the third fragment is
A body of mass 2 kg moving with a velocity of \( 6 \, m/s \) strikes elastically with another body of mass 4 kg initially at rest. The amount of heat evolved during this collision is
Two particles of equal mass \( m \) go round a circle of radius \( R \) under the action of their mutual gravitational attraction. The speed of each particle is
Four equal charges \( Q \) each are placed at four corners of a square of side \( a \). Work done in carrying a charge \( -q \) from its centre to infinity is
A network of resistances, cell and capacitor \( C = (2 + 4) \, F \) is shown in the adjoining figure. In steady state condition, the charge on \( 2 \, F \) capacitor is \( Q \), while \( R \) is unknown resistance. Values of \( Q \) and \( R \) are respectively
As the electron in Bohr’s orbit of hydrogen atom passes from state \( n = 2 \) to \( n = 1 \), the KE (K) and the potential energy (U) changes as
To get an OR gate from a NAND gate, we need
If a current \( I \) is flowing in a loop of radius \( r \) as shown in the adjoining figure, then the magnetic field induction at the center O will be
Two identical magnetic dipoles of magnetic moment \( 1.0 \, Am^2 \) each, placed at a separation of 2 m with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is
A lead shot of 1 mm diameter falls through a long column of glycerine. The variation of the velocity with distance covered (s) is correctly represented by
If \( \epsilon_0 \) and \( \mu_0 \) represent the permittivity and permeability of vacuum and \( \epsilon \) and \( \mu \) represent the permittivity and permeability of medium, then refractive index of the medium is given by
A student plots a graph between inverse of magnification \( \frac{1}{m} \) produced by a convex thin lens and the object distance \( u \) as shown in figure. What was the focal length of the lens used?
Two waves \( y_1 = A_1 \sin (\omega t - \beta_1 x) \) and \( y_2 = A_2 \sin (\omega t - \beta_2 x) \) superimpose to form a resultant wave whose amplitude is
When a certain metallic surface is illuminated with monochromatic light of wavelength \( \lambda \), the stopping potential for photoelectric current is \( V_0 \). When the same surface is illuminated with a light of wavelength \( 2\lambda \), the stopping potential is \( V_1 \). The threshold wavelength for this surface to photoelectric effect is
In the \( I-V \) diagram shown in adjoining figure, what is the relation between \( P_1 \) and \( P_2 \)?
If a gas mixture contains 2 moles of O\(_2\) and 4 moles of Ar at temperature \( T \), then what will be the total energy of the system (neglecting all vibrational modes)?
In the adjoining figure, two pulses in a stretched string are shown. If initially their centres are 8 cm apart and they are moving towards each other, with speed of 2 cm/s, then total energy of the pulses after 2 s will be
When two waves of almost equal frequency \( n_1 \) and \( n_2 \) are produced simultaneously, then the time interval between successive maxima is
A long glass capillary tube is dipped in water. It is known that water wets glass. The water level rises by \( h \) in the tube. The tube is now pushed down so that only a length \( h/2 \) is outside the water surface. The angle of contact at the water surface at the upper end of the tube will be
In the adjoining circuit, if reading of voltmeter \( V_1 \) and \( V_2 \) are 300 volts, each, then the reading voltmeter \( V_3 \) and ammeter \( A \) are respectively
If the work done in turning a magnet of magnetic moment \( M \) by an angle of \( 90^\circ \) from the magnetic meridian is in times the corresponding work done to turn it through an angle of \( 60^\circ \), then the value of \( n \) is
The capacitance of a parallel plate capacitor with air as dielectric is \( C \). If a slab of dielectric constant \( K \) and of the same thickness as the separation between the plates is introduced so as to fill \( \frac{1}{4} \)th of the capacitor (shown in figure), then the new capacitance is
Seven resistances are connected between points A and B as shown in adjoining figure. The equivalent resistance between A and B is
Which of the following does not undergo benzoin condensation?
Benzene diazonium chloride on treatment with hypophosphorous acid and water yields benzene. Which of the following is used as a catalyst in this reaction?
When a monosaccharide forms a cyclic hemiacetal, the carbon atom that contained the carbonyl group is identified as the … carbon atom, because
Which of the following is/are \( \alpha \)-amino acid?
Calculate pH of a buffer prepared by adding 10 mL of 0.10 M acetic acid to 20 mL of 1 M sodium acetate [\( CH_3COOH \)] at \( pH = 4.74 \).
The equivalent conductance of silver nitrate solution at 250°C for an infinite dilution was found to be \( 133.30 \, S cm^2 equiv^{-1} \). The transport number of \( Ag^+ \) ions in very dilute solution of \( AgNO_3 \) is 0.464. Equivalent conductances of \( Ag^+ \) and \( NO_3^- \) at infinite dilution are respectively
Treating anisole with the following reagents, the major product obtained is
I. \( CH_3 \), CCl\(_3\), II. Cl\(_2\), FeCl\(_3\), III. HBr, Heat
Ketones \( [R-C(R)=O] \), where \( R = alkyl \) group can be obtained in one step by
An optically active compound \( X \) has molecular formula \( C_4H_8O_3 \), it evolves \( CO_2 \) with aqueous NaHCO\(_3\). \( X \) reacts with LiAlH\(_4\) to give an achiral compound. \( X \) is
Glycerol \( C_3 H_8 O_3 \) reacts with \(HCl \), the product A is obtained. What is the structure of A?
Phenol is heated with phthalic anhydride in the presence of cone. H\(_2\)SO\(_4\). The product gives pink colour with alkaline ferric chloride. The product is
\( \gamma \) \( H_2 O \) → \( Z \) is identified as
B can be obtained from halide by van-Arkel method. This involves reaction
\( NH_4 Cl \) is heated in a test tube. Vapours are brought in contact with red litmus paper, which changes it to blue and then to red. It is because of
Out of \( H_2 SO_4 \), \( H_2 SO_3 \), \( H_2 S_2 O_8 \), peroxy acids are
The density of solid argon is 1.65 g per cc at 233°C. If the argon atom is assumed to be a sphere of radius \( 1.54 \times 10^{-8} \) cm, what percent of solid argon is apparently empty space? \( A_r = 40 \)
When 1 mole of CO\(_2\) occupying volume 10L at 27°C is expanded under adiabatic condition, temperature falls to 150 K. Hence, final volume is
Acid hydrolysis of ester is first order reaction and rate constant is given by \[ k = \frac{2.303}{t} \log \frac{V_0 - V}{V_0 - V_t} \]
where \( V_0 \), \( V_t \), and \( V_\infty \) are the volume of standard NaOH required to neutralise acid present at a given time, if ester is 50% neutralised then
A near UV photon of 300 nm is absorbed by a gas and then re-emitted as two photons. One photon is red with wavelength of the second photon is
Which of these ions is expected to be coloured in aqueous solution?
Select the correct statements(s)
End product of the following reaction is
Which is more basic oxygen in an ester?
In a Claisen condensation reaction (when an ester is treated with a strong base)
An organic compound \( B \) is formed by the reaction of ethyl magnesium iodide with a substance \( A \), followed by treatment with dilute aqueous acid. Compound \( B \) does not react with PCC or PDC in dichloromethane. Which of the following is a possible compound for \( A \)?
\( CH_3CH_2CH_2COCH_3 \) reacts with \( CH_3 MgBr \) (one mole) followed by treatment with \( H_2 O \). The compound \( A \) formed in this reaction is
For the cell reaction \( 2Cu^{2+} + Co \rightarrow 2Co^{2+} + Cu \), \( E^\circ_{cell} \) is 1.89V. If \( E^\circ_{Co^{2+}/Co} \) is -0.28V, what is the value of \( E^\circ_{Cu^{2+}/Cu} \)?
A constant current of 30 A is passed through an aqueous solution of NaCl for a time of 1.00 h. What is the volume of Cl\(_2\) gas at STP produced?
The reaction of zinc with \( Cu^{2+} \) produces the following.
Entropy change \( \Delta S \) is given by \( 96.5 J \cdot mol^{-1} \cdot K^{-1} \).
What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition, \( n = 4 \) to \( n = 2 \) of He\(^+\) spectrum?
What is the degeneracy of the level of H-atom that has energy \( \frac{R_H}{9} \)?
Match the following and choose the correct option given below.
Compound/Type \(\quad\) Use
A. Dry ice 1. Anti-knocking compound
B. Semiconductor 2. Electronic diode or triode
C. Solder 3. Joining circuits
D. TEL 4. Refrigerant for preserving food
Which of the following ligands is tetradentate?
What is the EAN of \( [Al(C_4O_4)_3]^{3-} \)?
The relation \( R \) defined on set \( A = \{x : |x| < 3, x \in \mathbb{R} \} \) by \( R = \{(x, y): y = |x|\} \) is
The solution of the differential equation \[ \frac{dy}{dx} = \frac{y}{f(x)} - y^2 \]
is
If \( a \), \( b \), and \( c \) are in AP, then determinant
\[ \begin{vmatrix} x+2 & x+3 & x+4
x+4 & x+5 & x+6
x+7 & x+8 & x+9 \end{vmatrix} \]
If two events A and B. If odds against A are 2:1 and those in favour of \( A \cup B \) are 3:1, then
The value of \( 2 \tan^{-1} x - \left( cosec \, \tan^{-1} x - \tan \, \cot \, x \right) \)
The proposition \( \neg (p \iff q) \) is equivalent to
If truth values of \( p \) be F and \( q \) be T, then truth value of \( \neg(p \vee q) \) is
The rate of change of the surface area of a sphere of radius \( r \), when the radius is increasing at the rate of \( 2 \, cm/s \), is proportional to
If \( N \) denote the set of all natural numbers and \( R \) the relation on \( N \times N \) defined by \( (a, b) R (c, d) \), if \( a(b + c) = b(a + d) \), then \( R \) is
A complex number \( z \) is such that \( \arg \left( \frac{-2}{3} + \frac{2i}{3} \right) = \frac{\pi}{3} \). The points representing this complex number will lie on
If \( a_1, a_2, a_3 \) be any positive real numbers, then which of the following statement is true?
If \( x^2 + 2x - 5 = 0 \), then the values of \( x \) are
The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is
A tower \( A \) leans towards west making an angle \( \theta \) with the vertical. The angular elevation of \( B \), the topmost point of the tower is \( \beta \) as observed from a point \( C \) at a distance \( d' \) from \( B \). If the angular elevation of \( B \) from point \( D \) due east of \( C \) is the same and \( 2d \) from \( C \), then \( \theta \) can be given as
\( \theta \) and \( \gamma \) are the roots of the equation \( x^2 - \alpha x + \beta = 0 \) and if \( \theta + \gamma = \alpha \), then what is the value of \( \theta^2 + \gamma^2 \)?
The angle of intersection of the circles \( x^2 + y^2 - 8x - 9 = 0 \) and \( x^2 + y^2 + 2x - 4y - 11 = 0 \) is
Which of the following is the correct expansion of the series
\[ \sum_{n=0}^{\infty} \left( \binom{C}{n} \right) \left( \frac{3}{5} \right)^n \left( \frac{2}{5} \right)^{n+1} \]
The vector \( \mathbf{r} = 3\hat{i} + 4\hat{k} \) can be written as the sum of a vector \( \mathbf{v} \), parallel to \( \hat{i} + \hat{k} \), and a vector \( \mathbf{u} \), perpendicular to \( \hat{i} + \hat{k} \). Then, the value of \( \mathbf{v} \) is
If the points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are collinear, then the rank of the matrix
\[ \begin{bmatrix} x_1 & y_1 & 1
x_2 & y_2 & 1
x_3 & y_3 & 1 \end{bmatrix} \]
The value of the determinant
\[ \begin{vmatrix} \cos(\alpha - \beta) & \cos \alpha & \cos \beta
\cos(\alpha - \beta) & 1 & \cos \beta
\cos \alpha & \cos \beta & 1 \end{vmatrix} \]
The number of integral values of \( K \), for which the equation \( 7 \cos x + 5 \sin x = 2K + 1 \) has a solution, is
The line joining two points \( A(2,0) \), \( B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an angle of \( 15^\circ \). The equation of the line in the new position is
The line \( 2x + \sqrt{6}y = 2 \) is tangent to the curve \( x^2 - 2y^2 = 4 \). The point of contact is
The number of integral points (integral point means both the coordinates should be integers) exactly in the interior of the triangle with vertices \( (0, 0), (0, 21), (21, 0) \) is
\( \int (x + 1)(x - x^2) e^x \, dx \) is equal to
If \( f(x) = x - \lfloor x \rfloor \), for every real number \( x \), where \( \lfloor x \rfloor \) is the integral part of \( x \), then
\[ \int f(x) \, dx \]
is equal to
The value of the integral
\[ \int_1^\infty \frac{x+1}{|x-1|} \left( \frac{x-1}{x+1} \right)^{1/2} \, dx \]
is
If a tangent having slope \( \frac{-4}{3} \) to the ellipse
\[ \frac{x^2}{18} + \frac{y^2}{32} = 1 \]
intersects the major and minor axes in points A and B respectively, then the area of \( \triangle OAB \) is equal to
The locus of mid points of tangents intercepted between the axes of ellipse
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
is
If \( P \) is a double ordinate of hyperbola
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
such that \( OPQ \) is an equilateral triangle, \( O \) being the centre of the hyperbola, then the eccentricity \( e \) of the hyperbola satisfies
The sides \( AB \), \( BC \), and \( CA \) of a triangle \( \triangle ABC \) have respectively 3, 4, and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is
In the expansion of \( a + bx \), the coefficient of \( x^r \) is
If \( n = 1999 \), then \( \sum_{i=1}^{1999} \log x_i \) is equal to
\( P \) is a fixed point \( (a, a, a) \) on a line through the origin equally inclined to the axes, then any plane through \( P \) perpendicular to \( OP \), makes intercepts on the axes, the sum of whose reciprocals is equal to
For which of the following values of \( m \), the area of the region bounded by the curve \( y = x - x^2 \) and the line \( y = mx \) equals 5?
If \( R \to R \) be such that \( f(1) = 3 \) and \( f'(1) = 6 \), then \( f(x) \) is equal to
If \( f(x) = \left\{ \begin{array}{ll} 1 + \left| \sin x \right|, & for -\pi \leq x < 0
e^{x/2}, & for 0 \leq x < \pi
\end{array} \right. \)
then the value of \( a \) and \( b \), if \( f \) is continuous at \( x = 0 \), are respectively
The domain of the function
\[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \]
is
The solution of the differential equation
\[ (1 + y^2) \, \frac{dy}{dx} = e^{-(x - y)} \]
is
If the gradient of the tangent at any point \( (x, y) \) of a curve passing through the point \( (1, \frac{\pi}{4}) \) is
\[ \left| \frac{dy}{dx} \right| = \frac{1}{x} \cdot \left| \log \left( \frac{y}{x} \right) \right| \]
then the equation of the curve is
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