VITEEE 2015 Question Paper is available for download here. VITEEE 2015 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 2015 Question Paper with Solution PDF using the link below.
VITEEE 2015 Question Paper with Solution PDF
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When a hydrogen atom is raised from ground energy level to excited energy level, then
The half-life for \(\alpha\)-decay of uranium \( U^{228} \) is 4.47 × 10\(^8\) yr. If a rock contains 60% of the original \( U^{228} \) atoms, then its age is
A nuclear transformation is given by \[ Y(n, \alpha) \rightarrow L_i^{1} \] . The nucleus of element Y is
The angular momentum of an electron in Bohr’s hydrogen atom whose energy is -3.4 eV is
When the momentum of a photon is changed by an amount \( p' \), then the corresponding change in the de-Broglie wavelength is found to be 0.20%. Then, the original momentum of the photon was
Suppose a beam of electrons with each electron having energy \( E_0 \) incident on a metal surface kept in an evacuated chamber. Then,
An n-type semiconductor is
The de-Broglie wavelength of an electron moving with a velocity of \(10^6\) m/s is:
The ionization energy of hydrogen in the ground state is
The electric field at the center of a uniformly charged spherical shell is
Equal charges \( q \) each are placed at the vertices of an equilateral triangle of side \( r \). The magnitude of electric field intensity at any vertex is
Two points masses, \( m \) each carrying charges \( -q \) and \( +q \) are attached to the ends of a massless rigid non-conducting wire of length \( L \). When this arrangement is placed in a uniform electric field, then it deflects through an angle \( \theta \). The minimum time needed by rod to align itself along the field is
A condenser of capacitance \( C \) is fully charged by a 200V supply. It is then discharged through a small coil of resistance \( r \) embedded in thermally insulated block of specific heat 250 J/K-g and mass 100 g. If the temperature of the block rises by 0.4 K, then the value of \( C \) is
The masses of three copper wires are in the ratio 3 : 2 : 5 and their lengths are in the ratio 3 : 2 : 5. Then, the ratio of their electrical resistances is
A 30V-90W lamp is operated on a 120V DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance
The magnetic field at the centroid of the triangle is
In a potentiometer experiment, the balancing length of a cell is 560 cm. When an external resistance of 10 \(\Omega\) is connected in parallel to the cell, the balancing length changes by 60 cm. The internal resistance of a cell is
Two sources of equal emf are connected to a resistance \( R \). The internal resistance of the sources are \( r_1 \) and \( r_2 \), \( (r_1 > r_2) \). If the potential difference across the source having internal resistance \( r_2 \) is zero, then
An electron of mass \( 9.0 \times 10^{-31} \) kg under the action of a magnetic field moves in a circle of radius 2 cm at a speed of \( 3 \times 10^6 \) m/s. A proton of mass \( 1.8 \times 10^{-27} \) kg moves in a circle of same radius in the same magnetic field, then its speed will become
A horizontal rod of mass 0.01 kg and length 10 cm is placed on a frictionless plane inclined at an angle 60° with the horizontal and with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field is applied ‘Vertically downwards’. The current through the rod is 1.7 A, then the value of magnetic field induction \( B \) for which the rod remains stationary in the inclined plane is
A current of 2 A is flowing in the sides of an equilateral triangle of side 9 cm. The magnetic field at the centroid of the triangle is
The direction of magnetic field \( dB \) due to current element \( dl \) at a distance \( r \) is the direction of
A galvanometer with a scale divided into 100 equal divisions has a current sensitivity of 10 divisions per milliampere and a voltage sensitivity of 2 divisions per millivolt. The galvanometer resistance will be
The earth is considered as a short magnet with its centre coinciding with the geometric centre of earth. The angle of dip \( \delta \) related to the magnetic latitude \( \lambda \) is
Which of the following statement related to hysteresis loop is incorrect?
A magnetic needle lying parallel to the magnetic field requires \( W \) units of work to turn it through an angle 45°. The torque required to maintain the needle in this position will be
An induced emf has
A coil of area 5 cm² having 20 turns is placed in a uniform magnetic field of \( 10^3 \, gauss \). The normal to the plane of coil makes an angle 30° with the magnetic field. The flux through the coil is
The current graph for resonance in an \( LC \) circuit is
The value of inductance \( L \) for which the current is maximum in series \( LCR \) circuit with \( C = 10 \, \mu F \) and \( R = 1000 \, \Omega \) is
A ray of light is incident on a plane mirror at an angle of 30°. At what angle with the horizontal must a plane mirror be placed so that the reflected ray becomes vertically upwards?
A compound microscope having magnifying power 35 with its eye-piece of focal length 10 cm. Assume that the final image is at least distance of distinct vision then the magnification produced by the objective is
The refractive index for a prism is given as \( \mu = \cot \frac{A}{2} \). Then, angle of minimum deviation in terms of angle of prism is
Two convex lenses of power 2D and 5D are separated by a distance \( \frac{1}{3} \, m \). The power of optical system formed is
Two light rays having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path \( L_1 \) through a medium of refractive index \( \mu_1 \), while the second ray travels a path \( L_2 \) through a medium of refractive index \( \mu_2 \). The two waves are then combined to observe interference. The phase difference between the two waves is
Two polaroids are kept crossed to each other. If one of them is rotated an angle 60°, the percentage of incident light now transmitted through the system is
An electromagnetic wave propagating along north lies its electric field vertically upward. The magnetic field vector points towards
Pick out the wrong statement.
When sunlight is scattered by atmospheric atoms and molecules the amount of scattering of light of wavelength 880 nm is \( A \). Then, the amount of scattering of light of wavelength 330 nm is approximately
The rate of volume occupied by an atom to the volume of the nucleus is
When copper is treated with a certain concentration of nitric acid, nitric oxide and nitrogen dioxide are liberated in equal volumes according to the equation, \[ xCu + yHNO_3 \rightarrow Cu(NO_3)_2 + NO + NO_2 + H_2O \]
The coefficients of \( x \) and \( y \) are respectively
A saturated solution of \( H_2S \) in 0.1M HCl at 25°C contains \( S^{2-} \) ion concentration of \( 10^{-23} \, mol L^{-1} \). The solubility product of some sulfides are \( CuS = 10^{-44} \), \( FeS = 10^{-14} \), and \( MnS = 10^{-25} \). If 0.01M solution of these salts in 1M HCl are saturated with \( H_2S \), which of these will be precipitated?
Consider the water gas equilibrium reaction, \[ C(s) + H_2O(g) \rightleftharpoons CO(g) + H_2(g) \]
Which of the following statements is true at equilibrium?
The chemical composition of slag formed during the smelting process in the extraction of copper is
\( XCl_2 \) (excess) + \( YCl_2 \) \( \rightarrow XCl_4 + YI \)
Ore of \( Y \) formed is
For the given reaction, \[ H_2(g) + Cl_2(g) \rightleftharpoons 2HCl(aq) + 2ClT(aq); \, \Delta G = -262kJ \]
The value of free energy of formation (\( \Delta G_f \)) for the ion C\( T_1 \) is
The molarity of \( NO_3^- \) in the solution after 2L of 3M \( AgNO_3 \) is mixed with 3L of 1M BaCl2 is
Amongst \( NO_3^- \), \( SO_3^{2-} \), \( CO_3^{2-} \), \( SO_4^{2-} \) the non-planar species are
View Solution
This reaction involves the conversion of alcohols where the alcohol group is converted to \( CH_3OH \) and \( CH_2OH \) based on the reaction conditions. Quick Tip: The conversion of alcohols involves substitution or elimination reactions depending on the conditions of the reaction.
A certain metal when irradiated by light (\( r = 3.2 \times 10^{16} \, Hz \)) emits photoelectrons with twice kinetic energy as did photoelectrons when the same metal is irradiated by light (\( r = 2.0 \times 10^{16} \, Hz \)). The \( \nu \) of metal is
Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction, \[ C_6H_6(g) + 3H_2(g) \xrightarrow{Ni} C_6H_{12}(g) \]
A mixture of \( C_6H_6 \) and excess \( H_2 \) has a pressure of 60 mm of Hg in an unknown volume. After the gas had been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg in the same volume at the same temperature. The fraction of \( C_6H_6 \) (by volume) present in the original volume is
An alloy of copper, silver and gold is found to have copper atom constituting the ccp lattice. If silver atoms occupy the edge centres and gold atoms are present at body centres, the alloy has a formula
Given, \( \Delta G^\circ = -nFE_{cell} \) and \( \Delta G^\circ = -RT \ln K \). The value of \( n = 2 \) will be given by the slope of which line in the figure
The false statements among the following are
I. A primary carbocation is less stable than a tertiary carbocation.
II. A secondary propyl carbocation is less stable than allyl carbocation.
III. A tertiary free radical is more stable than a primary free radical.
IV. Isopropyl carbocation is more stable than ethyl carbocation.
A colourless water soluble solid \( A \) on heating gives equimolar quantities of \( B \) and \( C \). B gives dense white fumes with HCl and C does so with NH\(_3\). B gives brown precipitate with Nessler’s reagent and C gives white precipitate with nitrates of \( Ag^+ \), \( Pb^{2+} \) and Hg\(^{2+} \). A is
Caffeine has a molecular weight of 194.1 g/l. It contains 28.9% by mass of nitrogen, number of atoms of nitrogen in one molecule of caffeine is
A compound \( X \) on heating gives a colourless gas. The residue is dissolved in water to obtain \( Y \). Excess \( CO_2 \) is passed through aqueous solution of \( Y \) when \( Z \) is formed. \( Z \) on gentle heating gives back \( X \). The compound \( X \) is
Which two sets of reactants best represent the amphoteric character of \( Zn(OH)_2 \)?
Set I \( Zn(OH)_2(s) \) and \( OH^-(aq) \)
Set II \( Zn(OH)_2(s) \) and \( H_2O(l) \)
Set III \( Zn(OH)_2(s) \) and \( H^+(aq) \)
Set IV \( Zn(OH)_2(s) \) and \( NH_3(aq) \)
A and B respectively are
View Solution
The reaction described involves the reduction of nitrobenzene to aniline. Zinc dust is used to reduce the nitro group to an amine, resulting in the formation of aniline (\( NH_2 \)). Quick Tip: Reduction of nitro compounds to amines typically involves reducing agents like zinc dust or tin and HCl.
Point out incorrect stability order
Consider the following changes: \[ M(s) \xrightarrow{} M(g) \quad (1)
M(g) \xrightarrow{} M^{2+}(g) + 2e^- \quad (2)
M(g) \xrightarrow{} M^+(g) + e^- \quad (3)
M^+(g) \xrightarrow{} M^{2+}(g) + e^- \quad (4) \]
The second ionisation energy of \( M \) could be determined from the energy values associated with
In benzene, the triple bond consists of
In keto-enol tautomerism of dicarbonyl compounds, the enol-form is preferred in contrast to the keto-form, this is due to
An organic compound having carbon, hydrogen and sulphur contains 4% of sulphur. The minimum molecular weight of the compound is
Which one of the following is a case of negative adsorption?
The concentrations of the reactant A in the reaction \( A \rightarrow B \) at different times are given below
Concentration (M) \(\quad\) Time (Minutes) \[ 0.069 \quad 0 \quad 0.052 \quad 17 \quad 0.035 \quad 34 \quad 0.018 \quad 51 \]
The rate constant of the reaction according to the correct order of reaction is
The ratio of slopes of \( K_{max} \) vs \( V \) and \( V_0 \) vs \( v \) curves in the photoelectric effect gives
With excess of water, both \( P_2O_5 \) and \( PCl_5 \) give
The dissolution of \( Al(OH)_3 \) by a solution of NaOH results in the formation of
Which of the following does not exist?
If the ionisation energy and electron affinity of an element are 275 and 86 kcal/mol respectively, then the electronegativity of the element on the Mulliken scale is
For the preparation of paracetamol
A compound which gives a negative test with ninhydrin, it cannot be a protein or an amino acid. As, it gives a positive test with Benedict’s solution. The compound is
The compound used for making super glue or crazy glue is
\( X' \) and \( Y' \) respectively are
In the Cannizzaro reaction given below: \[ 2Ph - CHO \xrightarrow{NaOH} Ph - CH_2OH + Ph - CO_2 \]
the slowest step is
The reaction of 1-bromo-3-chlorocyclobutane with metallic sodium in dioxane under reflux conditions gives
Identify \( Z \) in the following reaction sequence \[ CH_3CH_2CH_2OH \xrightarrow{H_2SO_4, 160^\circ C} CH_3CH_2CH = CH_2 \xrightarrow{NaNH_2} Z \]
Which of the following reactions is used to prepare isobutane?
The differential equation \( (3x + 4y + 1) dx + (4x + 5y + 1) dy = 0 \) represents a family of
If \( \Delta r = \left| \sum_{r=1}^{n} r \right| \), then \( \sum_{r=1}^{n} \Delta r \) is equal to
If \( A, B, C \) are three events associated with a random experiment, then \( P(A \,|\, B) \) is
If \( A = \begin{pmatrix} 1 & 2
3 & 1 \end{pmatrix} \), then rank \( A \) is
The probability of getting a double six in one throw of two dice
The rate constant of the reaction \( A \rightarrow B \) at different times are given below: \[ Concentration (M) \quad Time (Minutes)
0.069 \quad 0 \quad 0.052 \quad 17 \quad 0.035 \quad 34 \quad 0.018 \quad 51 \]
The rate constant of the reaction according to the correct order of reaction is
If the complex number \( z \) lies on a circle with center at the origin and radius \( \frac{1}{4} \), then the complex number \( 1 + z \) lies on a circle with radius
If \( l = x^2 + y^2 + z^2 \) is a normal to the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1, \]
then
If \( line \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \]
then \( c^2 \) is equal to
Correct result is as follows: \[ P \, (\neg \, Q) \, \equiv (P \, \vee \, Q) \, \implies (P \, \vee \, Q) \, \implies \, R \, \implies \, S \]
The matrix \( A = \begin{pmatrix} 1 & 2
3 & 1 \end{pmatrix} \), then adj \( (A) \) is equal to
The correct result of the equation \( 3x^2 + 2x + 7y^2 - 14y + 4 \) is
The structure \( (N_3) \) satisfies the closure property, associativity and commutativity but the identity element 0 does not belong to \( N \).
The integral \( \int \frac{dx}{\cos x + \sqrt{5} \sin x} \) equals
If \( (2, 7, 3) \) is one end of a diameter of the sphere \( x^2 + y^2 + z^2 - 6x - 12y - 2z + 20 = 0 \), then the coordinates of the other end of the diameter are
Given lines are \[ x = my + n, \, z = py + q \]
and \[ x = m'y + n', \, z = p'y + q' \]
Above equations can be rewritten as \[ x - n' = p', \quad m = 1, \, p = 1 \]
Lines will be perpendicular if
A tetrahedron has vertices at \( O(0, 0, 0) \), \( A(1, -2, 1) \), \( B(2, 1, 1) \), and \( C(1, -1, 2) \). Then, the angle between the faces \( OAB \) and \( ABC \) is
If a line segment OP makes angles of \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with the X-axis and Y-axis, respectively, then the direction cosines are
If \( p, q \) are simple propositions with truth values \( T, F \), then the truth value of \( (\neg p \vee q) \wedge \neg r \) is
Let \( f(x) = 25x^{24}(1 - x)^{75} \), on the interval \( [0, 1] \), then \[ f'(x) = 25x^{24}(1 - x)^{75} - 75x^{25}(1 - x)^{74} = 25x^{24}(1 - x)^{74}[(1 - x) - 3x] \]
If \( |z| \geq 3 \), then the least value of \( |z + 4| \) is
The normal at the point \( (a t^2, 2 a t) \) on the parabola meets the parabola again at the point \( (a t^2, 2 a t) \). The equation of the normal is
If \( a = i - j + 2k \) and \( b = 2i - j + k \), then the angle \( \theta \) between \( a \) and \( b \) is given by
The area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{\pi}{2} \) is
If \( a, b, c \) are three non-coplanar vectors, then \[ (a + b) \times (c + b) = (a - b) \times (c - b) = b \times c \]
If there is an error of \( m% \) in measuring the edge of a cube, then the percent error in estimating its surface area is
The given equation of rectangular hyperbola is \[ x^2 - y^2 = 6^2 \quad (length of latus rectum is 16) \]
The asymptotes are parallel to each other
The equation of tangents to the hyperbola \( 3x^2 - 2y^2 = 6 \) which is perpendicular to the line \( x - 3y = 3 \) is
The limit of \( \int \frac{1}{\cos x} dx \) as \( b \to 0 \) is
The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is
For any three vectors \( a, b, c \), \[ [a + b + c] = [a b c] = [a b c] \]
Let \( I = \int_{0}^{\frac{\pi}{2}} \log (\cos x) \, dx \)
If the mean and variance of a binomial distribution are 4 and 2, respectively. Then, the probability of at least 7 successes is
The shortest distance between the lines \[ \frac{x - 7}{3} = \frac{y + 4}{-16} = \frac{z - 6}{7} \]
and \[ \frac{x - 10}{3} = \frac{y - 30}{8} = \frac{z - 6}{5} \]
is
If a plane passing through the point \( (2, 2, 1) \) and is perpendicular to the planes \( 3x + 2y + 4z = 10 \) and \( 2x + y + 3z = 2 \), then the equation of the plane is
From a city population, the probability of selecting a male or smoker is \( \frac{7}{10} \), a male smoker is \( \frac{2}{5} \) and a male, if a smoker is already selected, is \( \frac{3}{5} \). Then, the probability of
At \( t = 0 \), the function \( f(t) = \sin \frac{t}{t} \) has
Using Rolle’s theorem, the equation \( a_0x^n + a_1x^{n-1} + \dots + a_n = 0 \) has at least one root between 0 and 1 if,
Which of the following inequality is true for \( x > 0 \)?
The solution of \( \frac{d^2x}{dy^2} = k \), where \( k \) is a non-zero constant, vanishes when \( y = 0 \) and tends to finite limit as \( y \to \infty \), is
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