VITEEE 2021 Question Paper is available for download here. VITEEE 2021 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 2021 Question Paper with Solution PDF using the link below.
VITEEE 2021 Question Paper with Solution PDF
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The distance of the centres of moon and earth is \( D \). The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero?
Two wires A and B are of the same material. Their lengths are in the ratio \( 1:2 \) and the diameter is in the ratio \( 2:1 \). If they are pulled by the same force, then increase in length will be in the ratio of
If \( x = at + bt^2 \), where \( x \) is the distance travelled by the body in kilometers while \( t \) is the time in seconds, then the unit of \( b \) is
A soap bubble of radius \( r_1 \) is placed on another soap bubble of radius \( r_2 \) (\( r_1 < r_2 \)). The radius \( R \) of the soapy film separating the two bubbles is
A charge \( q \) is moving with a velocity \( v \) parallel to a magnetic field \( B \). Force on the charge due to magnetic field is
Two spheres A and B of masses \( m \) and \( 2m \) and radii \( R \) and \( 2R \) respectively are placed in contact as shown. The COM of the system lies
Identify the correct statement.
The distance travelled by a particle starting from rest and moving with an acceleration \(3 \, m/s^2\) in the third second is:
Photocathode work function is \( 1 \, eV \). Light of wavelength \( \lambda = 3000 \, Å \) falls on it. The photoelectron comes out with a maximum velocity of \( 1 \times 10^6 \, m/s \). What is the energy of the photon?
A steam engine operating between \( 100^\circ C \) and \( 40^\circ C \) has an efficiency of \( 25% \). The heat absorbed by the engine is:
Two point charges \( +q \) and \( -q \) are placed at a distance \( d \) apart. The electric potential at the midpoint will be
Two bodies of the same mass are projected with the same velocity at an angle \( 30^\circ \) and \( 60^\circ \) respectively. The ratio of their horizontal ranges will be:
Two point charges \( +3 \, \mu C \) and \( +8 \, \mu C \) repel each other with a force of 40 N. If a charge of \( -5 \, \mu C \) is added to each of them, then the force between them will become:
A sphere rolls down an inclined plane of inclination \( \theta \). What is the acceleration as the sphere reaches the bottom?
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and same material such that P, Q, and R are now combined as shown in figure. The ray will now suffer
The root mean square velocity of hydrogen molecules at 300 K is 1930 meters/second. The velocity of oxygen molecules at 1200 K will be:
A magnetic field of 5 T is applied perpendicular to a coil with 5 turns. The induced emf in the coil is 10 V. The rate of change of magnetic flux is:
A parallel plate capacitor with air between the plates has a capacitance of 3 μF. Calculate the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant \( k \).
A body executing SHM has displacement \( y = A \cos \omega t \). Identify the graph which represents the variation of potential energy (PE) as a function of time \( t \) and displacement.
A radioactive sample contains 5 × 10\(^7\) kg of each of two isotopes A and B with half-lives of 5 days and 8 days respectively. The fraction of A that decays in 3 days after a period of 3 days is:
A string of length 3 m and mass 0.035 kg is stretched with a tension of 50 N. The speed of the wave on the string is:
A particle of mass 10 kg is moving with a velocity of 5 m/s. The kinetic energy of the particle is:
A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity of 17 m/s. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air = 340 m/s):
Consider the following reactions: \[ NaCl + K_2Cr_2O_7 + H_2SO_4 (Conc.) \rightarrow (A) + Side products \] \[ (B) + H_2SO_4 (dilute) + H_2O_2 \rightarrow (C) + Side products \]
The sum of the total number of atoms in one molecule each of (A), (B) and (C) is __________.
Xenon hexafluoride on partial hydrolysis produces compounds 'X' and 'Y'. Compounds 'X', 'Y' and the oxidation state of Xe are respectively:
The edge length of unit cell of a metal having molecular weight 75 g/mol is 5 Å which crystallizes in cubic lattice. If the density is 2 g/cc, then find the radius of the metal atom. (\( N_A = 6 \times 10^{23} \)) Give the answer in pm.
Consider the following statements:
I. Increase in concentration of reactant increases the rate of a zero order reaction.
II. Rate constant \( k \) is equal to collision frequency if \( E_a = 0 \).
III. Rate constant \( k \) is equal to collision frequency if \( E_a = \infty \).
IV. \( \ln k \) vs \( T \) is a straight line.
V. \( 1/T \) vs \( \ln k \) is a straight line.
Correct statements are:
To deposit 0.634 g of copper by electrolysis of aqueous cupric sulphate solution, the amount of electricity required (in coulombs) is:
In the following skew conformation of ethane, the \( H' - C - C - H'' \) dihedral angle is:
What is the product of the following reaction?
Hex-3-ynal + (i) NaBH\(_4\), (ii) Pb\(_3\), (iii) Mg/ether, (iv) CO\(_2\)/H\(_2\)O → ?
In the following sequence of reactions, \[ CH_3CH_2OH \xrightarrow{P_1,2} A \xrightarrow{Mg/ether} B \xrightarrow{HCHO} C \xrightarrow{H_2O} D \]
The compound D is:
Which of the following reactions can produce aniline as the main product?
Secondary structure of protein refers to:
The increasing order for the values of e/m (charge/mass) is:
In which of the following pairs both the ions are coloured in aqueous solutions?
The total number of possible isomers for square-planar \( [Pt(Cl)(NO_2)(NO_3)(SCN)]^{2-} \) is:
For the reaction, \[ 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g), \] \[ \Delta H = -57.2 \, kJ/mol \quad and \quad K_c = 1.7 \times 10^{16} \]
Which of the following statement is INCORRECT?
The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is:
A galvanic cell is set up from electrodes A and B
Electrode A: \( Cr_2O_7^{2-} / Cr^{3+}, \, E^\circ_{red} = +1.33 \, V \)
Electrode B: \( Fe^{3+} / Fe^{2+}, \, E^\circ_{red} = +0.77 \, V \)
Which of the following statements is false?
Keto-enol tautomerism is observed in:
In a set of reactions, ethylbenzene yields a product D. \[ CH_3C_6H_5 \xrightarrow{KMnO_4} Br_2 \xrightarrow{FeCl_3} C_6H_5COOH \xrightarrow{H_2O} D \]
Identify D:
What will be the final product in the following reaction sequence: \[ CH_3CH_2CN \xrightarrow{H^+ / H_2O} A \xrightarrow{NH_3} B \xrightarrow{NaOBR} C \]
In a set of reactions, acetic acid yields a product D: \[ CH_3COOH \xrightarrow{SOCl_2} Benzene \xrightarrow{AlCl_3} (B) \] \[ HCN \xrightarrow{(C)} HOH \xrightarrow{H_2O} (D) \]
The structure of \( D \) would be:
In fructose, the possible optical isomers are:
The position of both, an electron and a helium atom is known within 1.0 nm. Further the momentum of the electron is known within \( 5.0 \times 10^{-26} \, kg \, ms^{-1} \). The minimum uncertainty in the measurement of the momentum of the helium atom is:
The value of \( \log_{10} K \) for a reaction \( A \rightleftharpoons B \) is
(Given: \( \Delta H^\circ_{298K} = -54.07 \, kJ mol^{-1} \), \( \Delta S^\circ_{298K} = 10 \, JK^{-1} \, mol^{-1} \) and \( R = 8.314 \, JK^{-1} \, mol^{-1} \)) \[ 2.303 \times 8.314 \times 298 = 5705 \] \[ (a) 5 \quad (b) 10 \quad (c) 95 \quad (d) 100 \]
If \( C(s) + O_2(g) \rightleftharpoons CO_2(g) \), \( \Delta H = R \) and \[ CO(g) + \frac{1}{2} O_2(g) \rightleftharpoons CO_2(g), \quad \Delta H = S \]
then heat of formation of CO is:
Which of the following compounds does not follow Markovnikov's law?
The value of \( c \) in Rolle’s Theorem for the function \( f(x) = e^x \sin x, x \in [0, \pi] \) is:
The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:
The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) is:
If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:
If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)
Radius of the circle \( (x + 5)^2 + (y - 3)^2 = 36 \) is:
If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:
If \( (-4, 5) \) is one vertex and \( 7x - y + 8 = 0 \) is one diagonal of a square, then the equation of second diagonal is:
\( P = Q \) can also be written as:
Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \]
then
Which of the following is an infinite set?
The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \]
is:
Area bounded by the curve \( y = \log x \) and the coordinate axes is:
The angle of intersection of the curve \( y = x^2 \), \( dy = 7 - x^2 \) at \( (1, 1) \) is:
The angle formed by the positive Y-axis and the tangent to \( y = x^2 + 4x - 17 \) at \( (2, -3) \) is:
The value of \( (1 + i)^4 \) is:
The relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5\} \) by \( R = \{(x, y) : |x^2 - y^2| < 16 \} \) is given by:
\[ \int \frac{2dx}{(e^x + e^{-x})^2} = ? \]
The value of \( \tan^{-1} (1) + \tan^{-1} (0) + \tan^{-1} (2) + \tan^{-1} (3) \) is equal to:
In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000 if the rate of growth of bacteria is proportional to the number present?
What is the angle between the two straight lines \[ y = (2 - \sqrt{3})x + 5 \quad and \quad y = (2 + \sqrt{3})x - 7? \]
If the angle \( \theta \) between the line \[ \frac{x + 1}{2} = \frac{z - 2}{2} = \frac{y + 4}{\sqrt{n}} \]
and the plane \( 2x - y + z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( n \) is:
The distance of the point \( (-5, -5, -10) \) from the point of intersection of the line \[ r = -2i - j + 2k + \lambda(3i + 4j + 2k) \]
and the plane \( r \cdot (i - j + k) = 5 \) is:
\[ \int_{\log \sqrt{n}}^{\log \sqrt{r}} 2x \sec^2\left( \frac{1}{3} \cdot 2x \right) \, dx \]
is equal to:
If \( |x + 3| + x > 1 \), then \( x \in \):
Potential F.A.S.T. members can attend less than half of F.A.S.T. drills if they:
Which of the following is the main subject of the passage?
Applicants must be available for training:
Jatin starting from a fixed point, goes 15 m towards North and then after turning to his right, he goes 15 m. Then, he goes 10 m, 15 m and 15 m after turning to his left each time. How far is he from his starting point?
Examine the following statements:
1. All members of Mohan’s family are honest.
2. Some members of Mohan’s family are not employed.
3. Some employed persons are not honest.
4. Some honest persons are not employed.
Which one of the following inferences can be drawn from the above statements?
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