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JEE Main 2022 28 Jul Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202228 Jul, Morning shift

Physics 23Chemistry 22Mathematics 30

Physics

Q55The frequencies at which the current amplitude in an LCR series circuit becomes 1/(√(2)) times its maximum value, are 212 rad s⁻¹ and 232 rad s⁻¹. The value…Electromagnetic Induction and Alternating Currents
Q57A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after…Atoms and Nuclei
Q63Two electric dipoles of dipole moments 1.2 × 10⁻³⁰ Cm and 2.4 × 10⁻³⁰ Cm are placed in two different uniform electric fields of strengths 5 × 10⁴ NC⁻¹ and 15…Electrostatics
Q70The diameter of an air bubble which was initially 2 ~mm, rises steadily through a solution of density 1750 ~kg ~m⁻³ at the rate of 0.35 cms⁻¹. The coefficient…Properties of Solids and Liquids
Q73If the projection of 2 i+4 j-2 k on i+2 j+α k is zero. Then, the value of α will be _ _ _ _ _ _.Kinematics
Q74In a Young's double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes' separation of 7.2 mm. Now…Optics
Q76The frequency of echo will be _ _ _ _ _ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which…Oscillations and Waves
Q5911The equation of current in a purely inductive circuit is 5 sin (49 π t-30^(°)). If the inductance is 30 mH then the equation for the voltage across the…Electromagnetic Induction and Alternating Currents
Q6124The half life period of a radioactive substance is 60 days. The time taken for 7/8 th of its original mass to disintegrate will be:Atoms and Nuclei
Q6159Two capacitors, each having capacitance 40 μ F are connected in series. The space between one of the capacitors is filled with dielectric material of…Electrostatics
Q6246In two different experiments, an object of mass 5 ~kg moving with a speed of 25 ~ms⁻¹ hits two different walls and comes to rest within (i) 3 second, (ii) 5…Rotational Motion
Q6365In the case of amplitude modulation to avoid distortion the modulation index (μ) should be:Communication Systems
Q6518A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:Current Electricity
Q6576The equation λ=1.227/x ~nm can be used to find the de-Brogli wavelength of an electron. In this equation x stands for: Where m= mass of electron P= momentum…Dual Nature of Matter and Radiation
Q7070In normal adujstment, for a refracting telescope, the distance between objective and eye piece is 30 ~cm. The focal length of the objective, when the angular…Optics
Q7153If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately:Gravitation
Q7406Given below are two statements: Statement I: The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II: The rms…Kinetic Theory of Gases
Q7771The current sensitivity of a galvanometer can be increased by: (A) decreasing the number of turns (B) increasing the magnetic field (C) decreasing the area of…Magnetic Effects of Current and Magnetism
Q7866A NCC parade is going at a uniform speed of 9 ~km / h under a mango tree on which a monkey is sitting at a height of 19.6 ~m. At any particular instant, the…Kinematics
Q7915A balloon has mass of 10 ~g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 ~cm / s. If the balloon shrinks in 5 ~s completely…Properties of Solids and Liquids
Q7951The force required to stretch a wire of cross-section 1 ~cm² to double its length will be: (Given Yong's modulus of the wire =2 × 10¹¹ ~N / m²)Properties of Solids and Liquids
Q8261The dimensions of ((B²)/(μ₀)) will be: (if μ₀: permeability of free space and B: magnetic field)Units and Measurements
Q8508In the wave equation y=0.5 sin (2 π)/(λ)(400 t-x) m the velocity of the wave will be:Oscillations and Waves

Chemistry

Q1The number of interhalogens from the following having square pyramidal structure is: ClF₃, IF₇, BrF₅, BrF₃, I₂ Cl₆, IF₅, ClF, ClF₅Chemical Bonding and Molecular Structure
Q2The number of paramagnetic species among the following is _ _ _ _ _ _. B₂, Li₂, C₂, C₂⁻, O₂²⁻, O₂⁺ and He₂⁺Chemical Bonding and Molecular Structure
Q4For the given first order reaction A → B the half life of the reaction is 0.3010 ~min. The ratio of the initial concentration of reactant to the concentration…Chemical Kinetics
Q5Total number of relatively more stable isomer(s) possible for octahedral complex [Cu(en)₂(SCN)₂] will be _ _ _ _ _.Coordination Compounds
Q7The disproportionation of MnO₄²⁻ in acidic medium resulted in the formation of two manganese compounds A and B. If the oxidation state of Mn in B is smaller…d- and f-Block Elements
Q12K a for butyric acid (C₃ H₇ COOH) is 2 × 10⁻⁵. The pH of 0.2 M solution of butyric acid is _ _ _ _ _ × 10⁻¹. (Nearest integer) [Given log 2=0.30 ]Equilibrium
Q17An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 ~g ~cm⁻³. The number of atoms…Solid State
Q18150 ~g of acetic acid was contaminated with 10.2 ~g ascorbic acid (C₆ H₈ O₆) to lower down its freezing point by (x × 10⁻¹)^(°) C. The value of x is _ _ _ _ _…Solutions
Q19In the given reaction, X+Y+3 Z X YZ₃ if one mole of each of X and Y with 0.05 ~mol of Z gives compound X Y Z₃. (Given: Atomic masses of X, Y and Z are 10, 20…Some Basic Concepts in Chemistry
Q20On complete combustion of 0.492 ~g of an organic compound containing C, H and O, 0.7938 ~g of CO₂ and 0.4428 ~g of H₂ O was produced. The% composition of…Some Basic Concepts in Chemistry
Q454For kinetic study of the reaction of iodide ion with H₂ O₂ at room temperature: (A) Always use freshly prepared starch solution. (B) Always keep the…Chemical Kinetics
Q778Match List - I with List - II, match the gas evolved during each reaction. List - I List - II (A) (NH₄)₂ Cr₂ O₇ Δ (I) H₂ (B) KMnO₄+HCl → (II) N₂ (C)…d- and f-Block Elements
Q887Which of the following has least tendency to liberate H₂ from mineral acids?d- and f-Block Elements
Q917Match List - I with List - II. List - I List - II (A) Cd(s) + 2Ni (OH)₃ (s) → CdO(s) + 2Ni (OH)₂ (s) + H₂O(l) (I) Primary battery (B) Zn(Hg) + HgO(s) → ZnO(s)…Redox Reactions and Electrochemistry
Q1100Given below are two statements: Statement I: In polluted water values of both dissolved oxygen and BOD are very low. Statement II: Eutrophication results in…Environmental Chemistry
Q1202The metal salts formed during softening of hardwater using Clark's method are:Hydrogen
Q1360Which of the reaction is suitable for concentrating ore by leaching process ?Isolation of Elements
Q1579In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or identical? (A) Rb and Cs (B) Na and K (C) Ar and Kr…Classification of Elements and Periodicity in Properties
Q1861Which of the following statement is incorrect?S Block Elements
Q2124Identify the incorrect statement from the following.Atomic Structure
Q2226Match List - I with List - II. List - I Reaction List - II Catalyst (A) 4N H₃ (g) + 5O₂(g) → 4NO(g) + 6H₂O(g) (I) NO(g) (B) N₂(g) + 3H₂(g) → 2N H₃ (g) (II)…Surface Chemistry
Q2329Which of the following relation is not correct?Chemical Thermodynamics

Mathematics

Q24Let P(-2,-1,1) and Q(56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are α,-1, β, where both α and β are…Three Dimensional Geometry
Q32If ∫₀^(√(3)) (15 x³)/(√(1+x²+√((1+x²)³))) ~d x=α √(2)+β √(3), where α, β are integers, then α+β is equal to _ _ _ _ _.Integral Calculus
Q36For p, q R, consider the real valued function f(x)=(x-p)²-q, x R and q>0. Let a₁, a 2^() a₃ and a₄ be in an arithmetic progression with mean p and positive…Sets, Relations and Functions
Q37For the hyperbola H: x²-y²=1 and the ellipse E: (x²)/(a²)+(y²)/(~b²)=1, a >b>0, let the (1) eccentricity of E be reciprocal of the eccentricity of H, and (2)…Coordinate Geometry
Q40Let f:[0,1] → R be a twice differentiable function in (0,1) such that f(0)=3 and f(1)=5. If the line y=2 x+3 intersects the graph of f at only two distinct…Limit, Continuity and Differentiability
Q41lim x → 0 (((x+2 cos x)³+2(x+2 cos x)²+3 sin (x+2 cos x))/((x+2)³+2(x+2)²+3 sin (x+2)))^(100/x) is equal to _ _ _ _ _ _.Limit, Continuity and Differentiability
Q43Let A=[ cc1 -1 2 α ] and B=[ ccβ 1 1 0 ], α, β R. Let α₁ be the value of α which satisfies (A+B)²=A²+[ ll2 2 2 2 ] and α₂ be the value of α which satisfies…Matrices and Determinants
Q46Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from, B, C, D, E or a number from…Permutations and Combinations
Q48The sum of all real values of x for which (3 x²-9 x+17)/(x²+3 x+10)=(5 x²-7 x+19)/(3 x²+5 x+12) is equal to _ _ _ _ _.Complex Numbers and Quadratic Equations
Q51Let x₁, x₂, x₃,, x₂₀ be in geometric progression with x₁=3 and the common ratio 1/2. A new data is constructed replacing each x i by (x i -i)². If x is the…Statistics and Probability
Q2598The foot of the perpendicular from a point on the circle x²+y²=1, z=0 to the plane 2 x+3 y+z=6 lies on which one of the following curves?Three Dimensional Geometry
Q2671If the minimum value of f(x)=(5 x²)/2+(α)/(x⁵), x>0, is 14, then the value of α is equal to:Limit, Continuity and Differentiability
Q2898The remainder when 7²⁰²²+3²⁰²² is divided by 5 is:Binomial Theorem and Its Simple Applications
Q3059Let C be the centre of the circle x²+y²-x+2 y=11/4 and P be a point on the circle. A line passes through the point C, makes an angle of (π)/4 with the line CP…Coordinate Geometry
Q3113For t (0,2 π), if ABC is an equilateral triangle with vertices A(sin t,- cos t), B(cost, sin t) and C(a, b) such that its orthocentre lies on a circle with…Coordinate Geometry
Q3266Let S₁= ₁ C:|z₁-3|=1/2 and S₂= ₂ C:|z₂-| z₂+1||=|z₂+| z₂-1||. Then, for z₁ S₁ and z₂ S₂, the least value of |z₂-z₁| is:Complex Numbers and Quadratic Equations
Q3317The minimum value of the twice differentiable function f(x)=∫₀ˣ e^(x-t) f^()(t) dt-(x²-x+1) eˣ, x R, is:Integral Calculus
Q3628Let the solution curve of the differential equation x ~d y=(√(x²+y²)+y) d x, x>0, intersect the line x=1 at y=0 and the line x=2 at y=α. Then the value of α is:Differential Equations
Q3629If y=y(x), x (0, π / 2) be the solution curve of the differential equation (sin ² 2 x) (d y)/(d x)+(8 sin ² 2 x+2 sin 4 x) y=2 e⁻⁴ˣ(2 sin 2 x+ cos 2 x), with…Differential Equations
Q3830Let α, β and γ be three positive real numbers. Let f(x)=α x⁵+β x³+γ x, x R and g: R → R be such that g(f(x))=x for all x R. If a₁, a₂, a₃,, a n be in…Sets, Relations and Functions
Q4077Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x)= cos ⁻¹((x²-4 x+2)/(x²+3)) is:Trigonometry
Q4078Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos ⁻¹(x)-2 sin ⁻¹(x)= cos ⁻¹(2 x) is…Trigonometry
Q4375Let the operations, wedge,. If (p q) (p q) is a tautology, then the ordered pair (,) is:Mathematical Reasoning
Q4536Let the matrix A=[ lll0 1 0 0 0 1 1 0 0 ] and the matrix B₀=A⁴⁹+2 A⁹⁸. If B n =A d j(B n-1) for all n ≥ 1, then det(B₄) is equal to:Matrices and Determinants
Q4753If the tangents drawn at the points P and Q on the parabola y²=2 x-3 intersect at the point R(0,1), then the orthocentre of the triangle P Q R is:Coordinate Geometry
Q4964Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is twice the number of…Statistics and Probability
Q5337Consider the sequence a₁, a₂, a₃, such that a₁=1, a₂=2 and a n+2 =2/(a n+1)+a n for n=1,2,3,. If ((a₁+1/(a₂))/(a₃)) ·((a₂+1/(a₃))/(a₄)) ·((a₃+1/(a₄))/(a₅))…Sequence and Series
Q5383For α N, consider a relation R on N given by R=\(x, y): 3 x+α y is a multiple of 7. The relation R is an equivalence relation if and only if:Sets, Relations and Functions
Q5696Let the vectors a=(1+t) i+(1-t) j+k, b=(1-t) i+(1+t) j+2 k and c=t i-t j+k, t R be such that for α, β, γ R, α a+β b+γ c=0 ⇒ α=β=γ=0. Then, the set of all…Vector Algebra
Q5828Let a vector a has magnitude 9. Let a vector b be such that for every (x, y) R × R-\(0,0), the vector (x a+y b) is perpendicular to the vector (6 y a-18 x b)…Vector Algebra