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JEE Main 2022 26 Jul Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 202226 Jul, Morning shift

Physics 22Chemistry 21Mathematics 29

Physics

Q52In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be "a λ '' between the wavelength of…Atoms and Nuclei
Q65If the initial velocity in horizontal direction of a projectile is unit vector i and the equation of trajectory is y=5 x(1-x). The y component vector of the…Kinematics
Q66In an experiment to determine the Young's modulus of wire of a length exactly 1 ~m, the extension in the length of the wire is measured as 0.4 ~mm with an…Properties of Solids and Liquids
Q68A disc of mass 1 ~kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same…Rotational Motion
Q72When a car is approaching the observer, the frequency of horn is 100 ~Hz. After passing the observer, it is 50 ~Hz. If the observer moves with the car, the…Oscillations and Waves
Q5908In a series L R circuit X L =R and power factor of the circuit is P₁. When capacitor with capacitance C such that X L =X C is put in series, the power factor…Electromagnetic Induction and Alternating Currents
Q6120The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250…Atoms and Nuclei
Q6172The total charge on the system of capacitors C₁=1 μ F, C₂=2 μ F, C₃=4 μ F and C₄=3 μ F connected in parallel is: (Assume a battery of 20 ~V is connected to…Electrostatics
Q6363A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be:Communication Systems
Q6604A parallel beam of light of wavelength 900 ~nm and intensity 100 Wm⁻² is incident on a surface perpendicular to the beam. The number of photons crossing 1…Dual Nature of Matter and Radiation
Q6796The magnetic field of a plane electromagnetic wave is given by: B=2 × 10⁻⁸ sin (0.5 × 10³ x+1.5 × 10¹¹ t) j ~T. The amplitude of the electric field would be:Electromagnetic Waves
Q7152The percentage decrease in the weight of a rocket, when taken to a height of 32 ~km above the surface of earth will, be: (Radius of earth =6400 ~km)Gravitation
Q74047 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 ~K at constant pressure. The increase in the internal energy of the gas in this…Thermodynamics
Q7492A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:Thermodynamics
Q7593A monkey of mass 50 ~kg climbs on a rope which can withstand the tension (T) of 350 ~N. If monkey initially climbs down with an acceleration of 4 ~m / s² and…Laws of Motion
Q7689B X and B Y are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 ~cm radius and…Magnetic Effects of Current and Magnetism
Q7712A charge particle is moving in a uniform magnetic field (2 i+3 j) T. If it has an acceleration of (α i-4 j) m / s², then the value of α will be:Magnetic Effects of Current and Magnetism
Q7795Two projectiles thrown at 30^(°) and 45^(°) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is:Kinematics
Q8020A water drop of radius 1 ~cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/ cm, then the gain in surface energy upto first decimal…Properties of Solids and Liquids
Q8168When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be:Oscillations and Waves
Q8338A screw gauge of pitch 0.5 ~mm is used to measure the diameter of uniform wire of length 6.8 ~cm, the main scale reading is 1.5 ~mm and circular scale reading…Experimental Skills
Q8447In Young's double slit experiment, the fringe width is 12 ~mm. If the entire arrangement is placed in water of refractive index 4/3, then the fringe width…Optics

Chemistry

Q4At 298 ~K, the equilibrium constant is 2 × 10¹⁵ for the reaction: Cu(s)+2 Ag⁺(aq) Cu²⁺(aq)+2 Ag(s) The equilibrium constant for the reaction 1/2…Equilibrium
Q5For a reaction A → 2 ~B+C the half lives are 100 ~s and 50 ~s when the concentration of reactant A is 0.5 and 1.0 ~mol ~L⁻¹ respectively. The order of the…Chemical Kinetics
Q7The difference between spin only magnetic moment values of [Co(H₂ O)₆]Cl₂ and [Cr(H₂ O)₆] Cl₃ is _ _ _ _ _ _.Coordination Compounds
Q9The amount of charge in F (Faraday) required to obtain one mole of iron from Fe₃ O₄ is _ _ _ _ _ _. (Nearest Integer)Redox Reactions and Electrochemistry
Q10A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is bar. (Nearest Integer)Gaseous State
Q11In the presence of sunlight, benzene reacts with Cl₂ to give product, X. The number of hydrogens in X is _ _ _ _ _ _ _.Organic Compounds Containing Halogens
Q18Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 ~L solution of Mg of concentration 48 ppm. The number of atoms of Mg in…Some Basic Concepts in Chemistry
Q19When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of nitric acid is evaporated. The molarity of the remaining…Some Basic Concepts in Chemistry
Q20The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is _ _ _ _…Atomic Structure
Q212.4 ~g coal is burnt in a bomb calorimeter in excess of oxygen at 298 ~K and 1 ~atm pressure. The temperature of the calorimeter rises from 298 ~K to 300 ~K…Chemical Thermodynamics
Q28The difference in the reaction of phenol with bromine in chloroform and bromine in water medium is due to:Organic Compounds Containing Oxygen
Q134Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p -nitrophenol and picric acid ?Some Basic Principles of Organic Chemistry
Q312Match List-I with List-II: List I (Compound) List II (Shape) (A) BrF ₅ (I) bent (B) [CrF ₆ ] ³⁻ (II) square pyramidal (C) O ₃ (III) trigonal bipyramidal (D)…Chemical Bonding and Molecular Structure
Q541Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Experimental reaction of CH₃ Cl with…Organic Compounds Containing Nitrogen
Q774The dark purple colour of KMnO₄ disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the…d- and f-Block Elements
Q1181Cl +CH₄ → A+B A and B in the above atmospheric reaction step are:Hydrocarbons
Q1229Which of the following can be used to prevent the decomposition of H₂ O₂ ?Hydrogen
Q1401Refining using liquation method is the most suitable for metals with:Isolation of Elements
Q1494Match List - I with List - II. List I (Processes / Reactions) List II (Catalyst) (A) 2SO ₂ (g) + O ₂ (g) → 2SO ₃ (g) (I) Fe(s) (B) 4NH ₃ (g) + 5O ₂ (g) →…p-Block Elements
Q1563Given two statements below: Statement I: In Cl₂ molecule the covalent radius is double of the atomic radius of chlorine. Statement II: Radius of anionic…Classification of Elements and Periodicity in Properties
Q1817Which of the given reactions is not an example of disproportionation reaction?Redox Reactions and Electrochemistry

Mathematics

Q23Let Q and R be two points on the line (x+1)/2=(y+2)/3=(z-1)/2 at a distance √(26) from the point P(4,2,7). Then the square of the area of the triangle P Q R…Three Dimensional Geometry
Q24Let the function f(x)=2 x²- log e x, x>0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y²=4 a x at a point P on it passes…Limit, Continuity and Differentiability
Q26If the coefficients of x and x² in the expansion of (1+x)^(p)(1-x)^(q), p, q ≤ 15, are -3 and -5 respectively, then the coefficient of x³ is equal to _ _ _ _…Binomial Theorem and Its Simple Applications
Q29If n(2 n+1) ∫₀¹(1-xⁿ)²ⁿ d x=1177 ∫₀¹(1-xⁿ)²ⁿ⁺¹ ~d x, then n N is equal to _ _ _ _ _ _ _.Integral Calculus
Q30Let a curve y=y(x) pass through the point (3,3) and the area of the region under this curve, above the x -axis and between the abscissae 3 and x(>3) be…Differential Equations
Q41The number of 5-digit natural numbers, such that the product of their digits is 36, is _ _ _ _ _.Permutations and Combinations
Q44If for some p, q, r R, not all have same sign, one of the roots of the equation (p²+q²) x²-2 q(p+r) x+q²+r²=0 is also a root of the equation x²+2 x-8=0, then…Complex Numbers and Quadratic Equations
Q45The number of distinct real roots of the equation x⁵(x³-x²-x+1)+x(3 x³-4 x²-2 x+4)-1=0 is _ _ _ _ _ _ _.Complex Numbers and Quadratic Equations
Q47The series of positive multiples of 3 is divided into sets: \3 \6,9,12 \15,18,21,24,27 Then the sum of the elements in the 11^(th) set is equal to _ _ _ _ _ _.Sequence and Series
Q48The equations of the sides AB, BC and CA of a triangle ABC are 2 x+y=0, x+p y=15 a and x-y=3 respectively. If its orthocentre is (2, a),-1/2<a<2, then p is…Coordinate Geometry
Q2506The length of the perpendicular from the point (1,-2,5) on the line passing through (1,2,4) and parallel to the line x+y-z=0=x-2 y+3 z-5 is:Three Dimensional Geometry
Q2846The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y^(a) is 364/3, is equal to:Integral Calculus
Q3194Let O be the origin and A be the point z₁ = 1 + 2i. If B is the point z₂, Re (z₂) < 0, such that OAB is a right angled isosceles triangle with OB as…Complex Numbers and Quadratic Equations
Q3294If a = lim n → ∞ Σ k = 1 ⁿ 2n/(n² + k²) and f(x) = √((1 - cos x)/(1 + cos x)), x (0,1), then:Integral Calculus
Q3547If dy/dx + 2y tan x = sin x, 0 < x < (π)/2 and y((π)/3) = 0, then the maximum value of y(x) is:Differential Equations
Q3955Let the tangent drawn to the parabola y²=24 x at the point (α, β) is perpendicular to the line 2 x+2 y=5. Then the normal to the hyperbola…Coordinate Geometry
Q4111tan (2 tan ⁻¹ 1/5+ sec ⁻¹ (√(5))/2+2 tan ⁻¹ 1/8) is equal to:Trigonometry
Q4153Let f: R → R be a continuous function such that f(3x) - f(x) = x. If f(8) = 7, then f(14) is equal to:Limit, Continuity and Differentiability
Q4154If f(x) = \ x + a, x ≤ 0 |x - 4|, x > 0. and g(x) = \ x + 1, x < 0 (x - 4)² + b, x ≥ 0. are continuous on R, then (gof)(2) + (fog)(- 2) is equal to:Limit, Continuity and Differentiability
Q4155Let f(x) = \ x³ - x² + 10x - 7, x ≤ 1 - 2x + log ₂(b² - 4), x > 1.. Then the set of all values of b, for which f(x) has maximum value at x = 1, is:Limit, Continuity and Differentiability
Q4262If the function f(x) = \ (log e (1 - x + x²) + log e (1 + x + x²))/(sec x - cos x), x ((- π)/2,(π)/2) - 0 k, x = 0. is continuous at x = 0, then k is equal to:Limit, Continuity and Differentiability
Q4371The statement ((p q)) q is:Mathematical Reasoning
Q4534Let A be a 2 × 2 matrix with det (A) = - 1 and det ((A + I) (Adj (A) + I)) = 4. Then the sum of the diagonal elements of A can be:Matrices and Determinants
Q4613If the system of linear equations. 8x + y + 4z = - 2 x + y + z = 0 λ x - 3y = μ has infinitely many solutions, then the distance of the point (λ,μ, - 1/2)…Matrices and Determinants
Q4892The mean and variance of a binomial distribution are α and (α)/3 respectively. If P(X=1)=4/243, then P(X=4 or 5) is equal to:Statistics and Probability
Q5022Let E₁, E₂, E₃ be three mutually exclusive events such that P(E₁)=(2+3 p)/6, P(E₂)=(2-p)/8 and P(E₃)=(1-p)/2. If the maximum and minimum values of p are p₁…Statistics and Probability
Q5183Consider two G.Ps. 2, 2², 2³,..... and 4, 4², 4³,.... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is (2)^(225/8), then Σ k =…Sequence and Series
Q5570A point P moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is 14. Let f(x, y)=0 be the locus of P, which intersects the x…Coordinate Geometry
Q5826Let a=α i+j-k and b=2 i+j-α k, α>0. If the projection of a × b on the vector -i+2 j-2 k is 30, then α is equal to:Vector Algebra