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JEE Main 2019 10 Jan Morning shift Question Paper with Solutions | JEE Arc

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JEE Main 201910 Jan, Morning shift

Physics 22Chemistry 18Mathematics 29

Physics

Q6091Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it…Atoms and Nuclei
Q6217A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward…Rotational Motion
Q6306A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be…Communication Systems
Q6381A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -Current Electricity
Q6423A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is -Current Electricity
Q6539In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10^–12 m, the…Dual Nature of Matter and Radiation
Q6701A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the…Electromagnetic Induction and Alternating Currents
Q6756If the magnetic field of a plane electromagnetic wave is given by (the speed of light = 3 × 10⁸ B = 100 × 10^–6 sin [ 2π × 2 × 10¹⁵(t - x/c) ] then the…Electromagnetic Waves
Q7011A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one…Electrostatics
Q7041A plano convex lens of refractive index μ ₁ and focal length ƒ₁ is kept in contact with another plano concave lens of refractive index μ ₂ and focal length…Optics
Q7187A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just…Gravitation
Q7341A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 mthick. Given that the thermal conductivity of…Properties of Solids and Liquids
Q7612A magnet of total magnetic moment 10⁻² i A-m² is placed in a time varying magnetic field, B i (cos ω t) where B = 1 Tesla and ω = 0.125 rad/s. The work done…Magnetic Effects of Current and Magnetism
Q7721An insulating thin rod of length l has a linear charge density ρ (x) = ρ ₀x/l on it. The rod is rotated about an axis passing through the origin (x = 0) and…Magnetic Effects of Current and Magnetism
Q7779Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions…Kinematics
Q7897Water flows into a large tank with flat bottom at the rate of 10^–4m³s^–1. Water is also leaking out of a hole ofarea 1 cm² at its bottom. If the height of…Properties of Solids and Liquids
Q8068A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular…Rotational Motion
Q8110To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed…Rotational Motion
Q8341The density of a material in SI units is 128 kg m^–3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value…Units and Measurements
Q8422In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 by using light of wavelength λ ₁. When the light…Optics
Q8491A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of…Oscillations and Waves
Q8523A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ₁. If the speed of…Oscillations and Waves

Chemistry

Q118If dichloromethane (DCM) and water (H₂O) are used for differential extraction, which one of the following statements is correct ?Some Basic Principles of Organic Chemistry
Q291The type of hybridisation and number of lone pair (s) of electrons of Xe in XeOF₄, respectively, are:Chemical Bonding and Molecular Structure
Q365Two pi and half sigma bonds are present in:Chemical Bonding and Molecular Structure
Q676The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO₂)] isCoordination Compounds
Q760Wilkinson catalyst is: (Et = C₂H₅)d- and f-Block Elements
Q813The effect of lanthanoid contraction in the lanthanoid series of elements by and large means:d- and f-Block Elements
Q993Consider the following reduction processes: Zn²⁺ + 2e^– → Zn(s); E^(o) = – 0.76 V Ca²⁺ + 2e^– → Ca(s); E^(o) = –2.87 V Mg²⁺ + 2e^– → Mg(s); E^(o) = – 2.36 V…Redox Reactions and Electrochemistry
Q1084Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is:Environmental Chemistry
Q1213The chemical nature of hydrogen peroxide is:Hydrogen
Q1243The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are:Hydrogen
Q1337A mixture of 100 m mol of Ca(OH)₂ and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed…Equilibrium
Q1379Hall- Heroult's process is given by:Isolation of Elements
Q1588The electronegativity of aluminium is similar to:Classification of Elements and Periodicity in Properties
Q1878The metal used for marking X–ray tube window is:S Block Elements
Q1921Which premitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles different from 90^(o)?Solid State
Q2013Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vaapor pressures of pure A and pure B are 7 × 10³ Pa and 12 × 10³ Pa…Solutions
Q2223Which of the following is not an example of heterogenous catalytic reaction?Surface Chemistry
Q2299A process has Δ H = 200 J mol^–1 and Δ S = 40 JK^–1 mol^–1. Out of the values given below, choose the minimum temperature above which the process will be…Chemical Thermodynamics

Mathematics

Q2571Let A be a point on the line r = (1 - 3μ) i + (μ - 1) j + (2 + 5μ) k and B(3, 2, 6) be a point in the space. Then the value of μ for which the vector AB is…Three Dimensional Geometry
Q2572The plane passing through the point (4, –1, 2) and parallel to the lines (x + 2)/3 = (y - 2)/(- 1) = (z + 1)/2 and (x - 2)/1 = (y - 3)/2 = (z - 4)/3 also…Three Dimensional Geometry
Q2644The shortest distance between the point (3/2,0) and the curve y = x, (x > 0), is -Limit, Continuity and Differentiability
Q2819If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -Integral Calculus
Q2921If the third term in the binomial expansion of (1 + x^(log ₂x))⁵ equals 2560, then a possible value of x is -Binomial Theorem and Its Simple Applications
Q2986If Σ i = 1 ²⁰ ((²⁰C i - 1)/(²⁰C i + ²⁰C i - 1)) ³ = k/21 then k is equal toBinomial Theorem and Its Simple Applications
Q3070If a circle C passing through the point (4, 0) touches the circle x² + y² + 4x – 6y = 12 externally at the point (1, – 1), then the radius of C is:Coordinate Geometry
Q3253Let z₁ and z₂ be any two non-zero complex numbers such that 3| z₁ | = 4| z₂ |. If z = 3z₁/2z₂ + 2z₂/3z₁ then:Complex Numbers and Quadratic Equations
Q3374Let I = ∫ a ^(b) (x⁴ - 2x²) dx. If I is minimum then the ordered pair (a, b) is -Integral Calculus
Q3589If dy/dx + 3/(cos ²x)y = 1/(cos ²x), x ((- π)/3,(π)/3) and y((π)/4) = 4/3, then y(- (π)/4) equals -Differential Equations
Q3706Let f: R → R be a function such that f(x) = x³ + x²f'(1) + xf''(2) + f'''(3), x R. Then f(2) equals -Limit, Continuity and Differentiability
Q3912Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30^(o) at B. The…Height and Distance
Q3986The equation of a tangent to the hyperbola 4x² – 5y² = 20 parallel to the line x – y = 2 is:Coordinate Geometry
Q4009Let n ≥ 2 be a natural number and 0 < θ < (π)/2. Then ∫ (sin ⁿθ - sin θ)^(1/n) cos θ sin ⁿ⁺¹θ dθ is equal to - (where C is a constant of integration)Integral Calculus
Q4191Let f(x) = \ max | x |,x² | x | ≤ 2 8 - 2| x | 2 < | x | ≤ 4. Let S be the set of points in the interval (– 4, 4) at which f is not differentiable. Then SLimit, Continuity and Differentiability
Q4278For each t R, let [t] be the greatest integer less than or equal to t Then lim x → 1⁺ ((1 - | x | + sin | 1 - x |) sin ((π)/2[ 1 - x ]))/(| 1 - x |.[ 1 - x ])Limit, Continuity and Differentiability
Q4407Consider the statement: "P(n): n² – n + 41 is prime". Then which one of the following is true ?Mathematical Reasoning
Q4456Let d R, and A = [ - 2 4 + d (sin θ) - 2 1 (sin θ) + 2 d 5 (2 sin θ) - d (- sin θ) + 2 + 2d ], θ [ 0,2π ] If the minimum value of det(A) is 8, then a value of…Matrices and Determinants
Q4571If the system of equations x + y + z = 5 x + 2y + 3z = 9 x + 3y + az = β has infinitely many solutions, then β - α equals -Matrices and Determinants
Q4707If the parabolas y² = 4b(x – c) and y² = 8ax have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?Coordinate Geometry
Q4948An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss…Statistics and Probability
Q5074Consider the quadratic equation (c – 5)x² – 2cx + (c – 4) = 0, c ≠ 5. Let S be the set of all integral values of c for which one root of the equation lies in…Complex Numbers and Quadratic Equations
Q5207The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -Sequence and Series
Q5400In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course…Sets, Relations and Functions
Q5448The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations…Statistics and Probability
Q5516If 5, 5r, 5r² are the lengths of the sides of a triangle, then r cannot be equal to:Coordinate Geometry
Q5531A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of Δ PQR is a line:Coordinate Geometry
Q5532If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin…Coordinate Geometry
Q5770Let a = 2 i + λ ₁ j + 3 k, b = 4 i + (3 - λ ₂) j + 6 k, and c = 3 i + 6 j + (λ ₃ - 1) k be three vectors such that b = 2 a and a is perpendicular to c. Then a…Vector Algebra