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JEE Main 2018 Session Shift 1 Question Paper with Solutions | JEE Arc

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JEE Main 2018Session, Shift 1

Physics 25Chemistry 19Mathematics 27

Physics

Q5875In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20 sin (30t - (π)/4) In one cycle of a.c., the average power…Electromagnetic Induction and Alternating Currents
Q5954For an RLC circuit driven with voltage of amplitude vm and frequency ω ₀ = 1/(√(LC)) the current exhibits resonance. The quality factor, Q is given by:Electromagnetic Induction and Alternating Currents
Q5958It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p d; while for its similar…Atoms and Nuclei
Q5983If the series limit frequency of the Lyman series is ν L, then the series limit frequency of the Pfund series is:Atoms and Nuclei
Q5984An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ n, λ g be the de Broglie wavelength of the electron…Atoms and Nuclei
Q6149A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted…Electrostatics
Q6207The mass of a hydrogen molecule is 3.32 × 10⁻²⁷ kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2 cm² at an angle of 45^(o) to the…Rotational Motion
Q6209In a collinear collision, a particle with an initial speed v₀ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater…Rotational Motion
Q6304A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be…Communication Systems
Q6489Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 Ω. The internal resistances of the two batteries are 1 Ω and 2 Ω…Current Electricity
Q6491On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k Ω. How…Current Electricity
Q6501In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the…Current Electricity
Q6743An EM wave from air enters a medium. The electric fields are E₁ = E₀₁ x cos [ 2π v(z/c - t) ] in air and E₂ = E₀₂ x cos [ k(2z - ct) ] in medium, where the…Electromagnetic Waves
Q7006Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities + σ, - σ and + σ respectively. The potential…Electrostatics
Q7252A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n^(t)h power of R. If the period of…Gravitation
Q7474Two moles of an ideal monatomic gas occupies a volume V at 27^(o)C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the…Thermodynamics
Q7674The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B₁. When the dipole moment is doubled by…Magnetic Effects of Current and Magnetism
Q7742An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r e, r p, r _α respectively in a uniform…Magnetic Effects of Current and Magnetism
Q7930A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats…Properties of Solids and Liquids
Q8189A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10¹²/sec. What is the force constant of the bonds…Oscillations and Waves
Q8293The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass…Units and Measurements
Q8395The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 μ m. The slit is illuminated by monochromatic…Optics
Q8459Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is…Optics
Q8489A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 10³ kg/m³ and its…Oscillations and Waves
Q8579A particle is moving in a circular path of radius a under the action of an attractive potential U = - k/(2r²) Its total energy is:Work, Energy and Power

Chemistry

Q152Glucose on prolonged heating with HI givesBiomolecules
Q260Which of the following compounds contain(s) no covalent bond(s)? KCl, PH₃, O₂, B₂H₆, H₂SO₄Chemical Bonding and Molecular Structure
Q290Total number of lone pair of electrons in I₃⁻ⁱon isChemical Bonding and Molecular Structure
Q359According to molecular orbital theory, which of the following will not be a viable molecule?Chemical Bonding and Molecular Structure
Q452At 518^(o)C the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr, was 1.00 Torr s^–1 when 5% had reacted and 0.5…Chemical Kinetics
Q589The oxidation states of Cr in [Cr(H₂O)₆]Cl₃, [Cr(C₆H₆)₂] and K₂[Cr(CN)₂(O)₂(O₂)(NH₃)] respectively are:Coordination Compounds
Q675Consider the following reaction and statements: [Co(NH₃)₄Br₂]⁺ + Br⁻ → [Co(NH₃)₃Br₃] + NH₃ (I) Two isomers are produced if the reactant complex ion is a…Coordination Compounds
Q936How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of…Redox Reactions and Electrochemistry
Q1212Hydrogen peroxide oxidises [Fe(CN)₆]⁴⁻ to [Fe(CN)₆]³⁻ in acidic medium but reduces [Fe(CN)₆]³⁻ to [Fe(CN)₆]⁴⁻ in alkaline medium. The other products formed…Hydrogen
Q1282Which of the following are Lewis acids?Equilibrium
Q1300An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?Equilibrium
Q1318An aqueous solution contains 0.10 M H₂S and 0.20 M HCl. If the equilibrium constants for the formation of HS^– from H₂S is 1.0 × 10^–7 and that of S²⁻ from…Equilibrium
Q1319Which of the following salts is the most basic in aqueous solution?Equilibrium
Q1331An aqueous solution contains an unknown concentration of Ba²⁺. When 50 mL of a 1 M solution of Na₂SO₄ is added, BaSO₄ just begins to precipitate. The final…Equilibrium
Q1484The compound that does not produce nitrogen gas by the thermal decomposition is:p-Block Elements
Q1934Which type of ‘defect’ has the presence of cations in the interstitial sites?Solid State
Q1962For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?Solutions
Q2031The ratio of mass percent of C and H of an organic compound (C X H Y O Z) is 6: 1. If one molecule of the above compound (C X H Y O Z) contains half as much…Some Basic Concepts in Chemistry
Q2350The combustion of benzene(l) gives CO₂(g) and H₂O(l). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol^–1 at 25^(o)C; heat of…Chemical Thermodynamics

Mathematics

Q2404The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x + y + z = 7 is:Three Dimensional Geometry
Q2559If L₁ is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L₂ is the line of intersection of the planes x + 2y - z - 3 = 0…Three Dimensional Geometry
Q2636Let f(x) = x² + 1/(x²) and g(x) = x - 1/x, x R - - 1,0,1. If h(x) = (f(x))/(g(x)), then the local minimum value of h(x) isLimit, Continuity and Differentiability
Q2765If the curves y² = 6x, 9x² + by² = 16 intersect each other at right angles, then the value of b is:Limit, Continuity and Differentiability
Q2879Let g(x) = cosx², f(x) = x and α,β (α < β) be the roots of the quadratic equation 18x² - 9 π x + π ² = 0. Then the area (in sq. units) bounded by the curve y…Integral Calculus
Q3121If the tangent at (1, 7) to the curve x² = y - 6 touches the circle x² + y² + 16x + 12y + c = 0, then the value of c is:Coordinate Geometry
Q3233If α,β C are the distinct roots of the equation x² - x + 1 = 0, then α ¹⁰¹ + β ¹⁰⁷ is equal to:Complex Numbers and Quadratic Equations
Q3358The value of ∫ - π /2 ^(π /2) (sin ²x)/(1 + 2ˣ) dx isIntegral Calculus
Q3513Let y = y(x) be the solution of the differential equation sin xdy/dx + y cos x = 4x, x (0,π). If y((π)/2) = 0, then y((π)/6) is equal to:Differential Equations
Q3908PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R…Height and Distance
Q3985Tangents are drawn to the hyperbola 4x² - y² = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of Δ…Coordinate Geometry
Q4008The integral ∫ sin ²x cos ² x (sin ⁵x + cos ³x sin ² x + sin ³x cos ² x + cos ⁵x) ² dx is equal toIntegral Calculus
Q4182Let S = t R:f(x) = | x - π |.(e^(| x |) - 1) sin | x | is not differentiable at t, then the set S is equal toLimit, Continuity and Differentiability
Q4224For each t R, let [t] be the greatest integer less than or equal to t. Then lim x → 0⁺ x([ 1/x ] + [ 2/x ] +..... + [ 15/x ])Limit, Continuity and Differentiability
Q4315The Boolean expression (p q) (p q) is equvalent to:Mathematical Reasoning
Q4445If | x - 4 2x 2x 2x x - 4 2x 2x 2x x - 4 | = (A + Bx)(x - A)² then the ordered pair (A, B) is equal to:Matrices and Determinants
Q4559If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then xz/(y²) is equal toMatrices and Determinants
Q4706Tangent and normal are drawn at P(16, 16) on the parabola y² = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of…Coordinate Geometry
Q4843From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is…Permutations and Combinations
Q5009A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the…Statistics and Probability
Q5079Let S = x R: x ≥ 0 and 2| x - 3 | + x (x - 6) + 6 = 0. Then SComplex Numbers and Quadratic Equations
Q5196Let a₁, a₂, a₃,........., a₄₉ be in A.P. such that Σ k = 0 ¹² a 4k + 1 = 416 and a₉ + a₄₃ = 66. a₁² + a₂² +....... + a₁₇² = 140m, then m is equal toSequence and Series
Q5298Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1² + 2.2² + 3² + 2.4² + 5² + 2.6²........... If B - 2A = 100 λ…Sequence and Series
Q5354Two sets A and B are as under: A = (a, b) R × R: | a - 5| < 1 and |b - 5| < 1; B = (a, b) R × R: 4(a - 6)² + 9(b - 5)² ≤ 36; ThenSets, Relations and Functions
Q5436If Σ i = 1 ⁹ (x i - 5) = 9 and Σ i = 1 ⁹ (x i - 5)² = 45, then the standard deviation of the 9 items x₁,x₂,.......,x₉ isStatistics and Probability
Q5566A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is…Coordinate Geometry
Q5766Let u be a vector coplanar with the vectors a = 2 i + 3 j - k and b = j + k. If u is perpendicular to a and u. b = 24, then | u |² is equal toVector Algebra