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JEE Main 2017 Session Shift 1 Question Paper with Solutions | JEE Arc

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JEE Main 2017Session, Shift 1

Physics 21Chemistry 19Mathematics 29

Physics

Q6085A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A…Atoms and Nuclei
Q6144A capacitance of 2 μ F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 μ F capacitors are available which…Electrostatics
Q6340In amplitude modulation, sinusoidal carrier frequency used is denoted by ω c and the signal frequency is denoted by ω m. The bandwidth (Δ ω m) of the signal…Communication Systems
Q6454When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be…Current Electricity
Q6488Which of the following statements is false?Current Electricity
Q6534A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the…Dual Nature of Matter and Radiation
Q6899In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:Electronic Devices
Q6940An electric dipole has a fixed dipole moment p, which makes angle θ with respect to x-axis. When subjected to an electric field E₁^ → = E i, it experiences a…Electrostatics
Q7033A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitude of focal length 20cm. A beam of…Optics
Q7358The temperature of an open room of volume 30 m³ increases from 17^(o)C to 27^(o)C due to the sunshine. The atmospheric pressure in the room remains 1 × 10⁵…Thermodynamics
Q7359C P and C v are specific heats at constant pressure and constant volume respectively. It is observed that C P – C v = a for hydrogen gas C P – C v = b for…Thermodynamics
Q7445A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature…Properties of Solids and Liquids
Q7511An external pressure P is applied on a cube at 0^(o)C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α…Properties of Solids and Liquids
Q7611A magnetic needle of magnetic moment 6.7 × 10⁻² A m² and moment of inertia 7.5 × 10⁻⁶ kg m² is performing simple harmonic oscillations in a magnetic field of…Magnetic Effects of Current and Magnetism
Q7929A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change…Properties of Solids and Liquids
Q8085The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/R such that the moment of…Rotational Motion
Q8291The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 × 10⁻² m rise of water…Units and Measurements
Q8417In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650…Optics
Q8520An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the…Oscillations and Waves
Q8576A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy…Work, Energy and Power
Q8577A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:Work, Energy and Power

Chemistry

Q356Which of the following species is not paramagnetic?Chemical Bonding and Molecular Structure
Q443Two reactions R₁ and R₂ have identical pre-exponential factors. Activation energy of R₁ exceeds that of R₂ by 10 kJ mol^–1. If k₁ and k₂ are rate constants…Chemical Kinetics
Q715On treatment of 100 mL of 0.1 M solution of CoCl₃. 6H₂O with excess AgNO₃; 1.2 × 10²² ions are precipitated. The complex is:Coordination Compounds
Q862In the following reactions, ZnO is respectively acting as a/an: (a) ZnO + Na₂O → Na₂ZnO₂ (b) ZnO + CO₂ → ZnCO₃d- and f-Block Elements
Q981Given E_ C l₂ /C l^ - ^(o) = 1.36 V, E_ C r³⁺ /Cr ^(o) = - 0.74 V E_ C r₂ O₇ ²⁻/C r³⁺ ^(o) = 1.33 V, E_ Mn O₄ ^ - /Mn ²⁺ ^(o) = 1.51 V Among the following…Redox Reactions and Electrochemistry
Q1080A water sample has ppm level concentration of following anions F⁻ = 10; SO₄²⁻ = 100; NO₃^- = 50 The anion/anions that make/makes the water sample unsuitable…Environmental Chemistry
Q11433-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is:Organic Compounds Containing Halogens
Q1297pK a of a weak acid (HA) and pK b of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is:Equilibrium
Q1677The formation of which of the following polymers involves hydrolysis reaction?Polymers
Q1874Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is:S Block Elements
Q1918A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach between two atoms in metallic crystal…Solid State
Q1960The freezing point of benzene decreases by 0.45⁰C when 0.2 g of acetic acid is added to 20g of benzene. If acetic acid associates to form a dimer in benzene…Solutions
Q20681 gram of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01186 mole of CO₂. The molar mass of M₂CO₃ in g mol^–1 is:Some Basic Concepts in Chemistry
Q2069The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight…Some Basic Concepts in Chemistry
Q2113The radius of the second Bohr orbit for hydrogen atom is: (Planck’s Const. h = 6.6262 × 10⁻³⁴ Js; mass of electron = 9.1091 × 10⁻³¹ kg; charge of electron (e)…Atomic Structure
Q2138The group having isoelectronic species is:Atomic Structure
Q2234The Tyndall effect is observed only when following conditions are satisfied: (a) The diameter of the dispersed particles is much smaller than the wavelength…Surface Chemistry
Q2315Δ U is equal to:Chemical Thermodynamics
Q2349Given, C (graphite) + O₂ → C O₂ (g); Δ r H^(o) = - 393.5 kJ mol⁻¹ H₂(g) + 1/2O₂(g) → H₂ O(l) Δ r H^(o) = - 285.8 kJ mol⁻¹ C O₂ (g) + 2 H₂ O(l) → C H₄ (g) +…Chemical Thermodynamics

Mathematics

Q2399If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, x/1 = y/4 = z/5 is Q, then PQ is equal to:Three Dimensional Geometry
Q2400The distance of the point (1, 3, – 7) from the plane passing through the point (1, –1, – 1), having normal perpendicular to both the lines (x - 1)/1 = (y +…Three Dimensional Geometry
Q2635Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:Limit, Continuity and Differentiability
Q2762The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point:Limit, Continuity and Differentiability
Q2808The area (in sq. units) of the region (x,y):x ≥ 0,x + y ≤ 3,x² ≤ 4y and y ≤ 1 + x isIntegral Calculus
Q3120The radius of a circle, having minimum area, which touches the curve y = 4 – x² and the lines, y = |x| is:Coordinate Geometry
Q3149Let ω be a complex number such that 2 ω + 1 = z where z = √(-3). If | 1 1 1 1 - ω ² - 1 ω ² 1 ω ² ω ⁷ | = 3k, then k is equal to:Complex Numbers and Quadratic Equations
Q3356The integral ∫ (π)/4 ^((3π)/4) dx/(1 + cos x) is equal toIntegral Calculus
Q3510If (2 + sin x)dy/dx + (y + 1) cos x = 0 and y(0) = 1, then y((π)/2) is equal to:Differential Equations
Q3676If for x (0,1/4), the derivatives of tan ⁻¹((6x x)/(1 - 9x³)) is x.g(x), then g(x) equalsLimit, Continuity and Differentiability
Q3727The eccentricity of an ellipse whose centre is at the origin is 1/2. If one of its directrices is x = – 4, then the equation of the normal to it at (1,3/2) is:Coordinate Geometry
Q3795The function f:R → [ - 1/2,1/2 ] defined as f(x) = x/(1 + x²), isSets, Relations and Functions
Q3859Let a, b, c R. If f (x) = ax² + bx + c is such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, x,y R, then Σ n = 1 ¹⁰ f(n) is equal toSets, Relations and Functions
Q3907Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If BPC = β, then…Height and Distance
Q3984A hyperbola passes through the point P (2, 3) and has foci at (± 2,0). Then the tangent to this hyperbola at P also passes through the point:Coordinate Geometry
Q4006Let I n = ∫ tan ⁿx dx, (n > 1). If I₄ + I₆ = a tan ⁵ x + b x⁵ + C, where C is a constant of integration, then the ordered pair (a,b) is equal toIntegral Calculus
Q4271lim x → (π)/2 (cot x - cos x)/((π - 2x)³) equalsLimit, Continuity and Differentiability
Q4314The following statement (p → q) → [ (p → q) → q ] is:Mathematical Reasoning
Q4424If A = [ 2 - 3 - 4 1 ], then adj(3A² + 12A) is equal toMatrices and Determinants
Q4557If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution…Matrices and Determinants
Q4822A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common…Permutations and Combinations
Q4875A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls…Statistics and Probability
Q4903If two different numbers are taken from the set 0, 1, 2, 3,........, 10; then the probability that their sum as well as absolute difference are both multiple…Statistics and Probability
Q5016For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = 1/4 and P(All the three…Statistics and Probability
Q5125If for a positive integer n, the quadratic equation x(x + 1) + (x + 1)(x + 2) +.... + (x + n - 1)(x + n) = 10n has two consecutive integral solutions, then n…Complex Numbers and Quadratic Equations
Q5295For any three positive real numbers a, b and c, 9(25 a² + b²) + 25(c² - 3 a c) = 15b(3 a + c). ThenSequence and Series
Q5529Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the…Coordinate Geometry
Q5649If 5(tan ²x - cos ²x) = 2 cos 2x + 9, then the value of cos 4x is:Trigonometry
Q5801Let a = 2 i + j -2 k and b = i + j. Let c be a vector such that | c - a | = 3, | (a × b) × c | = 3 and the angle between c and a × b is 30°. Then a. c is…Vector Algebra