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JEE Main 2011 Annual Paper 1 Question Paper with Solutions | JEE Arc

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JEE Main 2011Annual, Paper 1

Physics 29Chemistry 23Mathematics 32

Physics

Q5872A fully charged capacitor C with initial charge q₀ is connected to a coil of self inductance L at t=0. The time at which the energy is stored equally between…Electromagnetic Induction and Alternating Currents
Q5946A resistor 'R' and 2μ F capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V…Electromagnetic Induction and Alternating Currents
Q5971Energy required for the electron excitation in L i⁺⁺ from the first to the third Bohr orbit is:Atoms and Nuclei
Q6083The half life of a radioactive substance is 20 minutes. The approximate time interval (t₂ - t₁) between the time t₂ when 2/3 of it had decayed and time t₁…Atoms and Nuclei
Q6301This question has Statement - 1 and Statement - 2. Of the four choices given after the statements, choose the one that best describes the two statements…Communication Systems
Q6509If a wire is stretched to make it 0.1% longer, its resistance will:Current Electricity
Q6621This question has Statement - 1 and Statement - 2. Of the four choices given after the statements, choose the one that best describes the two statements…Dual Nature of Matter and Radiation
Q6719A boat is moving due east in a region where the earth's magnetic fields is 5.0 × 10⁻⁵ N A⁻¹ m⁻¹ due north and horizontal. The best carries a vertical aerial 2…Electromagnetic Induction and Alternating Currents
Q6917Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < 1) apart because of their…Electrostatics
Q7000The electrostatic potential inside a charged spherical ball is given by φ = a r² + b where r is the distance from the center and a,b are constants. Then the…Electrostatics
Q7076A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8m behind the first car is overtaking the first car at a relative speed…Optics
Q7095Let x - z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of 2 and medium 2 with z < 0 has a refractive index of…Optics
Q7228Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is…Gravitation
Q7289Three perfect gases at absolute temperatures T₁, T₂ and T₃ are mixed. The masses of molecules are m₁,m₂ and m₃ and the number of molecules are n₁, n₂ and n₃…Thermodynamics
Q7530A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and it's suddenly brought to…Thermodynamics
Q7531100g of water is heated from 30° C to 50° C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184…Thermodynamics
Q7672A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The magnitude of the magnetic induction along…Magnetic Effects of Current and Magnetism
Q7776A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that…Kinematics
Q7883An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by: dv/dt = - 2.5 v where v is the instantaneous speed. The time taken by the…Kinematics
Q7894Water is flowing continuously from a tap having an internal diameter 8 × 10⁻³ m. The water velocity as it leaves the tap is 0.4 m s⁻¹. The diameter of the…Properties of Solids and Liquids
Q8007Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03N m⁻¹,Properties of Solids and Liquids
Q8043A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The…Rotational Motion
Q8066A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a…Rotational Motion
Q8106A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of…Rotational Motion
Q8139A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A₁. When the mass M passes through its mean position then a smaller mass m is placed…Oscillations and Waves
Q8140Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x -axis. Their mean position is separated by distance…Oscillations and Waves
Q8326A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading: 0 mm Circular scale reading: 52 divisions Given…Experimental Skills
Q8414This question has a paragraph followed by two statements, Statement -1 and Statement -2. Of the given four alternatives after the statements, choose the one…Optics
Q8480The transverse displacement y(x, t) of a wave on a string is given by y(x,t) = e^ - (a x² + b t² + 2√(ab) xt). This represents a:Oscillations and Waves

Chemistry

Q43Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound…Organic Compounds Containing Oxygen
Q228The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?Biomolecules
Q283The structure of IF₇ is:Chemical Bonding and Molecular Structure
Q341Among the following the maximum covalent character is shown by the compound:Chemical Bonding and Molecular Structure
Q402A vessel at 1000 K contains CO₂ with a pressure of 0.5 atm. Some of the CO₂ is converted into CO on the addition of graphite. If the total pressure at…Equilibrium
Q505The rate of a chemical reaction doubles for every 10^(o)C rise of temperature. If the temperature is raised by 50^(o)C, the rate of the reaction increases by…Chemical Kinetics
Q711Which of the following facts about the complex [Cr (NH₃)₆ ]Cl₃ is wrong?Coordination Compounds
Q712The magnetic moment (spin only) of [NiCl₄]²− isCoordination Compounds
Q807In context of the lanthanoids, which of the following statements is not correct?d- and f-Block Elements
Q808The outer electron configuration of Gd (Atomic No. 64) is:d- and f-Block Elements
Q976The reduction potential of hydrogen half cell will be negative if:Redox Reactions and Electrochemistry
Q1123'a’ and b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane becauseGaseous State
Q1481Which of the following statement is wrong?p-Block Elements
Q1504Which of the following statements regarding sulphur is incorrect?p-Block Elements
Q1631Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?Classification of Elements and Periodicity in Properties
Q1645Outer electronic configuration of Gd (Atomic no: 64) is -Classification of Elements and Periodicity in Properties
Q1744Which of the following reagents may be used to distinguish between phenol and benzoic acid ?Principles Related to Practical Chemistry
Q1915In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of…Solid State
Q1956The degree of dissociation (α) of a weak electrolyte, A x B y is related to van’t Hoff factor (i) by the expression:Solutions
Q1976Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at…Solutions
Q2027A 5.2 molal aqueous solution of methyl alcohol, CH₃OH, is supplied. What is the mole fraction of methyl alcohol in the solution ?Some Basic Concepts in Chemistry
Q2171A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at:Atomic Structure
Q2290The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm³ to a volume of 100 dm³ at 27^(o)C is:Chemical Thermodynamics

Mathematics

Q2392If the angle between the line x = (y - 1)/2 = (z - 3)/(λ) and the plane x+2y+3z=4 is cos ⁻¹(√(5/14)), then λ equals:Three Dimensional Geometry
Q2483Statement - 1: The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line: x/1 = (y - 1)/2 = (z - 2)/3 Statement - 2: The line x/1 = (y - 1)/2 =…Three Dimensional Geometry
Q2628For x (0,(5π)/2), define f(x) = ∫₀ˣ t sin t dt. Then f hasLimit, Continuity and Differentiability
Q2756The shortest distance between line y-x=1 and curve x = y² isLimit, Continuity and Differentiability
Q2800The area of the region enclosed by the curves y = x,x = e,y = 1/x and the positive x -axis is:Integral Calculus
Q2972The coefficient of x⁷ in the expansion of (1 - x - x² + x³)⁶ isBinomial Theorem and Its Simple Applications
Q3089The two circles x² + y² = ax, and x² + y² = c² (c > 0) touch each other if:Coordinate Geometry
Q3175Let α,β be real and z be a complex number. If z² + α z + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that:Complex Numbers and Quadratic Equations
Q3232If ω (≠ 1) is a cube root of unity, and (1 + ω)⁷ = A + Bω. Then (A,B) equals:Complex Numbers and Quadratic Equations
Q3348The value of ∫₀¹ (8 log (1 + x))/(1 + x²) dx isIntegral Calculus
Q3507If dy/dx = y + 3 > 0 and y(0)=2, then y(ln 2) is equal to:Differential Equations
Q3580Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by…Differential Equations
Q3697d²x d y² equals:Limit, Continuity and Differentiability
Q3745Equation of the ellipse whose axes of coordinates and which passes through the point (-3,1) and has eccentricity √(2/5) is:Coordinate Geometry
Q3841The domain of the function f(x) = 1/(√(| x | - x)) isSets, Relations and Functions
Q4127The value of p and q for which the function f(x) = \ (sin (p + 1)x + sin x)/x,x < 0 q,x = 0 (√(x + x²) - x)/(x^(3/2)),x > 0. is continuous for all x in R, areLimit, Continuity and Differentiability
Q4266lim x → 2 ((√(1 - cos 2(x - 2) \))/(x - 2))Limit, Continuity and Differentiability
Q4401Consider the following statements P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, “Suman is brilliant and dishonest…Mathematical Reasoning
Q4553The number of values of k for which the linear equations 4x + ky + 2z = 0,kx + 4y + z = 0 and 2x+2y+z=0 possess a non-zero solution is:Matrices and Determinants
Q4642Let A and B be two symmetric matrices of order 3. Statement - 1: A(BA) and (AB) A are symmetric matrices. Statement - 2: AB is symmetric matrix if matrix…Matrices and Determinants
Q4815These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:Permutations and Combinations
Q4816Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is ⁹C₃. Statement - 2: The number of ways…Permutations and Combinations
Q4872Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32…Statistics and Probability
Q4939If C and D are two events such that C D and P(D) ≠ 0, then the correct statement among the following is:Statistics and Probability
Q5193A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increases by ₹ 40 more than the saving of…Sequence and Series
Q5372Let R be the set of real numbers. Statement I: A=\(x, y) R × R: y-x is an integer is an equivalence relation on R. Statement II: B=\(x, y) R × R: x=α y for…Sets, Relations and Functions
Q5428If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equalsStatistics and Probability
Q5509The lines L₁:y - x = 0 and L₂:2x + y = 0 intersect the line L₃:y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L₁ and L₂ intersects…Coordinate Geometry
Q5658If A = sin ²x + cos ⁴x, then for all real x:Trigonometry
Q5685Let a, b, c be three non-zero vectors which are pairwise non-collinear. If a+3 b is collinear with c and b+2 c is collinear with a, then a+ b+6 c is:Vector Algebra
Q5715If a = 1/(√(10))(3 i + k) and b = 1/7(2 i + 3 j - 6 k), then the value of (2 a - b)[ (a × b) × (a + 2 b) ] is:Vector Algebra
Q5800The vectors a and b are not perpendicular and c and d are two vectors satisfying b × c = b × d and a. d = 0. Then the vector d is equal to:Vector Algebra