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2009 · Shift 2

57 questions · JEE Advanced

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2009 · Shift 2

2009 · Shift 2

57 questions · JEE Advanced

Chemistry19 questions Mathematics19 questions Physics19 questions

Chemical Kinetics and Nuclear ChemistryChemistry · 2 questions Coordination CompoundsChemistry · 2 questions Basics of Organic ChemistryChemistry · 3 questions ElectrochemistryChemistry · 1 questions ThermodynamicsChemistry · 2 questions P Block ElementsChemistry · 3 questions BiomoleculesChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 1 questions Gaseous StateChemistry · 1 questions Ionic EquilibriumChemistry · 1 questions D and F Block ElementsChemistry · 1 questions Solid StateChemistry · 1 questions Definite IntegrationMathematics · 2 questions Trigonometric Functions and EquationsMathematics · 2 questions Differential EquationsMathematics · 1 questions 3D GeometryMathematics · 1 questions Application of DerivativesMathematics · 3 questions FunctionsMathematics · 1 questions Quadratic Equation and InequalitiesMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions Sequences and SeriesMathematics · 1 questions CircleMathematics · 1 questions EllipseMathematics · 2 questions ParabolaMathematics · 2 questions Properties of TriangleMathematics · 1 questions Laws of MotionPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions Simple Harmonic MotionPhysics · 3 questions Heat and ThermodynamicsPhysics · 3 questions WavesPhysics · 2 questions Electromagnetic InductionPhysics · 1 questions Rotational MotionPhysics · 1 questions Wave OpticsPhysics · 1 questions Work Power and EnergyPhysics · 2 questions Properties of MatterPhysics · 2 questions MagnetismPhysics · 1 questions ElectrostaticsPhysics · 1 questions

Q1.For a first-order reaction A $\to$ P, the temperature (T) dependent rate constant (k) was found to follow the equation $lo g k = - (2000) \frac{1}{T} + 6.0$ . The pre-exponential factor A and activation energy $E_{a}$ , respectively, are
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q2.The spin only magnetic moment value (in Bohr magneton units) of Cr(CO) $_{6}$ is
Chemistry · Coordination Compounds · MCQ
Q3.In the following carbocation, H/ $C H_{3}$ that is most likely to migrate to the positively charged carbon is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q4.The correct stability order of the following resonance structures is Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q5.For the reduction of NO $_{3}^{-}$ ion in an aqueous solution, E $^{0}$ is + 0.96 V. Values of E $^{0}$ for some metal ions are given below: $V^{2 +} (a q .) + 2 e^{-} \to V F e^{3 +} (a q .) + 3 e^{-} \to F e A u^{3 +} (a q) + 3 e^{-} \to A u H g^{2 +} (a q) + 2 e^{-} \to H g E^{0} = - 1.19 V E^{0} = - 0.04 V E^{0} = + 1.40 V E^{0} = + 0.86 V$ …
Chemistry · Electrochemistry · Multiple correct
Q6.Among the following, the state function(s) is(are)
Chemistry · Thermodynamics · Multiple correct
Q7.In the reaction $2X + B_{2} H_{6} \to [B H_{2} (X)_{2}]^{+} [B H_{4}]^{-}$ the amine(s) X is(are) :
Chemistry · P Block Elements · Multiple correct
Q8.The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)
Chemistry · P Block Elements · Multiple correct
Q9.The correct statement(s) about the following sugar X and Y is(are) Includes diagram
Chemistry · Biomolecules · Multiple correct
Q10.Match each of the reactions given in Column I with the corresponding product(s) given in Column II: Includes table
Chemistry · P Block Elements · MCQ
Q11.Match each of the compounds given in Column I with the reaction(s), that they can undergo, given in Column II. Includes table Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q12.In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that…
Chemistry · Thermodynamics · Numerical
Q13.At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is .
Chemistry · Gaseous State · Numerical
Q14.The dissociation constant of a substituted benzoic acid at 25 $^{\circ}$ C is 1.0 $\times$ 10 $^{- 4}$ . The pH of a 0.01 M solution of its sodium salt is .
Chemistry · Ionic Equilibrium · Numerical
Q15.The total number of $α$ and $β$ particles emitted in the nuclear reaction $_{92}^{238} U \to_{82}^{214} P b$ is .
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q16.The oxidation number of Mn in the product of alkaline oxidative fusion of MnO $_{2}$ is .
Chemistry · D and F Block Elements · Numerical
Q17.The number of water molecule(s) directly bonded to the centre in CuSO $_{4}$ . 5H $_{2}$ O is .
Chemistry · Coordination Compounds · Numerical
Q18.The coordination number of Al in the crystalline state of AlCl $_{3}$ is .
Chemistry · Solid State · Numerical
Q19.The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula C $_{5}$ H $_{10}$ is .
Chemistry · Basics of Organic Chemistry · Numerical
Q20.Let $f : R \to R$ be a continuous function which satisfies $f (x) = 0 \int x f (t) d t$ . Then, the value of $f (ln 5)$ is .
Mathematics · Definite Integration · Numerical
Q21.For $0 < θ < \frac{π}{2},$ the solution (s) of $m = 1 \sum 6 csc (θ + \frac{( m - 1 ) π}{4}) csc (θ + \frac{mπ}{4}) = 42$ is (are)
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q22.Match the statements/expressions in Column I with the values given in Column II: Includes table
Mathematics · Differential Equations · MCQ
Q23.Match the statements/expressions in Column I with the values given in Column II: Includes table
Mathematics · Trigonometric Functions and Equations · MCQ
Q24.A line with positive direction cosines passes through the point P(2, $-$ 1, 2) and makes equal angles with the coordinate axes. The line meets the plane $2 x + y + z = 9$ at point Q. The length of the line segment PQ equals
Mathematics · 3D Geometry · MCQ
Q25.If $I_{n} = - π \int π \frac{s i n n x}{( 1 + π ^{x} ) s i n x} d x, n = 0, 1, 2,$ .... then
Mathematics · Definite Integration · Multiple correct
Q26.The maximum value of the function $f (x) = 2 x^{3} - 15 x^{2} + 36 x - 48$ on the set $A = {x ∣ x^{2} + 20 \leq 9 x ∣}$ is .
Mathematics · Application of Derivatives · Numerical
Q27.Let $p (x)$ be a polynomial of degree $4$ having extremum at $x = 1, 2$ and $x \to 0 lim (1 + \frac{p ( x )}{x ^{2}}) = 2$ . Then the value of $p (2)$ is
Mathematics · Application of Derivatives · Numerical
Q28.For the function $f (x) = x cos \frac{1}{x}, x \geq 1,$
Mathematics · Application of Derivatives · Multiple correct
Q29.If the function $f (x) = x^{3} + e^{x /2}$ and $g (x) = f^{- 1} (x)$ , then the value of $g^{'} (1)$ is .
Mathematics · Functions · Numerical
Q30.The smallest value of $k$ , for which both the roots of the equation $x^{2} - 8 k x + 16 (k^{2} - k + 1) = 0$ are real, distinct and have values at least 4, is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q31.Let $(x, y, z)$ be points with integer coordinates satisfying the system of homogeneous equation: $3 x - y - z = 0 - 3 x + z = 0 - 3 x + 2 y + z = 0$ Then the number of such…
Mathematics · Permutations and Combinations · Numerical
Q32.If the sum of first $n$ terms of an A.P. is $c n^{2}$ , then the sum of squares of these $n$ terms is
Mathematics · Sequences and Series · MCQ
Q33.The centres of two circles $C_{1}$ and $C_{2}$ each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segement joining the centres of $C_{1}$ and $C_{2}$ and C a circle touching circles $C_{1}$ …
Mathematics · Circle · Numerical
Q34.The normal at a point $P$ on the ellipse $x^{2} + 4 y^{2} = 16$ meets the $x$ - axis $Q$ . If $M$ is the mid point of the line segment $P Q$ , then the locus of $M$ intersects the latus rectums of the given ellipse at the points
Mathematics · Ellipse · MCQ
Q35.The tangent $P T$ and the normal $P N$ to the parabola $y^{2} = 4 a x$ at a point $P$ on it meet its axis at points $T$ and $N$ , respectively. The locus of the centroid of the triangle $P T N$ is a parabola whose
Mathematics · Parabola · Multiple correct
Q36.An ellipse intersects the hyperbola $2 x^{2} - 2 y^{2} = 1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then
Mathematics · Ellipse · Multiple correct
Q37.Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2 $2$ and angle B = 30 $^{\circ}$ . The absolute value of the difference between the areas of these triangles is .
Mathematics · Properties of Triangle · Numerical
Q38.The locus of the orthocentre of the triangle formed by the lines $(1 + p) x - p y + p (1 + p) = 0, (1 + q) x - q y + q (1 + q) = 0$ and $y = 0$ , where $p e q$ , is :
Mathematics · Parabola · MCQ
Q39.A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is…
Physics · Laws of Motion · MCQ
Q40.Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $ϕ_{p} = 2.0 eV$ , $ϕ_{q} = 2.5 eV$ and $ϕ_{r} = 3.0 eV$ , respecticely. A light beam containing…
Physics · Dual Nature of Radiation · MCQ
Q41.The mass M shown in the figure below oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q42.A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$ . The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the… Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q43.The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then, Includes diagram
Physics · Heat and Thermodynamics · Multiple correct
Q44.Under the influence of the Coulomb field of charge +Q, a charge $-$ q is moving around it in an elliptical orbit. Find out the correct statement(s):
Physics · Waves · Multiple correct
Q45.Two metallic rings A and B, identical in shape and size but having different resistivities $ρ_{A}$ and $ρ_{B}$ , are kept on top of two identical solenoids as shown in the figure below. When current I is switched on in both the solenoids… Includes diagram
Physics · Electromagnetic Induction · Multiple correct
Q46.A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then, Includes diagram
Physics · Rotational Motion · Multiple correct
Q47.A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first…
Physics · Simple Harmonic Motion · Multiple correct
Q48.Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II: Includes table
Physics · Heat and Thermodynamics · MCQ
Q49.Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits S $_{1}$ and S $_{2}$ . In each of these cases, S $_{1}$ P $_{0}$ = S $_{2}$ P $_{0}$ , S $_{1}$ P $_{1} -$ S $_{2}$ P $_{1}$ = $λ /4$ … Includes table Includes diagram
Physics · Wave Optics · MCQ
Q50.A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s2, find the work done (in joules) by the string on the block of mass 0.36 kg during… Includes diagram
Physics · Work Power and Energy · Numerical
Q51.Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m $^{2}$ . The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m.…
Physics · Properties of Matter · Numerical
Q52.A steady current I goes through a wire loop PQR having shape of a right angle triangle wit6h PQ = 3, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is $k (\frac{μ _{0} I}{48 π x})$ ,…
Physics · Magnetism · Numerical
Q53.A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened.…
Physics · Properties of Matter · Numerical
Q54.A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. find the separation (in cm) between the…
Physics · Waves · Numerical
Q55.A solid sphere of radius R has a charge Q distributed in its volume with a charge density $ρ = K r^{a}$ , where K and a are constants and r is the distance from its centre. If the electric field at $r = R /2$ is 1/8 times than at $r = R$ ,…
Physics · Electrostatics · Numerical
Q56.A metal rod AB of length 10x has its one end A in ice at 0 $^{\circ}$ C and the other end B in water at 100 $^{\circ}$ C. If a point P on the rod is maintained at 400 $^{\circ}$ C, then it is found that equal amounts of water and ice evaporate…
Physics · Heat and Thermodynamics · Numerical
Q57.Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B…
Physics · Work Power and Energy · Numerical