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2015 · Shift 2

60 questions · JEE Advanced

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2015 · Shift 2

2015 · Shift 2

60 questions · JEE Advanced

Chemistry20 questions Mathematics20 questions Physics20 questions

Chemical Kinetics and Nuclear ChemistryChemistry · 2 questions ElectrochemistryChemistry · 1 questions Surface ChemistryChemistry · 1 questions Ionic EquilibriumChemistry · 2 questions Alcohols Phenols and EthersChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 3 questions Coordination CompoundsChemistry · 2 questions P Block ElementsChemistry · 2 questions HydrocarbonsChemistry · 2 questions Compounds Containing NitrogenChemistry · 1 questions D and F Block ElementsChemistry · 1 questions PolymersChemistry · 1 questions Gaseous StateChemistry · 1 questions Quadratic Equation and InequalitiesMathematics · 1 questions Complex NumbersMathematics · 1 questions Vector AlgebraMathematics · 1 questions ProbabilityMathematics · 2 questions Application of IntegrationMathematics · 2 questions Sequences and SeriesMathematics · 2 questions EllipseMathematics · 1 questions HyperbolaMathematics · 1 questions ParabolaMathematics · 1 questions Inverse Trigonometric FunctionsMathematics · 1 questions Application of DerivativesMathematics · 1 questions Definite IntegrationMathematics · 4 questions DifferentiationMathematics · 1 questions Limits Continuity and DifferentiabilityMathematics · 1 questions ElectrostaticsPhysics · 1 questions Properties of MatterPhysics · 3 questions Rotational MotionPhysics · 1 questions Units and MeasurementsPhysics · 1 questions Electromagnetic WavesPhysics · 1 questions WavesPhysics · 1 questions Atoms and NucleiPhysics · 2 questions Geometrical OpticsPhysics · 3 questions Current ElectricityPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions GravitationPhysics · 1 questions CapacitorPhysics · 1 questions Heat and ThermodynamicsPhysics · 1 questions MagnetismPhysics · 2 questions

Q1.In dilute aqueous $H_{2} S O_{4}$ , the complex diaquodioxalatoferrate(II) is oxidized by $M n O_{4}^{-}$ . For this reaction, the ratio of the rate of change of [H+] to the rate of change of $[M n O_{4}^{-}]$ is
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q2.A closed vessel with rigid walls contains 1 mol of $_{92}^{238} U$ and 1 mol of air at 298 K. Considering complete decay of $_{92}^{238} U$ to $_{82}^{206} P b$ , the ratio of the final pressure to the initial pressure of the system at…
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q3.The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If $λ_{x^{-}}^{0} \approx λ_{y^{-}}^{0}$ the difference in their pKa…
Chemistry · Electrochemistry · Numerical
Q4.When $O_{2}$ is adsorbed on a metallic surface, electron transfer occurs from the metal to $O_{2}$ . The true statement(s) regarding this adsorption is(are)
Chemistry · Surface Chemistry · Multiple correct
Q5.Paragraph When 100 mL of 1.0 M KCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7o C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of…
Chemistry · Ionic Equilibrium · Multiple correct
Q6.Paragraph When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of 5.7o C was measured for the beaker and its contents (Expt. 1). Because the enthalpy of…
Chemistry · Ionic Equilibrium · Multiple correct
Q7.The number of hydroxyl group(s) in Q is . Includes diagram
Chemistry · Alcohols Phenols and Ethers · Numerical
Q8.Among the following the number of reactions that produces benzaldehyde is . Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q9.In the complex acetylbromidodicarbonylbis(triethylphosphine) iron(II), the number of $F e - C$ bond(s) is .
Chemistry · Coordination Compounds · Numerical
Q10.Among the complex ions, $[C o (N H_{2} - C H_{2} - C H_{2} - N H_{2})_{2} C l_{2}]^{+}$ , $[C r C l_{2} (C_{2} O_{4})_{2}]^{3 -}$ , $[F e (H_{2} O)_{4}) O H)_{2}]^{+}$ , $[F e (N H_{3})_{2} (C N)_{4}]^{-}$ , $[C o (N H_{2} - C H_{2} - C H_{2} - N H_{2})_{2} (N H_{3}) C l]^{2 +}$ and $[C o (N H_{3})_{4} (H_{2} O) C l]^{2 +}$ , the number of complex ions…
Chemistry · Coordination Compounds · Numerical
Q11.Three moles of $B_{2} H_{6}$ are completely reacted with methanol. The number of moles of boron containing product formed is .
Chemistry · P Block Elements · Numerical
Q12.In the following reactions, the product S is Includes diagram
Chemistry · Hydrocarbons · Multiple correct
Q13.The major product U in the following reactions is Includes diagram
Chemistry · Hydrocarbons · Multiple correct
Q14.In the following reactions, the major product W is Includes diagram
Chemistry · Compounds Containing Nitrogen · Multiple correct
Q15.The correct statements regarding (i) $H C l O$ , (ii) $H C l O_{2}$ , (iii) $H C l O_{3}$ and (iv) $H C l O_{4}$ is (are)
Chemistry · P Block Elements · Multiple correct
Q16.The pairs of ions where BOTH the ions are precipitated upon passing $H_{2} S$ gas in presence of dilute $H C l$ , is(are)
Chemistry · D and F Block Elements · Multiple correct
Q17.Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are
Chemistry · Polymers · Multiple correct
Q18.One mole of a monoatomic real gas satisfies the equation p(V $-$ b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by
Chemistry · Gaseous State · Multiple correct
Q19.In the following reactions Compound X is Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q20.In the following reactions The major compound Y is Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q21.Let $S$ be the set of all non-zero real numbers $α$ such that the quadratic equation $α x^{2} - x + α = 0$ has two distinct real roots $x_{1}$ and $x_{2}$ satisfying the inequality $∣ x_{1} - x_{2} ∣ < 1.$ …
Mathematics · Quadratic Equation and Inequalities · Multiple correct
Q22.For any integer k, let $a_{k} = cos (\frac{k π}{7}) + i sin (\frac{k π}{7})$ , where $i = - 1$ . The value of the expression $\frac{k = 1 \sum 12 ∣ α _{k + 1} - a _{k} ∣}{k = 1 \sum 3 ∣ α _{4 k - 1} - α _{4 k - 2} ∣}$ …
Mathematics · Complex Numbers · Numerical
Q23.Suppose that $p, q$ and $r$ are three non-coplanar vectors in $R^{3}$ . Let the components of a vector $s$ along $p, q$ and $r$ …
Mathematics · Vector Algebra · Numerical
Q24.Let $n_{1}$ and $n_{2}$ be the number of red and black balls, respectively, in box $I$ . Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively, in box $I I .$ One of the two boxes, box $I$ and box $I I,$ …
Mathematics · Probability · Multiple correct
Q25.Let $n_{1}$ and $n_{2}$ be the number of red and black balls, respectively, in box $I$ . Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively, in box $I I .$ A ball is drawn at random from box $I$ …
Mathematics · Probability · Multiple correct
Q26.Let $f : R \to R$ be a continuous odd function, which vanishes exactly at one point and $f (1) = \frac{1}{2.}$ Suppose that $F (x) = - 1 \int x f (t) d t$ for all $x \in [- 1, 2]$ …
Mathematics · Application of Integration · Numerical
Q27.Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the…
Mathematics · Sequences and Series · Numerical
Q28.The coefficient of $x^{9}$ in the expansion of (1 + x) (1 + $x^{2})$ (1 + $x^{3}$ ) .... $(1 + x^{100})$ is
Mathematics · Sequences and Series · Numerical
Q29.Let $E_{1}$ and $E_{2}$ be two ellipses whose centres are at the origin. The major axes of $E_{1}$ and $E_{2}$ lie along the $x$ -axis and the $y$ -axis, respectively. Let $S$ be the circle $x^{2} + (y - 1)^{2} = 2$ . The…
Mathematics · Ellipse · Multiple correct
Q30.Consider the hyperbola $H : x^{2} - y^{2} = 1$ and a circle $S$ with center $N (x_{2}, 0)$ . Suppose that $H$ and $S$ touch each other at a point $P (x_{1}, y_{1})$ with $x_{1} > 1$ and $y_{1} > 0$ . The…
Mathematics · Hyperbola · Multiple correct
Q31.Suppose that the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1$ are $(f_{1}, 0)$ and $(f_{2}, 0)$ where $f_{1} > 0$ and $f_{2} < 0$ . Let $P_{1}$ and $P_{2}$ be two parabolas with a…
Mathematics · Parabola · Numerical
Q32.If $α$ $= 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9}),$ where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are)
Mathematics · Inverse Trigonometric Functions · Multiple correct
Q33.Let $f, g :$ $[- 1, 2] \to R$ be continuous functions which are twice differentiable on the interval $(- 1, 2)$ . Let the values of f and g at the points $- 1, 0$ and $2$ be as given in the following table: In each of the… Includes table
Mathematics · Application of Derivatives · Multiple correct
Q34.Let $f (x) = 7 tan^{8} x + 7 tan^{6} x - 3 tan^{4} x - 3 tan^{2} x$ for all $x \in (- \frac{π}{2}, \frac{π}{2}) .$ Then the correct expression(s) is (are)
Mathematics · Definite Integration · Multiple correct
Q35.The option(s) with the values of a and $L$ that satisfy the following equation is (are) $\frac{0 \int 4 π e ^{t} ( s i n ^{6} a t + c o s ^{4} a t ) d t}{0 \int π e ^{t} ( s i n ^{6} a t + c o s ^{4} a t ) d t} = L ?$ …
Mathematics · Definite Integration · Multiple correct
Q36.Let $f^{'} (x) = \frac{192 x ^{3}}{2 + s i n ^{4} π x}$ for all $x \in R$ with $f (\frac{1}{2}) = 0$ . If $m \leq 1/2 \int 1 f (x) d x \leq M,$ then the possible values of $m$ and…
Mathematics · Definite Integration · MCQ
Q37.Let $F : R \to R$ be a thrice differentiable function. Suppose that $F (1) = 0, F (3) = - 4$ and $F (x) < 0$ for all $x \in (\frac{1}{2}, 3) .$ Let $f (x) = x F (x)$ …
Mathematics · Application of Integration · Multiple correct
Q38.Let $F : R \to R$ be a thrice differentiable function. Suppose that $F (1) = 0, F (3) = - 4$ and $F^{'} (x) < 0$ for all $x \in (\frac{1}{2}, 3) .$ Let $f (x) = x F (x)$ …
Mathematics · Differentiation · Multiple correct
Q39.If $α = 0 \int 1 (e^{9 x + 3 t a n^{- 1} x}) (\frac{12 + 9 x ^{2}}{1 + x ^{2}}) d x$ where $tan^{- 1} x$ takes only principal values, then the value of $(lo g_{e} ∣ 1 + α ∣ - \frac{3 π}{4})$ …
Mathematics · Definite Integration · Numerical
Q40.Let m and n be two positive integers greater than 1. If $α \to 0 lim (\frac{e ^{c o s (α^{n})} - e}{α ^{m}}) = - (\frac{e}{2})$ then the value of $\frac{m}{n}$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q41.Consider a uniform spherical charge distribution of radius $R_{1}$ centred at the origin $O .$ In this distribution, a spherical cavity of radius $R_{2},$ centred at $P$ with distance $O P = a = R_{1} - R_{2}$ (see figure) is made. If the… Includes diagram
Physics · Electrostatics · Multiple correct
Q42.A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)
Physics · Properties of Matter · Multiple correct
Q43.The densities of two solid spheres A and B of the same radii R vary with radial distance r as $ρ_{A} (r) = k (\frac{r}{R})$ and $ρ_{B} (r) = k (\frac{r}{R})^{5}$ , , respectively, where k is a constant.…
Physics · Rotational Motion · Numerical
Q44.The energy of a system as a function of time t is given as E(t) = $A^{2} exp (- α t)$ , where $α = 0.2 s^{- 1}$ . The measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %,…
Physics · Units and Measurements · Numerical
Q45.In terms of potential difference V, electric current I, permittivity $ε_{0}$ , permeability $μ_{0}$ and speed of light c, the dimensionally correct equation(s) is(are) :
Physics · Electromagnetic Waves · Multiple correct
Q46.Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, $\frac{π}{3}, \frac{2 π}{3}$ and $π$ . When they are superposed, the intensity of the resulting wave is nI0. The value of n is
Physics · Waves · Numerical
Q47.For a radioactive material, its activity A and rate of change of its activity R are defined as $A = - \frac{d N}{d t}$ and $R = - \frac{d A}{d t}$ , where N(t) is the number of nuclei at time t. Two radioactive source P(mean life…
Physics · Atoms and Nuclei · Numerical
Q48.A monochromatic beam of light is incident at 60 $^{\circ}$ on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle $θ$ (n) with the normal (see figure). For n = $3$ the value of $θ$ … Includes diagram
Physics · Geometrical Optics · Numerical
Q49.In the following circuit, the current through the resistor R(=2 $Ω$ ) is I amperes. The value of I is : Includes diagram
Physics · Current Electricity · Numerical
Q50.An electron in an excited state of Li2+ ion has angular momentum $\frac{3 h}{2 π}$ . The de Broglie wavelength of the electron in this state is p $π$ a0 (where a0 is the Bohr radius). The value of p is
Physics · Dual Nature of Radiation · Numerical
Q51.A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to… Includes diagram
Physics · Gravitation · Numerical
Q52.In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then, the correct statements is/are Includes diagram
Physics · Properties of Matter · Multiple correct
Q53.A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities ( $ε$ 1 = 2 and $ε$ 2 = 4) are introduced between the two… Includes diagram
Physics · Capacitor · Multiple correct
Q54.An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then… Includes diagram
Physics · Heat and Thermodynamics · Multiple correct
Q55.A fission reaction is given by $_{92}^{236} U \to_{54}^{140} X e +_{38}^{94} S r + x + y$ , where x and y are two particles. Considering $_{92}^{236} U$ to be at rest, the kinetic energies of the products are denoted by $K_{X e}, K_{S r}, K_{x} (2 M e V)$ …
Physics · Atoms and Nuclei · Multiple correct
Q56.Two spheres P and Q for equal radii have densities $ρ$ 1 and $ρ$ 2, respectively. The spheres are connected by a massless string and placed in liquids L1 and L2 of densities $σ$ 1 and $σ$ 2 and viscosities $η_{1}$ and $η_{2}$ … Includes diagram
Physics · Properties of Matter · Multiple correct
Q57.Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n1 surrounded by a medium of lower refractive index n2. The light guidance in the structure takes… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q58.Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n1 surrounded by a medium of lower refractive index n2. The light guidance in the structure takes… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q59.In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field B is applied on the… Includes diagram
Physics · Magnetism · Multiple correct
Q60.In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field B is applied on the… Includes diagram
Physics · Magnetism · Multiple correct