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2021 · Shift 2

57 questions · JEE Advanced

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2021 · Shift 2

2021 · Shift 2

57 questions · JEE Advanced

Chemistry19 questions Mathematics19 questions Physics19 questions

Compounds Containing NitrogenChemistry · 4 questions Chemical Kinetics and Nuclear ChemistryChemistry · 1 questions ElectrochemistryChemistry · 3 questions Coordination CompoundsChemistry · 1 questions P Block ElementsChemistry · 1 questions Redox ReactionsChemistry · 3 questions Basics of Organic ChemistryChemistry · 2 questions Salt AnalysisChemistry · 2 questions ThermodynamicsChemistry · 1 questions Structure of AtomChemistry · 1 questions Permutations and CombinationsMathematics · 1 questions Properties of TriangleMathematics · 1 questions Definite IntegrationMathematics · 6 questions Application of IntegrationMathematics · 3 questions Vector AlgebraMathematics · 1 questions ParabolaMathematics · 1 questions CircleMathematics · 4 questions ProbabilityMathematics · 1 questions EllipseMathematics · 1 questions Impulse and MomentumPhysics · 3 questions WavesPhysics · 1 questions Geometrical OpticsPhysics · 1 questions Units and MeasurementsPhysics · 1 questions Atoms and NucleiPhysics · 1 questions MagnetismPhysics · 3 questions Heat and ThermodynamicsPhysics · 4 questions Alternating CurrentPhysics · 2 questions Current ElectricityPhysics · 1 questions GravitationPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions

Q1.The reaction sequence(s) that would lead to o-xylene as the major product is(are)
Chemistry · Compounds Containing Nitrogen · Multiple correct
Q2.Correct option(s) for the following sequence of reactions is(are) Includes diagram
Chemistry · Compounds Containing Nitrogen · Multiple correct
Q3.For the following reaction, $2 X + Y k P$ the rate of reaction is $\frac{d [ P ]}{d t} = k [X]$ . Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The…
Chemistry · Chemical Kinetics and Nuclear Chemistry · Multiple correct
Q4.Some standard electrode potentials at 298 K are given below : $P b^{2 +}$ / $P b$ = $-$ 0.13 V $N i^{2 +}$ / $N i$ = $-$ 0.24 V $C d^{2 +}$ / $C d$ = $-$ 0.40 V $F e^{2 +}$ / $F e$ = $-$ 0.44 V To a solution containing 0.001 M of $X^{2 +}$ and 0.1 M of $Y^{2 +}$ …
Chemistry · Electrochemistry · Multiple correct
Q5.The pair(s) of complexes wherein both exhibit tetrahedral geometry is(are) (Note : py = pyridine) Given : Atomic numbers of Fe, Co, Ni and Cu are 26, 27, 28 and 29, respectively)
Chemistry · Coordination Compounds · Multiple correct
Q6.The correct statement(s) related to oxoacids of phosphorous is(are)
Chemistry · P Block Elements · Multiple correct
Q7.At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $\times$ 102 S cm2 mol $-$ 1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $α$ and the molar conductivity is y $\times$ 102 S cm2…
Chemistry · Electrochemistry · Numerical
Q8.At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 $\times$ 102 S cm2 mol $-$ 1. At 298 K, for an aqueous solution of the acid the degree of dissociation is $α$ and the molar conductivity is y $\times$ 102 S cm2…
Chemistry · Electrochemistry · Numerical
Q9.Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively). (Use Molar masses…
Chemistry · Compounds Containing Nitrogen · Numerical
Q10.Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively). (Use Molar masses…
Chemistry · Compounds Containing Nitrogen · Numerical
Q11.A sample (5.6 g) containing iron is completely dissolved in cold dilute $H C l$ to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M $K M n O_{4}$ solution to reach the end point. Number of moles of $F e^{2 +}$ …
Chemistry · Redox Reactions · Numerical
Q12.A sample (5.6 g) containing iron is completely dissolved in cold dilute $H C l$ to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M $K M n O_{4}$ solution to reach the end point. Number of moles of $F e^{2 +}$ …
Chemistry · Redox Reactions · Numerical
Q13.The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond… Includes table Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q14.The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond… Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q15.The reaction of $K_{3} [F e (C N)_{6}]$ with freshly prepared $F e S O_{4}$ solution produces a dark blue precipitate called Turnbull's blue. Reaction of $K_{4} [F e (C N)_{6}]$ with the $F e S O_{4}$ solution in complete absence of air produces a white precipitate…
Chemistry · Salt Analysis · MCQ
Q16.The reaction of $K_{3} [F e (C N)_{6}]$ with freshly prepared $F e S O_{4}$ solution produces a dark blue precipitate called Turnbull's blue. Reaction of $K_{4} [F e (C N)_{6}]$ with the $F e S O_{4}$ solution in complete absence of air produces a white precipitate…
Chemistry · Salt Analysis · MCQ
Q17.One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $ln \frac{V _{3}}{V _{2}}$ is .… Includes diagram
Chemistry · Thermodynamics · Numerical
Q18.Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s $-$ 1) of He atom after the photon absorption is . (Assume : Momentum is conserved when photon is…
Chemistry · Structure of Atom · Numerical
Q19.Ozonolysis of $C l O_{2}$ produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is .
Chemistry · Redox Reactions · Numerical
Q20.Let $S_{1} = {(i, j, k) : i, j, k \in {1, 2, ...., 10}}$ , $S_{2} = {(i, j) : 1 \leq i < j + 2 \leq 10, i, j \in {1, 2, ..., 10}}$ , $S_{3} = {(i, j, k, l) : 1 \leq i < j < k < l, i, j, k, l \in {1, 2, ..., 10}}$ …
Mathematics · Permutations and Combinations · Multiple correct
Q21.Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?
Mathematics · Properties of Triangle · Multiple correct
Q22.Let $f : [- \frac{π}{2}, \frac{π}{2}] \to R$ be a continuous function such that $f (0) = 1$ and $\int_{0}^{\frac{π}{3}} f (t) d t = 0$ . Then which of the following statements is(are) TRUE?
Mathematics · Definite Integration · Multiple correct
Q23.For any real numbers $α$ and $β$ , let $y_{α, β} (x)$ , x $\in$ R, be the solution of the differential equation $\frac{d y}{d x} + α y = x e^{β x}, y (1) = 1$ . Let $S = {y_{α, β} (x) : α, β \in R}$ …
Mathematics · Application of Integration · Multiple correct
Q24.Let O be the origin and $O A = 2 i + 2 j + k$ and $O B = i - 2 j + 2 k$ and $O C = \frac{1}{2} (O B - λ O A)$ …
Mathematics · Vector Algebra · Multiple correct
Q25.Let E denote the parabola y2 = 8x. Let P = ( $-$ 2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is(are) TRUE?
Mathematics · Parabola · Multiple correct
Q26.Consider the region R = {(x, y) $\in$ R $\times$ R : x $\geq$ 0 and y2 $\leq$ 4 $-$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles…
Mathematics · Circle · Numerical
Q27.Consider the region R = {(x, y) $\in$ R $\times$ R : x $\geq$ 0 and y2 $\leq$ 4 $-$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles…
Mathematics · Circle · Numerical
Q28.Let f1 : (0, $\infty$ ) $\to$ R and f2 : (0, $\infty$ ) $\to$ R be defined by $f_{1} (x) = 0 \int x j = 1 \prod 21 (t - j)^{j} d t$ , x > 0 and $f_{2} (x) = 98 (x - 1)^{50} - 600 (x - 1)^{49} + 2450, x > 0$ ,…
Mathematics · Application of Integration · Numerical
Q29.Let f1 : (0, $\infty$ ) $\to$ R and f2 : (0, $\infty$ ) $\to$ R be defined by $f_{1} (x) = 0 \int x j = 1 \prod 21 (t - j)^{j} d t$ , x > 0 and $f_{2} (x) = 98 (x - 1)^{50} - 600 (x - 1)^{49} + 2450, x > 0$ ,…
Mathematics · Application of Integration · Numerical
Q30.Let $g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2$ , and $f : [\frac{π}{8}, \frac{3 π}{8}] \to R$ be functions such that $g_{1} (x) = 1, g_{2} (x) = ∣4 x - π ∣$ and $f (x) = sin^{2} x$ , for all $x \in [\frac{π}{8}, \frac{3 π}{8}]$ …
Mathematics · Definite Integration · Numerical
Q31.Let $g_{i} : [\frac{π}{8}, \frac{3 π}{8}] \to R, i = 1, 2$ , and $f : [\frac{π}{8}, \frac{3 π}{8}] \to R$ be functions such that $g_{1} (x) = 1, g_{2} (x) = ∣4 x - π ∣$ and $f (x) = sin^{2} x$ , for all $x \in [\frac{π}{8}, \frac{3 π}{8}]$ …
Mathematics · Definite Integration · Numerical
Q32.Let $M = {(x, y) \in R \times R : x^{2} + y^{2} \leq r^{2}}$ , where r > 0. Consider the geometric progression $a_{n} = \frac{1}{2 ^{n - 1}}$ , n = 1, 2, 3, ...... . Let S0 = 0 and for n $\geq$ 1, let Sn denote the sum of the first n…
Mathematics · Circle · MCQ
Q33.Let $M = {(x, y) \in R \times R : x^{2} + y^{2} \leq r^{2}}$ , where r > 0. Consider the geometric progression $a_{n} = \frac{1}{2 ^{n - 1}}$ , n = 1, 2, 3, ...... . Let S0 = 0 and for n $\geq$ 1, let Sn denote the sum of the first n…
Mathematics · Circle · MCQ
Q34.Let $ψ_{1} : [0, \infty) \to R$ , $ψ_{2} : [0, \infty) \to R$ , f : (0, $\infty$ ) $\to$ R and g : [0, $\infty$ ) $\to$ R be functions such that f(0) = g(0) = 0, $ψ_{1} (x) = e^{- x} + x, x \geq 0$ , $ψ_{2} (x) = x^{2} - 2 x - 2 e^{- x} + 2, x \geq 0$ …
Mathematics · Definite Integration · MCQ
Q35.Let $ψ_{1} : [0, \infty) \to R$ , $ψ_{2} : [0, \infty) \to R$ , f : (0, $\infty$ ) $\to$ R and g : [0, $\infty$ ) $\to$ R be functions such that f(0) = g(0) = 0, $ψ_{1} (x) = e^{- x} + x, x \geq 0$ , $ψ_{2} (x) = x^{2} - 2 x - 2 e^{- x} + 2, x \geq 0$ …
Mathematics · Definite Integration · MCQ
Q36.A number of chosen at random from the set {1, 2, 3, ....., 2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is .
Mathematics · Probability · Numerical
Q37.Let E be the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ . For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment…
Mathematics · Ellipse · Numerical
Q38.For any real number x, let [ x ] denote the largest integer less than or equal to x. If $I = 0 \int 10 [\frac{10 x}{x + 1}] d x$ , then the value of 9I is .
Mathematics · Definite Integration · Numerical
Q39.One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge… Includes diagram
Physics · Impulse and Momentum · Multiple correct
Q40.A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and f0 is the fundamental frequency of the…
Physics · Waves · Multiple correct
Q41.For a prism of prism angle $θ$ = 60 $^{\circ}$ , the refractive indices of the left half and the right half are, respectively, n1 and n2 (n2 $\geq$ n1) as shown in the figure. The angle of incidence i is chosen such that the incident… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q42.A physical quantity $S$ is defined as $S = (E \times B) / μ_{0}$ , where $E$ is electric field, $B$ is magnetic field and $μ$ 0 is the…
Physics · Units and Measurements · Multiple correct
Q43.A heavy nucleus N, at rest, undergoes fission N $\to$ P + Q, where P and Q are two lighter nuclei. Let $δ$ = MN $-$ MP $-$ MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and…
Physics · Atoms and Nuclei · Multiple correct
Q44.Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the… Includes diagram
Physics · Magnetism · Multiple correct
Q45.A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5… Includes diagram
Physics · Heat and Thermodynamics · Numerical
Q46.A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5… Includes diagram
Physics · Heat and Thermodynamics · Numerical
Q47.A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is…
Physics · Impulse and Momentum · Numerical
Q48.A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is…
Physics · Impulse and Momentum · Numerical
Q49.In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance C $μ$ F across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no…
Physics · Alternating Current · Numerical
Q50.In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance C $μ$ F across a 200 V, 50 Hz supply. The power consumed by the lamp is 500 W while the voltage drop across it is 100 V. Assume that there is no…
Physics · Alternating Current · Numerical
Q51.A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop… Includes diagram
Physics · Magnetism · MCQ
Q52.A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop… Includes diagram
Physics · Magnetism · MCQ
Q53.A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant… Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q54.A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant… Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q55.In order to measure the internal resistance r1 of a cell of emf E, a meter bridge of wire resistance R0 = 50 $Ω$ , a resistance R0/2, another cell of emf E/2 (internal resistance r) and a galvanometer G are used in a circuit, as shown… Includes diagram
Physics · Current Electricity · Numerical
Q56.The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and MS is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits…
Physics · Gravitation · Numerical
Q57.In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, EQ and ER, respectively, and they are related by EP = 2EQ = 2ER. In this experiment, the same source of monochromatic light is…
Physics · Dual Nature of Radiation · Numerical