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2024 · Shift 2

51 questions · JEE Advanced

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2024 · Shift 2

2024 · Shift 2

51 questions · JEE Advanced

Chemistry17 questions Mathematics17 questions Physics17 questions

Structure of AtomChemistry · 1 questions Solid StateChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 4 questions P Block ElementsChemistry · 2 questions ElectrochemistryChemistry · 1 questions Compounds Containing NitrogenChemistry · 1 questions Surface ChemistryChemistry · 1 questions SolutionsChemistry · 1 questions BiomoleculesChemistry · 1 questions Chemical Kinetics and Nuclear ChemistryChemistry · 1 questions Coordination CompoundsChemistry · 1 questions Salt AnalysisChemistry · 2 questions Inverse Trigonometric FunctionsMathematics · 1 questions Application of IntegrationMathematics · 2 questions Limits Continuity and DifferentiabilityMathematics · 3 questions 3D GeometryMathematics · 1 questions ParabolaMathematics · 2 questions FunctionsMathematics · 2 questions ProbabilityMathematics · 1 questions Vector AlgebraMathematics · 1 questions Permutations and CombinationsMathematics · 2 questions Definite IntegrationMathematics · 2 questions Electromagnetic InductionPhysics · 1 questions GravitationPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions MagnetismPhysics · 2 questions ElectrostaticsPhysics · 3 questions Properties of MatterPhysics · 1 questions Units and MeasurementsPhysics · 1 questions MotionPhysics · 1 questions Geometrical OpticsPhysics · 1 questions Heat and ThermodynamicsPhysics · 1 questions Wave OpticsPhysics · 2 questions Simple Harmonic MotionPhysics · 2 questions

Q1.According to Bohr's model, the highest kinetic energy is associated with the electron in the
Chemistry · Structure of Atom · MCQ
Q2.In a metal deficient oxide sample, $M_{x} Y_{2} O_{4}$ ( $M$ and $Y$ are metals), $M$ is present in both +2 and +3 oxidation states and $Y$ is in +3 oxidation state. If the…
Chemistry · Solid State · MCQ
Q3.In the following reaction sequence, the major product $Q$ is Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are
Chemistry · P Block Elements · MCQ
Q5.An aqueous solution of hydrazine $(N_{2} H_{4})$ is electrochemically oxidized by $O_{2}$ , thereby releasing chemical energy in the form of electrical energy. One of the products generated from the…
Chemistry · Electrochemistry · Multiple correct
Q6.The option(s) with correct sequence of reagents for the conversion of $P$ to $Q$ is(are) Includes diagram
Chemistry · Compounds Containing Nitrogen · Multiple correct
Q7.The compound(s) having peroxide linkage is(are)
Chemistry · P Block Elements · Multiple correct
Q8.To form a complete monolayer of acetic acid on $100 mL$ of charcoal, $0.5 M$ of $0.5 M$ acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40…
Chemistry · Surface Chemistry · Numerical
Q9.Vessel-1 contains $w_{2} g$ of a non-volatile solute $X$ dissolved in $w_{1} g$ of water. Vessel- 2 contains $w_{2} g$ of another non-volatile solute $Y$ dissolved in $w_{1} g$ …
Chemistry · Solutions · Numerical
Q10.For a double strand DNA, one strand is given below: The amount of energy required to split the double strand DNA into two single strands is kcal $mol^{- 1}$ . [Given: Average energy per H-bond for… Includes diagram
Chemistry · Biomolecules · Numerical
Q11.A sample initially contains only $U$ -238 isotope of uranium. With time, some of the $U$ -238 radioactively decays into $Pb - 206$ while the rest of it remains undisintegrated. When the age of the sample is $P \times 1 0^{8}$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q12.Among $[Co (CN)_{4}]^{4 -}, [Co (CO)_{3} (NO)], XeF_{4}, [PCl_{4}]^{+}, [PdCl_{4}]^{2 -}, [ICl_{4}]^{-}, [Cu (CN)_{4}]^{3 -}$ …
Chemistry · Coordination Compounds · Numerical
Q13.An organic compound $P$ having molecular formula $C_{6} H_{6} O_{3}$ gives ferric chloride test and does not have intramolecular hydrogen bond. The compound $P$ reacts with 3 equivalents of $NH_{2} OH$ …
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q14.An organic compound $P$ with molecular formula $C_{9} H_{18} O_{2}$ decolorizes bromine water and also shows positive iodoform test. $P$ on ozonolysis followed by treatment with $H_{2} O_{2}$ …
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q15.An organic compound $P$ with molecular formula $C_{9} H_{18} O_{2}$ decolorizes bromine water and also shows positive iodoform test. $P$ on ozonolysis followed by treatment with $H_{2} O_{2}$ …
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q16.When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex $P$ is formed. In a strong acidic medium, the equilibrium shifts completely towards…
Chemistry · Salt Analysis · Numerical
Q17.When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex $P$ is formed. In a strong acidic medium, the equilibrium shifts completely towards…
Chemistry · Salt Analysis · Numerical
Q18.Considering only the principal values of the inverse trigonometric functions, the value of $tan (sin^{- 1} (\frac{3}{5}) - 2 cos^{- 1} (\frac{2}{5}))$ is
Mathematics · Inverse Trigonometric Functions · MCQ
Q19.Let $S = {(x, y) \in R \times R : x \geq 0, y \geq 0, y^{2} \leq 4 x, y^{2} \leq 12 - 2 x$ and $3 y + 8 x \leq 58}$ . If the area of the region $S$ is $α 2$ , then $α$ is equal…
Mathematics · Application of Integration · MCQ
Q20.Let $k \in R$ . If $x \to 0 + lim (sin (sin k x) + cos x + x)^{\frac{2}{x}} = e^{6}$ , then the value of $k$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q21.Let $f : R \to R$ be a function defined by $f (x) = {x^{2} sin (\frac{π}{x ^{2}}), 0, if x e q 0, if x = 0.$ Then which of the…
Mathematics · Limits Continuity and Differentiability · MCQ
Q22.Let $S$ be the set of all $(α, β) \in R \times R$ such that $x \to \infty lim \frac{s i n ( x ^{2} ) ( l o g _{e} x ) ^{α} s i n ( \frac{1}{x ^{2}} )}{x ^{α β} ( l o g _{e} ( 1 + x ) ) ^{β}} = 0.$ …
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q23.A straight line drawn from the point $P (1, 3, 2)$ , parallel to the line $\frac{x - 2}{1} = \frac{y - 4}{2} = \frac{z - 6}{1}$ , intersects the plane $L_{1} : x - y + 3 z = 6$ at the point $Q$ . Another straight line which passes through $Q$ and is perpendicular…
Mathematics · 3D Geometry · Multiple correct
Q24.Let $A_{1}, B_{1}, C_{1}$ be three points in the $x y$ -plane. Suppose that the lines $A_{1} C_{1}$ and $B_{1} C_{1}$ are tangents to the curve $y^{2} = 8 x$ at $A_{1}$ and $B_{1}$ , respectively. If $O = (0, 0)$ and $C_{1} = (- 4, 0)$ , then which of the following…
Mathematics · Parabola · Multiple correct
Q25.Let $f : R \to R$ be a function such that $f (x + y) = f (x) + f (y)$ for all $x, y \in R$ , and $g : R \to (0, \infty)$ be a function such that $g (x + y) = g (x) g (y)$ for all $x, y \in R$ . If $f (\frac{- 3}{5}) = 12$ …
Mathematics · Functions · Numerical
Q26.A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$ …
Mathematics · Probability · Numerical
Q27.Let the function $f : R \to R$ be defined by $f (x) = \frac{s i n x}{e ^{π x}} \frac{( x ^{2023} + 2024 x + 2025 )}{( x ^{2} - x + 3 )} + \frac{2}{e ^{π x}} \frac{( x ^{2023} + 2024 x + 2025 )}{( x ^{2} - x + 3 )} .$ …
Mathematics · Functions · Numerical
Q28.Let $p = 2 \hat{i} + \hat{j} + 3 \hat{k}$ and $q = \hat{i} - \hat{j} + \hat{k}$ . If for some real numbers $γ$ , and $γ$ , we have $15 \hat{i} + 10 \hat{j} + 6 \hat{k} = α (2 p + q) + β (p - 2 q) + γ (p \times q),$ …
Mathematics · Vector Algebra · Numerical
Q29.A normal with slope $\frac{1}{6}$ is drawn from the point $(0, - α)$ to the parabola $x^{2} = - 4 a y$ , where $a > 0$ . Let $L$ be the line passing through $(0, - α)$ and parallel to the directrix of the parabola. Suppose that $L$ …
Mathematics · Parabola · Numerical
Q30.Let the function $f : [1, \infty) \to R$ be defined by $f (t) = {(- 1)^{n + 1} \cdot 2 \frac{( 2 n + 1 - t )}{2} f (2 n - 1) + \frac{( t - ( 2 n - 1 ))}{2} f (2 n + 1) if t = 2 n - 1, n \in N if 2 n - 1 < t < 2 n + 1, n \in N$ …
Mathematics · Application of Integration · Numerical
Q31.Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $R$ has exactly 6 elements. ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ . Let $Y = {R \in X$ : The range of…
Mathematics · Permutations and Combinations · Numerical
Q32.Let $S = {1, 2, 3, 4, 5, 6}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $R$ has exactly 6 elements. ii. For each $(a, b) \in R$ , we have $∣ a - b ∣ \geq 2$ . Let $Y = {R \in X$ : The range of…
Mathematics · Permutations and Combinations · Numerical
Q33.Let $f : [0, \frac{π}{2}] \to [0, 1]$ be the function defined by $f (x) = sin^{2} x$ and let $g : [0, \frac{π}{2}] \to [0, \infty)$ be the function defined by $g (x) = \frac{π x}{2} - x^{2}$ .The value of $2 0 \int \frac{π}{2} f (x) g (x) d x - 0 \int \frac{π}{2} g (x) d x$ …
Mathematics · Definite Integration · Numerical
Q34.Let $f : [0, \frac{π}{2}] \to [0, 1]$ be the function defined by $f (x) = sin^{2} x$ and let $g : [0, \frac{π}{2}] \to [0, \infty)$ be the function defined by $g (x) = \frac{π x}{2} - x^{2}$ .The value of $\frac{16}{π ^{3}} 0 \int \frac{π}{2} f (x) g (x) d x$ …
Mathematics · Definite Integration · Numerical
Q35.A region in the form of an equilateral triangle (in $x - y$ plane) of height $L$ has a uniform magnetic field $B$ pointing in the $+ z$ -direction. A conducting loop $PQR$ , in the form of an equilateral triangle of the same… Includes diagram
Physics · Electromagnetic Induction · MCQ
Q36.A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M (≫ m)$ . The particle is moving in a circular orbit of radius $r_{0}$ with time period $T_{0}$ around the mass $M$ . Then, the particle is subjected…
Physics · Gravitation · MCQ
Q37.A metal target with atomic number $Z = 46$ is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio $r$ of the wavelengths of the $K_{α}$ -line and the cut-off is found to be $r = 2$ . If…
Physics · Dual Nature of Radiation · MCQ
Q38.A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_{0}$ , as… Includes diagram
Physics · Magnetism · MCQ
Q39.A small electric dipole $p_{0}$ , having a moment of inertia $I$ about its center, is kept at a distance $r$ from the center of a spherical shell of radius $R$ . The surface charge density $σ$ is uniformly distributed on the… Includes diagram
Physics · Electrostatics · Multiple correct
Q40.A table tennis ball has radius $(3/2) \times 1 0^{- 2} m$ and mass $(22/7) \times 1 0^{- 3} kg$ . It is slowly pushed down into a swimming pool to a depth of $d = 0.7 m$ below the water surface and then released…
Physics · Properties of Matter · Multiple correct
Q41.A positive, singly ionized atom of mass number $A_{M}$ is accelerated from rest by the voltage $w$ . Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_{0} = 0.1 \hat{k}$ Tesla, as shown… Includes diagram
Physics · Magnetism · Multiple correct
Q42.The dimensions of a cone are measured using a scale with a least count of $20.0 cm$ . The diameter of the base and the height are both measured to be $20.0 cm$ . The maximum percentage error in the determination of the…
Physics · Units and Measurements · Numerical
Q43.A ball is thrown from the location $(x_{0}, y_{0}) = (0, 0)$ of a horizontal playground with an initial speed $v_{0}$ at an angle $θ_{0}$ from the $+ x$ -direction. The ball is to be hit by a stone, which is thrown at the same time from…
Physics · Motion · Numerical
Q44.A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $θ$ at $P$ , as shown in the figure. When $θ = 3 0^{\circ}$ , then the electric flux through the curved surface of… Includes diagram
Physics · Electrostatics · Numerical
Q45.Two equilateral-triangular prisms $P_{1}$ and $P_{2}$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism $P_{1}$ at an angle of incidence $θ$ such that… Includes diagram
Physics · Geometrical Optics · Numerical
Q46.An infinitely long thin wire, having a uniform charge density per unit length of $5 nC / m$ , is passing through a spherical shell of radius $10 nC$ , as shown in the figure. A $10 nC$ charge is distributed… Includes diagram
Physics · Electrostatics · Numerical
Q47.A spherical soap bubble inside an air chamber at pressure $P_{0} = 1 0^{5} Pa$ has a certain radius so that the excess pressure inside the bubble is $Δ P = 144 Pa$ . Now, the chamber pressure is reduced to $8 P_{0} /27$ so…
Physics · Heat and Thermodynamics · Numerical
Q48.In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of $t$ . The distance between the slits at time $t$ is given by $d = (0.8 + 0.04 sin ω t) mm$ … Includes diagram
Physics · Wave Optics · Numerical
Q49.In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of $t$ . The distance between the slits at time $t$ is given by $d = (0.8 + 0.04 sin ω t) mm$ … Includes diagram
Physics · Wave Optics · Numerical
Q50.Two particles, 1 and 2, each of mass $m$ , are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_{0}$ , are oscillating with… Includes diagram
Physics · Simple Harmonic Motion · Numerical
Q51.Two particles, 1 and 2, each of mass $m$ , are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_{0}$ , are oscillating with… Includes diagram
Physics · Simple Harmonic Motion · Numerical