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2022 · Shift 2

54 questions · JEE Advanced

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2022 · Shift 2

2022 · Shift 2

54 questions · JEE Advanced

Chemistry18 questions Mathematics18 questions Physics18 questions

Ionic EquilibriumChemistry · 1 questions SolutionsChemistry · 1 questions ElectrochemistryChemistry · 1 questions D and F Block ElementsChemistry · 2 questions HydrocarbonsChemistry · 4 questions Some Basic Concepts of ChemistryChemistry · 1 questions ThermodynamicsChemistry · 1 questions P Block ElementsChemistry · 3 questions Isolation of ElementsChemistry · 1 questions PolymersChemistry · 1 questions Solid StateChemistry · 1 questions BiomoleculesChemistry · 1 questions Trigonometric Functions and EquationsMathematics · 2 questions Differential EquationsMathematics · 2 questions Definite IntegrationMathematics · 1 questions Quadratic Equation and InequalitiesMathematics · 1 questions Limits Continuity and DifferentiabilityMathematics · 2 questions Matrices and DeterminantsMathematics · 2 questions HyperbolaMathematics · 1 questions Application of IntegrationMathematics · 1 questions Application of DerivativesMathematics · 1 questions Complex NumbersMathematics · 1 questions CircleMathematics · 1 questions Vector AlgebraMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions ProbabilityMathematics · 1 questions Simple Harmonic MotionPhysics · 2 questions Atoms and NucleiPhysics · 1 questions Current ElectricityPhysics · 2 questions Units and MeasurementsPhysics · 2 questions Geometrical OpticsPhysics · 2 questions ElectrostaticsPhysics · 3 questions Properties of MatterPhysics · 1 questions Wave OpticsPhysics · 1 questions Heat and ThermodynamicsPhysics · 1 questions Rotational MotionPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions MagnetismPhysics · 1 questions

Q1.Concentration of $H_{2} SO_{4}$ and $Na_{2} SO_{4}$ in a solution is $1 M$ and $1.8 \times 1 0^{- 2} M$ , respectively. Molar solubility of $PbSO_{4}$ in the same solution is $X \times 1 0^{- Y} M$ …
Chemistry · Ionic Equilibrium · Numerical
Q2.An aqueous solution is prepared by dissolving $1.8 kg$ of an ionic salt in $3 5^{\circ} C$ of water at $3 5^{\circ} C$ . The salt remains $90%$ dissociated in the solution. The vapour pressure of the solution is $59.724 mm$ …
Chemistry · Solutions · Numerical
Q3.Consider the strong electrolytes $Z_{m} X_{n}, U_{m} Y_{p}$ and $V_{m} X_{n}$ . Limiting molar conductivity ( $Λ^{0}$ ) of $U_{m} Y_{p}$ and $V_{m} X_{n}$ are 250… Includes table Includes diagram
Chemistry · Electrochemistry · Numerical
Q4.The reaction of $Xe$ and $O_{2} F_{2}$ gives a $Xe$ compound $P$ . The number of moles of $HF$ produced by the complete hydrolysis of $P$ of $P$ is …
Chemistry · D and F Block Elements · Numerical
Q5.Thermal decomposition of $AgNO_{3}$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is …
Chemistry · D and F Block Elements · Numerical
Q6.The number of isomeric tetraenes (NOT containing $s p$ -hybridized carbon atoms) that can be formed from the following reaction sequence is . Includes diagram
Chemistry · Hydrocarbons · Numerical
Q7.The number of $- CH_{2} -$ (methylene) groups in the product formed from the following reaction sequence is . Includes diagram
Chemistry · Hydrocarbons · Numerical
Q8.The total number of chiral molecules formed from one molecule of $P$ on complete ozonolysis $(O_{3}, Zn / H_{2} O)$ is . Includes diagram
Chemistry · Hydrocarbons · Numerical
Q9.To check the principle of multiple proportions, a series of pure binary compounds $(P_{m} Q_{n})$ were analyzed and their composition is tabulated below. The correct option(s) is(are) Includes table
Chemistry · Some Basic Concepts of Chemistry · Multiple correct
Q10.The correct option(s) about entropy (S) is(are) $F =$ gas constant, $F =$ Faraday constant, $T =$ Temperature $]$
Chemistry · Thermodynamics · Multiple correct
Q11.The compound(s) which react(s) with $NH_{3}$ to give boron nitride (BN) is(are)
Chemistry · P Block Elements · Multiple correct
Q12.The correct option(s) related to the extraction of iron from its ore in the blast furnace operating in the temperature range $900 - 1500 K$ is(are)
Chemistry · Isolation of Elements · Multiple correct
Q13.Considering the following reaction sequence, the correct statement(s) is(are) Includes diagram
Chemistry · Hydrocarbons · Multiple correct
Q14.Among the following, the correct statement(s) about polymers is(are)
Chemistry · Polymers · Multiple correct
Q15.Atom $X$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to
Chemistry · Solid State · MCQ
Q16.The reaction of $HClO_{3}$ with $HCl$ gives a paramagnetic gas, which upon reaction with $O_{3}$ produces
Chemistry · P Block Elements · MCQ
Q17.The reaction of $Pb (NO_{3})_{2}$ and $NaCl$ in water produces a precipitate that dissolves upon the addition of $HCl$ of appropriate concentration. The dissolution of the precipitate is due to…
Chemistry · P Block Elements · MCQ
Q18.Treatment of D-glucose with aqueous $NaOH$ results in a mixture of monosaccharides, which are
Chemistry · Biomolecules · MCQ
Q19.Let $α$ and $β$ be real numbers such that $- \frac{π}{4} < β < 0 < α < \frac{π}{4}$ . If $sin (α + β) = \frac{1}{3}$ and $cos (α - β) = \frac{2}{3}$ , then the greatest integer less than or equal to $(\frac{s i n α}{c o s β} + \frac{c o s β}{s i n α} + \frac{c o s α}{s i n β} + \frac{s i n β}{c o s α})^{2}$ …
Mathematics · Trigonometric Functions and Equations · Numerical
Q20.If $y (x)$ is the solution of the differential equation $x d y - (y^{2} - 4 y) d x = 0 for x > 0, y (1) = 2,$ and the slope of the curve $y = y (x)$ is never zero, then the value of $10 y (2)$ is
Mathematics · Differential Equations · Numerical
Q21.The greatest integer less than or equal to $\int_{1}^{2} lo g_{2} (x^{3} + 1) d x + \int_{1}^{l o g_{2} 9} (2^{x} - 1)^{\frac{1}{3}} d x$ is .
Mathematics · Definite Integration · Numerical
Q22.The product of all positive real values of $x$ satisfying the equation $x^{(16 (l o g_{5} x)^{3} - 68 l o g_{5} x)} = 5^{- 16}$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q23.If $β = x \to 0 lim \frac{e ^{x^{3}} - ( 1 - x ^{3} ) ^{\frac{1}{3}} + ( ( 1 - x ^{2} ) ^{\frac{1}{2}} - 1 ) s i n x}{x s i n ^{2} x},$ then the value of $6 β$ is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q24.Let $β$ be a real number. Consider the matrix $A = β 23 011 1 - 2 - 2$ If $A^{7} - (β - 1) A^{6} - β A^{5}$ is a singular matrix, then the…
Mathematics · Matrices and Determinants · Numerical
Q25.Consider the hyperbola $\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1$ with foci at $S$ and $S_{1}$ , where $S$ lies on the positive $x$ -axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $∠ S P S_{1} = α$ , with $α < \frac{π}{2}$ …
Mathematics · Hyperbola · Numerical
Q26.Consider the functions $f, g : R \to R$ defined by $f (x) = x^{2} + \frac{5}{12} and g (x) = {2 (1 - \frac{4∣ x ∣}{3}), 0, ∣ x ∣ \leq \frac{3}{4} ∣ x ∣ > \frac{3}{4}$ …
Mathematics · Application of Integration · Numerical
Q27.Let $P QR S$ be a quadrilateral in a plane, where $QR = 1, ∠ P QR = ∠ QR S = 7 0^{\circ}, ∠ P QS = 1 5^{\circ}$ and $∠ P R S = 4 0^{\circ}$ . If $∠ R P S = θ^{\circ}, P Q = α$ and $P S = β$ , then the interval(s)…
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q28.Let $α = k = 1 \sum \infty sin^{2 k} (\frac{π}{6})$ Let $g : [0, 1] \to R$ be the function defined by $g (x) = 2^{α x} + 2^{α (1 - x)} .$ Then, which of the following statements is/are…
Mathematics · Application of Derivatives · Multiple correct
Q29.Let $\overset{z}{ˉ}$ denote the complex conjugate of a complex number $z$ . If $z$ is a non-zero complex number for which both real and imaginary parts of $(\overset{z}{ˉ})^{2} + \frac{1}{z ^{2}}$ are integers, then which of the following is/are possible…
Mathematics · Complex Numbers · Multiple correct
Q30.Let $G$ be a circle of radius $R > 0$ . Let $G_{1}, G_{2}, \dots, G_{n}$ be $n$ circles of equal radius $r > 0$ . Suppose each of the $n$ circles $G_{1}, G_{2}, \dots, G_{n}$ touches the circle $G$ externally. Also, for $i = 1, 2, \dots, n - 1$ …
Mathematics · Circle · Multiple correct
Q31.Let $\overset{}{^}, \overset{}{^}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let $a = 3 \overset{}{^} + \overset{}{^} - \hat{k}, b = \overset{}{^} + b_{2} \overset{}{^} + b_{3} \hat{k}, b_{2}, b_{3} \in R, c = c_{1} \overset{}{^} + c_{2} \overset{}{^} + c_{3} \hat{k}, c_{1}, c_{2}, c_{3} \in R$ …
Mathematics · Vector Algebra · Multiple correct
Q32.For $x \in R$ , let the function $y (x)$ be the solution of the differential equation $\frac{d y}{d x} + 12 y = cos (\frac{π}{12} x), y (0) = 0$ Then, which of the following statements is/are TRUE ?
Mathematics · Differential Equations · Multiple correct
Q33.Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue…
Mathematics · Permutations and Combinations · MCQ
Q34.If $M = (\frac{5}{2} - \frac{3}{2} \frac{3}{2} - \frac{1}{2})$ , then which of the following matrices is equal to $M^{2022} ?$
Mathematics · Matrices and Determinants · MCQ
Q35.Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 green and 3 yellow balls, Box-IV contains 10 green, 16 orange and 6 white balls. A ball is chosen…
Mathematics · Probability · MCQ
Q36.For positive integer $n$ , define $f (n) = n + \frac{16 + 5 n - 3 n ^{2}}{4 n + 3 n ^{2}} + \frac{32 + n - 3 n ^{2}}{8 n + 3 n ^{2}} + \frac{48 - 3 n - 3 n ^{2}}{12 n + 3 n ^{2}} + \dots + \frac{25 n - 7 n ^{2}}{7 n ^{2}} .$ Then, the value of $n \to \infty lim f (n)$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.A particle of mass $F = - k (x \overset{}{^} + y \overset{}{^}) kg m s^{- 2}$ is subjected to a force which depends on the position as $F = - k (x \overset{}{^} + y \overset{}{^}) kg m s^{- 2}$ with $k = 1 kg s^{- 2}$ . At time $t = 0$ , the…
Physics · Simple Harmonic Motion · Numerical
Q38.In a radioactive decay chain reaction, $_{90}^{230} Th$ nucleus decays into $_{84}^{214} Po$ nucleus. The ratio of the number of $α$ to number of $β^{-}$ particles emitted in this process is …
Physics · Atoms and Nuclei · Numerical
Q39.Two resistances $R_{1} = X Ω$ and $R_{2} = 1Ω$ are connected to a wire $A B$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $A$ at $A$ to $1 mm$ at… Includes diagram
Physics · Current Electricity · Numerical
Q40.In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$ , electron mass $m_{e}$ , Planck's constant $h$ , and Coulomb's constant $k = \frac{1}{4 π ϵ _{0}}$ , where $ϵ_{0}$ is the…
Physics · Units and Measurements · Numerical
Q41.Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h = \frac{1}{3} cm$ , and the second and third layers are of equal thickness $d = \frac{3 - 1}{2} cm$ … Includes diagram
Physics · Geometrical Optics · Numerical
Q42.A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$ , and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 ϵ _{0}}$ … Includes diagram
Physics · Electrostatics · Numerical
Q43.On a frictionless horizontal plane, a bob of mass $m = 0.1 kg$ is attached to a spring with natural length $l_{0} = 0.1 m$ . The spring constant is $k_{1} = 0.009 Nm^{- 1}$ when the length of the spring $l > l_{0}$ …
Physics · Simple Harmonic Motion · Numerical
Q44.An object and a concave mirror of focal length $f = 10 cm$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0} = 15 cm s^{- 1}$ towards the mirror with respect… Includes diagram
Physics · Geometrical Optics · Numerical
Q45.In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_{A} = 1$ , within which the electrostatic charge density varies with the radial distance $r$ from the center as $ρ_{A} = k r$ , where $k$ is positive. In the… Includes diagram
Physics · Electrostatics · Multiple correct
Q46.In Circuit-1 and Circuit- 2 shown in the figures, $R_{1} = 1 Ω, R_{2} = 2 Ω$ and $R_{3} = 3 Ω$ . $P_{1}$ and $P_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $S_{1}$ and… Includes diagram
Physics · Current Electricity · Multiple correct
Q47.A bubble has surface tension $S$ . The ideal gas inside the bubble has ratio of specific heats $γ = \frac{5}{3}$ . The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a 1}$ …
Physics · Properties of Matter · Multiple correct
Q48.A disk of radius $R$ with uniform positive charge density $σ$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$ -axis is $V (z) = \frac{σ}{2 ϵ _{0}} (R^{2} + z^{2} - z) .$ …
Physics · Electrostatics · Multiple correct
Q49.A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_{2}$ . The other slit is at the interface of this medium with another medium 1 of refractive index $n_{1} (e q n_{2})$ . The line… Includes diagram
Physics · Wave Optics · Multiple correct
Q50.In the given $P - V$ diagram, a monoatomic gas $(γ = \frac{5}{3})$ is first compressed adiabatically from state $A$ to state $B$ . Then it expands isothermally from state $B$ to state $C$ . [Given: $(\frac{1}{3})^{0.6} ≃ 0.5, ln 2 ≃ 0.7$ … Includes diagram
Physics · Heat and Thermodynamics · Multiple correct
Q51.A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$ , as shown in the figure. A… Includes diagram
Physics · Rotational Motion · MCQ
Q52.When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $0.6 V$ . This potential drops to $0.6 V$ if another source with wavelength four…
Physics · Dual Nature of Radiation · MCQ
Q53.Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$ . The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two… Includes table
Physics · Units and Measurements · MCQ
Q54.Which one of the following options represents the magnetic field $B$ at $O$ due to the current flowing in the given wire segments lying on the $x y$ plane? Includes diagram
Physics · Magnetism · MCQ