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2023 · Shift 2

51 questions · JEE Advanced

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2023 · Shift 2

2023 · Shift 2

51 questions · JEE Advanced

Chemistry17 questions Mathematics17 questions Physics17 questions

Chemical Bonding and Molecular StructureChemistry · 3 questions Surface ChemistryChemistry · 1 questions Haloalkanes and HaloarenesChemistry · 1 questions BiomoleculesChemistry · 1 questions Coordination CompoundsChemistry · 1 questions Solid StateChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 1 questions Some Basic Concepts of ChemistryChemistry · 1 questions Structure of AtomChemistry · 1 questions SolutionsChemistry · 1 questions Practical Organic ChemistryChemistry · 1 questions ThermodynamicsChemistry · 2 questions Compounds Containing NitrogenChemistry · 2 questions Differential EquationsMathematics · 2 questions ProbabilityMathematics · 4 questions Inverse Trigonometric FunctionsMathematics · 1 questions Vector AlgebraMathematics · 1 questions Matrices and DeterminantsMathematics · 2 questions Limits Continuity and DifferentiabilityMathematics · 1 questions DifferentiationMathematics · 1 questions Definite IntegrationMathematics · 1 questions CircleMathematics · 2 questions Properties of TriangleMathematics · 1 questions Trigonometric Functions and EquationsMathematics · 1 questions ElectrostaticsPhysics · 1 questions Units and MeasurementsPhysics · 1 questions Laws of MotionPhysics · 1 questions Heat and ThermodynamicsPhysics · 4 questions Geometrical OpticsPhysics · 1 questions Rotational MotionPhysics · 2 questions Electromagnetic WavesPhysics · 1 questions MagnetismPhysics · 1 questions WavesPhysics · 3 questions Properties of MatterPhysics · 1 questions Atoms and NucleiPhysics · 1 questions

Q1.The correct molecular orbital diagram for $F_{2}$ molecule in the ground state is :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q2.Consider the following statements related to colloids. (I) Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium. (II) For emulsions, both the dispersed phase and the dispersion medium are liquid.…
Chemistry · Surface Chemistry · MCQ
Q3.In the following reactions, $P, Q, R$ , and $S$ are the major products. The correct statement about $P, Q, R$ , and $S$ is : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q4.A disaccharide $X$ cannot be oxidised by bromine water. The acid hydrolysis of $X$ leads to a laevorotatory solution. The disaccharide $X$ is :
Chemistry · Biomolecules · MCQ
Q5.The complex(es), which can exhibit the type of isomerism shown by $[Pt (NH_{3})_{2} Br_{2}]$ , is(are) : [en $= H_{2} NCH_{2} CH_{2} NH_{2}$ ]
Chemistry · Coordination Compounds · Multiple correct
Q6.Atoms of metals $z$ , and $z$ form face-centred cubic (fcc) unit cell of edge length $L_{x}$ , body-centred cubic (bcc) unit cell of edge length $L_{y}$ , and simple cubic unit cell of…
Chemistry · Solid State · Multiple correct
Q7.In the following reactions, $P, Q, R$ , and $S$ are the major products. The correct statement(s) about $P, Q, R$ , and $S$ is(are) : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q8. $H_{2} S$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is $x$ , and the number of moles of electrons involved is $y$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q9.Among $[I_{3}]^{+}, [SiO_{4}]^{4 -}, SO_{2} Cl_{2}, XeF_{2}, SF_{4}, ClF_{3}, Ni (CO)_{4}, XeO_{2} F_{2}, [PtCl_{4}]^{2 -}, XeF_{4}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q10.Consider the following molecules: $Br_{3} O_{8}, F_{2} O, H_{2} S_{4} O_{6}, H_{2} S_{5} O_{6}$ , and $C_{3} O_{2}$ . Count the number of atoms existing…
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q11.For $He^{+}$ , a transition takes place from the orbit of radius $105.8 pm$ to the orbit of radius $26.45 pm$ . The wavelength (in nm) of the emitted photon during the transition is . [Use…
Chemistry · Structure of Atom · Numerical
Q12. $= 1.012 g mL^{- 1}$ of 0.2 molal urea solution (density $= 1.012 g mL^{- 1}$ at $250 mL$ ) is mixed with $0.06 g$ of a solution containing $0.06 g$ of urea. Both the solutions were prepared in…
Chemistry · Solutions · Numerical
Q13.The reaction of 4-methyloct-1-ene $(P, 2.52 g)$ with $HBr$ in the presence of $(C_{6} H_{5} CO)_{2} O_{2}$ gives two isomeric bromides in a $9 : 1$ ratio, with a combined…
Chemistry · Practical Organic Chemistry · Numerical
Q14.The entropy versus temperature plot for phases $α$ and $β$ at 1 bar pressure is given. $S_{T}$ and $S_{0}$ are entropies of the phases at temperatures $T$ and $0 K$ , respectively. The transition… Includes diagram
Chemistry · Thermodynamics · Numerical
Q15.The entropy versus temperature plot for phases $α$ and $β$ at 1 bar pressure is given. $S_{T}$ and $S_{0}$ are entropies of the phases at temperatures $T$ and $0 K$ , respectively. The transition… Includes diagram
Chemistry · Thermodynamics · Numerical
Q16.A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $Sn / HCl$ gives a major product, which on treatment with an excess of $NaNO_{2} / HCl$ at $0^{\circ} C$ …
Chemistry · Compounds Containing Nitrogen · Numerical
Q17.A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $Sn / HCl$ gives a major product, which on treatment with an excess of $NaNO_{2} / HCl$ at $0^{\circ} C$ …
Chemistry · Compounds Containing Nitrogen · Numerical
Q18.Let $f : [1, \infty) \to R$ be a differentiable function such that $f (1) = \frac{1}{3}$ and $3 1 \int x f (t) d t = x f (x) - \frac{x ^{3}}{3}, x \in [1, \infty)$ . Let $e$ denote the base of the natural logarithm. Then the value…
Mathematics · Differential Equations · MCQ
Q19.Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$ , then the probability that the experiment stops with head is :
Mathematics · Probability · MCQ
Q20.For any $y \in R$ , let $cot^{- 1} (y) \in (0, π)$ and $tan^{- 1} (y) \in (- \frac{π}{2}, \frac{π}{2})$ . Then the sum of all the solutions of the equation $tan^{- 1} (\frac{6 y}{9 - y ^{2}}) + cot^{- 1} (\frac{9 - y ^{2}}{6 y}) = \frac{2 π}{3}$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q21.Let the position vectors of the points $P, Q, R$ and $S$ be $a = \hat{i} + 2 \hat{j} - 5 \hat{k}, b = 3 \hat{i} + 6 \hat{j} + 3 \hat{k}$ , $c = \frac{17}{5} \hat{i} + \frac{16}{5} \hat{j} + 7 \hat{k}$ and $\vec{d}=2…
Mathematics · Vector Algebra · MCQ
Q22.Let $M = (a_{ij}), i, j \in {1, 2, 3}$ , be the $3 \times 3$ matrix such that $a_{ij} = 1$ if $j + 1$ is divisible by $i$ , otherwise $a_{ij} = 0$ . Then which of the following statements is(are) true?
Mathematics · Matrices and Determinants · Multiple correct
Q23.Let $f : (0, 1) \to R$ be the function defined as $f (x) = [4 x] (x - \frac{1}{4})^{2} (x - \frac{1}{2})$ , where $[x]$ denotes the greatest integer less than or equal to $x$ . Then which of the following statements…
Mathematics · Limits Continuity and Differentiability · Multiple correct
Q24.Let $S$ be the set of all twice differentiable functions $f$ from $R$ to $R$ such that $\frac{d ^{2} f}{d x ^{2}} (x) > 0$ for all $x \in (- 1, 1)$ . For $f \in S$ , let $X_{f}$ be the number of points $x \in (- 1, 1)$ for which…
Mathematics · Differentiation · Multiple correct
Q25.For $x \in R$ , let $tan^{- 1} (x) \in (- \frac{π}{2}, \frac{π}{2})$ . Then the minimum value of the function $f : R \to R$ defined by $f (x) = 0 \int x t a n^{- 1} x \frac{e ^{(t - c o s t)}}{1 + t ^{2023}} d t$ …
Mathematics · Definite Integration · Numerical
Q26.For $x \in R$ , let $y (x)$ be a solution of the differential equation $(x^{2} - 5) \frac{d y}{d x} - 2 x y = - 2 x (x^{2} - 5)^{2}$ such that $y (2) = 7$ . Then the maximum value of the function $y (x)$ is :
Mathematics · Differential Equations · Numerical
Q27.Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$ . Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional…
Mathematics · Probability · Numerical
Q28.Let $A_{1}, A_{2}, A_{3}, \dots, A_{8}$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a point on the circle and let $P A_{i}$ denote the distance between the points $P$ and $A_{i}$ for $i = 1, 2, \dots, 8$ . If $P$ …
Mathematics · Circle · Numerical
Q29.Let $R = ⎩ ⎨ ⎧ a c 0 325 b d 0 : a, b, c, d \in {0, 3, 5, 7, 11, 13, 17, 19} ⎭ ⎬ ⎫$ . Then the number of invertible matrices in $R$ is :
Mathematics · Matrices and Determinants · Numerical
Q30.Let $C_{1}$ be the circle of radius 1 with center at the origin. Let $C_{2}$ be the circle of radius $r$ with center at the point $A = (4, 1)$ , where $1 < r < 3$ . Two distinct common tangents $P Q$ and $S T$ of $C_{1}$ and $C_{2}$ are drawn. The…
Mathematics · Circle · Numerical
Q31.Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{π}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of…
Mathematics · Properties of Triangle · Numerical
Q32.Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{π}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of…
Mathematics · Trigonometric Functions and Equations · Numerical
Q33.Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \dots, A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column.… Includes diagram
Mathematics · Probability · Numerical
Q34.Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \dots, A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column.… Includes diagram
Mathematics · Probability · Numerical
Q35.An electric dipole is formed by two charges $+ q$ and $- q$ located in $x y$ -plane at $(0, 2) mm$ and $(0, - 2) mm$ , respectively, as shown in the figure. The electric potential at point $P (100, 100) mm$ due to the… Includes diagram
Physics · Electrostatics · MCQ
Q36.Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$ , Planck's constant $h$ and the speed of light $c$ , as $Y = c^{α} h^{β} G^{γ}$ . Which of the following is the…
Physics · Units and Measurements · MCQ
Q37.A particle of mass $m$ is moving in the $x y$ -plane such that its velocity at a point $(x, y)$ is given as $v = α (y \overset{x}{^} + 2 x \overset{y}{^})$ , where $α$ is a non-zero constant. What is the force $F$ …
Physics · Laws of Motion · MCQ
Q38.An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$ . The internal energy of one mole of the gas is $U_{n}$ and the speed of sound in the gas is $v_{n}$ . At a fixed temperature…
Physics · Heat and Thermodynamics · MCQ
Q39.A monochromatic light wave is incident normally on a glass slab of thickness $d$ , as shown in the figure. The refractive index of the slab increases linearly from $n_{1}$ to $n_{2}$ over the height $h$ . Which of the following statement(s)… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q40.An annular disk of mass $M$ , inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $μ$ , as shown in the figure. At some time, an impulse $J_{0} \overset{x}{^}$ is applied at a height $h$ above the… Includes diagram
Physics · Rotational Motion · Multiple correct
Q41.The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $E = 30 (2 \overset{x}{^} + \overset{y}{^}) sin [2 π (5 \times 1 0^{14} t - \frac{1 0 ^{7}}{3} z)] Vm^{- 1}$ . Which of…
Physics · Electromagnetic Waves · Multiple correct
Q42.A thin circular coin of mass $5 gm$ and radius $x y$ is initially in a horizontal $x y$ -plane. The coin is tossed vertically up ( $+ z$ direction) by applying an impulse of $\frac{π}{2} \times 1 0^{- 2} N$ … Includes diagram
Physics · Rotational Motion · Numerical
Q43.A rectangular conducting loop of length $2 cm$ and width $x y$ is in the $x y$ -plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{3}{2} \overset{x}{^} + \frac{1}{2} \overset{y}{^}$ … Includes diagram
Physics · Magnetism · Numerical
Q44.A string of length $2 \times 1 0^{- 5} kg$ and mass $2 \times 1 0^{- 5} kg$ is under tension $T$ . When the string vibrates, two successive harmonics are found to occur at frequencies $1000 Hz$ and $1000 Hz$ . The value of…
Physics · Waves · Numerical
Q45.An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 mm$ is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The… Includes diagram
Physics · Properties of Matter · Numerical
Q46.In a radioactive decay process, the activity is defined as $A = - \frac{d N}{d t}$ , where $N (t)$ is the number of radioactive nuclei at time $t$ . Two radioactive sources, $S_{1}$ and $S_{2}$ have same activity at time $t = 0$ . At a later time, the…
Physics · Atoms and Nuclei · Numerical
Q47.One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P - V$ diagrams below. In cycle I, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II,… Includes diagram
Physics · Heat and Thermodynamics · Numerical
Q48. $S_{1}$ and $S_{2}$ are two identical sound sources of frequency $S_{1}$ . The source $S_{1}$ is located at $O$ and $S_{2}$ moves anti-clockwise with a uniform speed $42 m s^{- 1}$ on a circular path around… Includes diagram
Physics · Waves · Numerical
Q49. $S_{1}$ and $S_{2}$ are two identical sound sources of frequency $S_{1}$ . The source $S_{1}$ is located at $O$ and $S_{2}$ moves anti-clockwise with a uniform speed $42 m s^{- 1}$ on a circular path around… Includes diagram
Physics · Waves · Numerical
Q50.A cylindrical furnace has height $(H)$ and diameter $(D)$ both $360 K$ . It is maintained at temperature $P_{a}$ . The air gets heated inside the furnace at constant pressure $P_{a}$ and its temperature becomes $T = 360 K$ … Includes diagram
Physics · Heat and Thermodynamics · Numerical
Q51.A cylindrical furnace has height $(H)$ and diameter $(D)$ both $360 K$ . It is maintained at temperature $P_{a}$ . The air gets heated inside the furnace at constant pressure $P_{a}$ and its temperature becomes $T = 360 K$ … Includes diagram
Physics · Heat and Thermodynamics · Numerical