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2024 · Shift 1

51 questions · JEE Advanced

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2024 · Shift 1

2024 · Shift 1

51 questions · JEE Advanced

Chemistry17 questions Mathematics17 questions Physics17 questions

Gaseous StateChemistry · 1 questions P Block ElementsChemistry · 1 questions Chemistry in Everyday LifeChemistry · 1 questions Coordination CompoundsChemistry · 3 questions Structure of AtomChemistry · 1 questions Alcohols Phenols and EthersChemistry · 1 questions Chemical Bonding and Molecular StructureChemistry · 2 questions ThermodynamicsChemistry · 1 questions Chemical Kinetics and Nuclear ChemistryChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 2 questions HydrocarbonsChemistry · 1 questions ElectrochemistryChemistry · 1 questions Compounds Containing NitrogenChemistry · 1 questions Differential EquationsMathematics · 1 questions ProbabilityMathematics · 2 questions Trigonometric Functions and EquationsMathematics · 1 questions EllipseMathematics · 1 questions Complex NumbersMathematics · 2 questions Matrices and DeterminantsMathematics · 3 questions 3D GeometryMathematics · 2 questions Quadratic Equation and InequalitiesMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions Vector AlgebraMathematics · 1 questions CircleMathematics · 1 questions Limits Continuity and DifferentiabilityMathematics · 1 questions Units and MeasurementsPhysics · 1 questions MagnetismPhysics · 1 questions ElectrostaticsPhysics · 1 questions Impulse and MomentumPhysics · 1 questions Atoms and NucleiPhysics · 1 questions WavesPhysics · 2 questions Geometrical OpticsPhysics · 2 questions Heat and ThermodynamicsPhysics · 2 questions Rotational MotionPhysics · 2 questions Wave OpticsPhysics · 1 questions Properties of MatterPhysics · 1 questions CapacitorPhysics · 1 questions Alternating CurrentPhysics · 1 questions

Q1.A closed vessel contains $X$ of an ideal gas $X$ at $2 atm$ , which exerts $80 g$ pressure. At the same temperature, $Y$ of another ideal gas $Y$ is added to it and the…
Chemistry · Gaseous State · MCQ
Q2.At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid $(HNO_{2})$ gives the species
Chemistry · P Block Elements · MCQ
Q3.Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is Includes diagram
Chemistry · Chemistry in Everyday Life · MCQ
Q4.Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other. $[en = H_{2} NCH_{2} CH_{2} NH_{2}]$ …
Chemistry · Coordination Compounds · MCQ
Q5.Among the following, the correct statement(s) for electrons in an atom is(are)
Chemistry · Structure of Atom · Multiple correct
Q6.Reaction of iso-propylbenzene with $O_{2}$ followed by the treatment with $H_{3} O^{+}$ forms phenol and a by-product $P$ . Reaction of $P$ with 3 equivalents of $Cl_{2}$ gives compound $Q$ …
Chemistry · Alcohols Phenols and Ethers · Multiple correct
Q7.The option(s) in which at least three molecules follow Octet Rule is(are)
Chemistry · Chemical Bonding and Molecular Structure · Multiple correct
Q8.Consider the following volume-temperature $(V - T)$ diagram for the expansion of 5 moles of an ideal monoatomic gas. Considering only $P - V$ work is involved, the total change in enthalpy (in Joule) for the… Includes diagram
Chemistry · Thermodynamics · Numerical
Q9.Consider the following reaction, $2 H_{2} (g) + 2 NO (g) \to N_{2} (g) + 2 H_{2} O (g)$ which follows the mechanism given below : $2 NO (g) k_{- 1} ⇌ k_{1} N_{2} O_{2} (g) N_{2} O_{2} (g) + H_{2} (g) k_{2} N_{2} O (g) + H_{2} O (g) N_{2} O (g) + H_{2} (g) k_{3} N_{2} (g) + H_{2} O (g) (fast equlibrium) (slow reaction) (fast reaction)$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q10.Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. $NaOH$ solution, gives $P$ and $Q$ . Compound $P$ does not give Tollens' test, whereas $Q$ on acidification…
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q11.Among $V (CO)_{6}, Cr (CO)_{5}, Cu (CO)_{3}, Mn (CO)_{5}, Fe (CO)_{5}, [Co (CO)_{3}]^{3 -}, [Cr (CO)_{4}]^{4 -}$ ,…
Chemistry · Coordination Compounds · Numerical
Q12.In the following reaction sequence, the major product $P$ is formed. Glycerol reacts completely with excess $P$ in the presence of an acid catalyst to form $Q$ . Reaction of $Q$ with excess… Includes diagram
Chemistry · Hydrocarbons · Numerical
Q13.Among the following complexes, the total number of diamagnetic species is . $[Mn (NH_{3})_{6}]^{3 +}, [MnCl_{6}]^{3 -}, [FeF_{6}]^{3 -}, [CoF_{6}]^{3 -}, [Fe (NH_{3})_{6}]^{3 +}$ …
Chemistry · Coordination Compounds · Numerical
Q14.In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition. The limiting ionic… Includes table Includes diagram
Chemistry · Electrochemistry · MCQ
Q15.Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option. Includes table
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q16.List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. Includes table Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q17.List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option. Includes table Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q18.Let $f (x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f (1) = 2$ and $t \to x lim \frac{t ^{10} f ( x ) - x ^{10} f ( t )}{t ^{9} - x ^{9}} = 1$ for each $x > 0$ . Then, for all $x > 0, f (x)$ is equal…
Mathematics · Differential Equations · MCQ
Q19.A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the…
Mathematics · Probability · MCQ
Q20.Let $\frac{π}{2}$ $(sin \frac{11 x}{2}) (sin 6 x - cos 6 x) + (cos \frac{11 x}{2}) (sin 6 x + cos 6 x)$ $ is equal to :
Mathematics · Trigonometric Functions and Equations · MCQ
Q21.Consider the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ . Let $S (p, q)$ be a point in the first quadrant such that $\frac{p ^{2}}{9} + \frac{q ^{2}}{4} > 1$ . Two tangents are drawn from $S$ to the ellipse, of which one meets the ellipse at one end…
Mathematics · Ellipse · MCQ
Q22.Let $S = {a + b 2 : a, b \in Z}, T_{1} = {(- 1 + 2)^{n} : n \in N}$ , and $T_{2} = {(1 + 2)^{n} : n \in N}$ . Then which of the following statements is (are) TRUE?
Mathematics · Complex Numbers · Multiple correct
Q23.Let $R^{2}$ denote $R \times R$ . Let $S = {(a, b, c) : a, b, c \in R and a x^{2} + 2 b x y + c y^{2} > 0 for all (x, y) \in R^{2} - {(0, 0)}} .$ Then which of the following…
Mathematics · Matrices and Determinants · Multiple correct
Q24.Let $R^{3}$ denote the three-dimensional space. Take two points $P = (1, 2, 3)$ and $Q = (4, 2, 7)$ . Let $dist (X, Y)$ denote the distance between two points $X$ and $Y$ in $R^{3}$ . Let $S = {X \in R^{3} : (dist (X, P))^{2} - (dist (X, Q))^{2} = 50} and T = {Y \in R^{3} : (dist (Y, Q))^{2} - (dist (Y, P))^{2} = 50} .$ …
Mathematics · 3D Geometry · Multiple correct
Q25.Let $a = 32$ and $b = \frac{1}{5 ^{1/6} 6}$ . If $x, y \in R$ are such that $3 x + 2 y = lo g_{a} (18)^{\frac{5}{4}} and 2 x - y = lo g_{b} (1080),$ then $4 x + 5 y$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q26.Let $f (x) = x^{4} + a x^{3} + b x^{2} + c$ be a polynomial with real coefficients such that $f (1) = - 9$ . Suppose that $i 3$ is a root of the equation $4 x^{3} + 3 a x^{2} + 2 b x = 0$ , where $i = - 1$ . If $α_{1}, α_{2}, α_{3}$ , and $α_{4}$ …
Mathematics · Complex Numbers · Numerical
Q27.Let $S = ⎩ ⎨ ⎧ A = 011 1 a b c d e : a, b, c, d, e \in {0, 1}$ and $∣ A ∣ \in {- 1, 1}}$ , where $∣ A ∣$ denotes the determinant of $A$ . Then…
Mathematics · Matrices and Determinants · Numerical
Q28.A group of 9 students, $s_{1}, s_{2}, \dots, s_{9}$ , is to be divided to form three teams $Z$ , and $Z$ of sizes 2,3 , and 4 , respectively. Suppose that $s_{1}$ cannot be selected for the team $X$ , and $s_{2}$ cannot be selected for the team…
Mathematics · Permutations and Combinations · Numerical
Q29.Let $O P = \frac{α - 1}{α} \hat{i} + \hat{j} + \hat{k}, O Q = \hat{i} + \frac{β - 1}{β} \hat{j} + \hat{k}$ and $O R = \hat{i} + \hat{j} + \frac{1}{2} \hat{k}$ be three vectors, where $α, β \in R - {0}$ …
Mathematics · Vector Algebra · Numerical
Q30.Let $X$ be a random variable, and let $P (X = x)$ denote the probability that $X$ takes the value $x$ . Suppose that the points $(x, P (X = x)), x = 0, 1, 2, 3, 4$ , lie on a fixed straight line in the $x y$ -plane, and $P (X = x) = 0$ for all $x \in R - {0, 1, 2, 3, 4}$ …
Mathematics · Probability · Numerical
Q31.Let $α$ and $β$ be the distinct roots of the equation $x^{2} + x - 1 = 0$ . Consider the set $T = {1, α, β}$ . For a $3 \times 3$ matrix $M = (a_{ij})_{3 \times 3}$ , define $R_{i} = a_{i 1} + a_{i 2} + a_{i 3}$ and $C_{j} = a_{1 j} + a_{2 j} + a_{3 j}$ … Includes table
Mathematics · Matrices and Determinants · MCQ
Q32.Let the straight line $y = 2 x$ touch a circle with center $(0, α), α > 0$ , and radius $r$ at a point $A_{1}$ . Let $B_{1}$ be the point on the circle such that the line segment $A_{1} B_{1}$ is a diameter of the circle. Let $α + r = 5 + 5$ … Includes table
Mathematics · Circle · MCQ
Q33.Let $γ \in R$ be such that the lines $L_{1} : \frac{x + 11}{1} = \frac{y + 21}{2} = \frac{z + 29}{3}$ and $L_{2} : \frac{x + 16}{3} = \frac{y + 11}{2} = \frac{z + 4}{γ}$ intersect. Let $R_{1}$ be the point of intersection of $L_{1}$ and $L_{2}$ . Let $O = (0, 0, 0)$ … Includes table
Mathematics · 3D Geometry · MCQ
Q34.Let $f : R \to R$ and $g : R \to R$ be functions defined by $f (x) = {x ∣ x ∣ sin (\frac{1}{x}), 0, x e q 0, x = 0, and g (x) = {1 - 2 x, 0, 0 \leq x \leq \frac{1}{2}, otherwise .$ … Includes table
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.A dimensionless quantity is constructed in terms of electronic charge $e$ , permittivity of free space $ε_{0}$ , Planck's constant $h$ , and speed of light $c$ . If the dimensionless quantity is written as $e^{α} ε_{0}^{β} h^{γ} c^{δ}$ …
Physics · Units and Measurements · MCQ
Q36.An infinitely long wire, located on the $z$ -axis, carries a current $I$ along the $+ z$ -direction and produces the magnetic field $B$ . The magnitude of the line integral $\int B \cdot d l$ along a straight line…
Physics · Magnetism · MCQ
Q37.Two beads, each with charge $q$ and mass $m$ , are on a horizontal, frictionless, non-conducting, circular hoop of radius $a$ . One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its…
Physics · Electrostatics · MCQ
Q38.A block of mass $x$ moves along the $x$ -direction subject to the force $F = (- 20 x + 10) N$ , with the value of $x$ in metre. At time $t = 0 s$ , it is at rest at position $x = 1 m$ . The position and…
Physics · Impulse and Momentum · MCQ
Q39.A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F (r) = - k r$ , corresponding to the potential energy $V (r) = k r^{2} /2$ , where $k$ is a positive force constant and $r$ is the radial distance from…
Physics · Atoms and Nuclei · Multiple correct
Q40.Two uniform strings of mass per unit length $μ$ and $4 μ$ , and length $L$ and $2 L$ , respectively, are joined at point $O$ , and tied at two fixed ends $P$ and $Q$ , as shown in the figure. The strings are… Includes diagram
Physics · Waves · Multiple correct
Q41.A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is $9 cm$ , while the planar surface (STU) acts as a mirror. This beaker is filled… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q42.The specific heat capacity of a substance is temperature dependent and is given by the formula $C = k T$ , where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the…
Physics · Heat and Thermodynamics · Numerical
Q43.A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass $M$ and… Includes diagram
Physics · Rotational Motion · Numerical
Q44.A point source $S$ emits unpolarized light uniformly in all directions. At two points $A$ and $B$ , the ratio $r = I_{A} / I_{B}$ of the intensities of light is 2 . If a set of two polaroids having $4 5^{\circ}$ angle…
Physics · Wave Optics · Numerical
Q45.A source (S) of sound has frequency $v$ . When the observer (O) and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the… Includes diagram
Physics · Waves · Numerical
Q46.Two large, identical water tanks, 1 and 2 , kept on the top of a building of height $H$ , are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A…
Physics · Properties of Matter · Numerical
Q47.A thin uniform rod of length $L$ and certain mass is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$ … Includes diagram
Physics · Rotational Motion · Numerical
Q48.One mole of a monatomic ideal gas undergoes the cyclic process $J \to K \to L \to M \to J$ , as shown in the P-T diagram. Match the quantities mentioned in List-I… Includes table Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q49.Four identical thin, square metal sheets, $S_{1}, S_{2}, S_{3}$ and $S_{4}$ , each of side $a$ are kept parallel to each other with equal distance $d (≪ a)$ between them, as shown in the figure. Let $C_{0} = \frac{ε _{0} a ^{2}}{d}$ ,… Includes table Includes diagram
Physics · Capacitor · MCQ
Q50.A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $θ_{0}$ . The ray partially refracts into the sphere with angle of refraction $ϕ_{0}$ and then partly reflects from the back surface.… Includes table
Physics · Geometrical Optics · MCQ
Q51.The circuit shown in the figure contains an inductor $L$ , a capacitor $C_{0}$ , a resistor $R_{0}$ and an ideal battery. The circuit also contains two keys $K_{1}$ and $K_{2}$ . Initially, both the keys are open and there is no… Includes table Includes diagram
Physics · Alternating Current · MCQ