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2022 · 27 Jul · Shift 1

72 questions · JEE Main

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2022 · 27 Jul · Shift 1

2022 · 27 Jul · Shift 1

72 questions · JEE Main

Chemistry23 questions Mathematics23 questions Physics26 questions

Some Basic Concepts of ChemistryChemistry · 3 questions Chemical Bonding and Molecular StructureChemistry · 3 questions Structure of AtomChemistry · 1 questions P Block ElementsChemistry · 1 questions SolutionsChemistry · 1 questions Periodic Table and PeriodicityChemistry · 1 questions D and F Block ElementsChemistry · 2 questions Basics of Organic ChemistryChemistry · 2 questions Alcohols Phenols and EthersChemistry · 2 questions BiomoleculesChemistry · 1 questions Compounds Containing NitrogenChemistry · 1 questions Chemical Kinetics and Nuclear ChemistryChemistry · 1 questions ThermodynamicsChemistry · 1 questions Ionic EquilibriumChemistry · 2 questions Coordination CompoundsChemistry · 1 questions Sets and RelationsMathematics · 1 questions FunctionsMathematics · 2 questions Complex NumbersMathematics · 2 questions Matrices and DeterminantsMathematics · 2 questions Binomial TheoremMathematics · 1 questions Sequences and SeriesMathematics · 1 questions Definite IntegrationMathematics · 3 questions Area Under the CurvesMathematics · 1 questions Differential EquationsMathematics · 2 questions Vector AlgebraMathematics · 1 questions ProbabilityMathematics · 1 questions Straight Lines and Pair of Straight LinesMathematics · 1 questions CircleMathematics · 1 questions Inverse Trigonometric FunctionsMathematics · 1 questions StatisticsMathematics · 1 questions HyperbolaMathematics · 1 questions EllipseMathematics · 1 questions Units and MeasurementsPhysics · 2 questions Motion in A Straight LinePhysics · 1 questions Work Power and EnergyPhysics · 1 questions Laws of MotionPhysics · 1 questions Properties of MatterPhysics · 2 questions GravitationPhysics · 1 questions Heat and ThermodynamicsPhysics · 3 questions ElectrostaticsPhysics · 2 questions Current ElectricityPhysics · 3 questions Alternating CurrentPhysics · 2 questions Electromagnetic WavesPhysics · 1 questions Geometrical OpticsPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions Electronic DevicesPhysics · 1 questions Wave OpticsPhysics · 1 questions Simple Harmonic MotionPhysics · 1 questions Rotational MotionPhysics · 1 questions Motion in A PlanePhysics · 1 questions

Q1. $D$ solution of $D$ -glucose in water contains $10.8%$ of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, $H, 1 u; C, 12 u; O, 16 u$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q2.Given below are two statements. Statement I: $O_{2}, Cu^{2 +}$ , and $Fe^{3 +}$ are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field. Statement II: $NaCl$ and $H_{2} O$ …
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q3.Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Energy of $2 s$ orbital of hydrogen atom is greater than that of $2 s$ orbital of lithium. Reason R:…
Chemistry · Structure of Atom · MCQ
Q4.Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Activated charcoal adsorbs $S O_{2}$ more efficiently than $C H_{4}$ . Reason R : Gases with lower critical temperatures are…
Chemistry · P Block Elements · MCQ
Q5.Boiling point of a $2%$ aqueous solution of a non-volatile solute A is equal to the boiling point of $8%$ aqueous solution of a non-volatile solute B. The relation between molecular weights of A and B is
Chemistry · Solutions · MCQ
Q6.The incorrect statement is
Chemistry · Periodic Table and Periodicity · MCQ
Q7.Given below are two statements. Statement I : Iron (III) catalyst, acidified $K_{2} Cr_{2} O_{7}$ and neutral $KMnO_{4}$ have the ability to oxidise $I^{-}$ to $I_{2}$ independently.…
Chemistry · D and F Block Elements · MCQ
Q8.The total number of $Mn = O$ bonds in $Mn_{2} O_{7}$ is .
Chemistry · D and F Block Elements · MCQ
Q9.Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R. Assertion A: [6] Annulene, [8] Annulene and cis-[10] Annulene, are respectively aromatic, not-aromatic and aromatic. Reason R: Planarity… Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q10.In the above reaction product B is : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q11.A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol gives the coloured product after sometime. Sugar 'X' is
Chemistry · Biomolecules · MCQ
Q12.In Carius method of estimation of halogen, $0.36 g$ of an organic compound gave $AgBr$ of $AgBr$ . Find out the percentage of bromine in the compound. (Molar masses : $AgBr = 188 g mol^{- 1}; Br = 80 g mol^{- 1}$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q13.Match List I with List II. Choose the correct answer from the options given below: Includes table
Chemistry · Compounds Containing Nitrogen · MCQ
Q14. $0.02 M K_{2} Cr_{2} O_{7}$ of $0.02 M K_{2} Cr_{2} O_{7}$ solution is used for the titration of $Fe^{2 +}$ of $Fe^{2 +}$ solution in the acidic medium. The molarity of $Fe^{2 +}$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q15. $2 NO + 2 H_{2} \to N_{2} + 2 H_{2} O$ The above reaction has been studied at $80 0^{\circ} C$ . The related data are given in the table below The order of the reaction with respect… Includes table
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q16.Amongst the following, the number of oxide(s) which are paramagnetic in nature is $Na_{2} O, KO_{2}, NO_{2}, N_{2} O, ClO_{2}, NO, SO_{2}, Cl_{2} O$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q17.The molar heat capacity for an ideal gas at constant pressure is $20.785 J K^{- 1} mol^{- 1}$ . The change in internal energy is $300 K$ upon heating it from $500 K$ to $500 K$ .…
Chemistry · Thermodynamics · Numerical
Q18.According to MO theory, number of species/ions from the following having identical bond order is . $CN^{-}, NO^{+}, O_{2}, O_{2}^{+}, O_{2}^{2 +}$
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q19.At $CaF_{2}$ , the solubility of $CaF_{2}$ in water is $2.34 \times 1 0^{- 3} g /100 mL$ . The solubility product of $CaF_{2}$ is $\times 1 0^{- 8} (mol / L)^{3}$ …
Chemistry · Ionic Equilibrium · Numerical
Q20.The conductivity of a solution of complex with formula $CoCl_{3} (NH_{3})_{4}$ corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is .
Chemistry · Coordination Compounds · Numerical
Q21.In the titration of $KMnO_{4}$ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is .
Chemistry · Ionic Equilibrium · Numerical
Q22.Optical activity of an enantiomeric mixture is $+ 12. 6^{\circ}$ and the specific rotation of $(+)$ isomer is $+ 3 0^{\circ}$ . The optical purity is $%$ .
Chemistry · Basics of Organic Chemistry · Numerical
Q23.In the following reaction The $%$ yield for reaction I is $60%$ and that of reaction II is $50%$ . The overall yield of the complete reaction is $%$ . [nearest integer] Includes diagram
Chemistry · Alcohols Phenols and Ethers · Numerical
Q24.Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R_{1} b \Leftrightarrow ab \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$ Then,
Mathematics · Sets and Relations · MCQ
Q25.Let $f, g : N - {1} \to N$ be functions defined by $f (a) = α$ , where $α$ is the maximum of the powers of those primes $p$ such that $p^{α}$ divides $a$ , and $g (a) = a + 1$ , for all $a \in N - {1}$ …
Mathematics · Functions · MCQ
Q26.Let the minimum value $v_{0}$ of $v = ∣ z ∣^{2} + ∣ z - 3 ∣^{2} + ∣ z - 6 i ∣^{2}, z \in C$ is attained at $z = z_{0}$ . Then $2 z_{0}^{2} - \overset{z}{ˉ}_{0}^{3} + 3^{2} + v_{0}^{2}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q27.Let $A = (1 - 2 2 - 5)$ . Let $α, β \in R$ be such that $α A^{2} + β A = 2 I$ . Then $α + β$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q28.The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by 7 is
Mathematics · Binomial Theorem · MCQ
Q29.Suppose $a_{1}, a_{2}, \dots, a_{n}$ , .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is $5 : 17$ and , $110 < a_{15} < 120$ , then the…
Mathematics · Sequences and Series · MCQ
Q30.Let $f : R \to R$ be a function defined as $f (x) = a sin (\frac{π [ x ]}{2}) + [2 - x], a \in R$ where $[t]$ is the greatest integer less than or equal to $t$ . If $x \to - 1 lim f (x)$ …
Mathematics · Definite Integration · MCQ
Q31.Let $I = \int_{π /4}^{π /3} (\frac{8 s i n x - s i n 2 x}{x}) d x$ . Then
Mathematics · Definite Integration · MCQ
Q32.The area of the smaller region enclosed by the curves $y^{2} = 8 x + 4$ and $x^{2} + y^{2} + 43 x - 4 = 0$ is equal to
Mathematics · Area Under the Curves · MCQ
Q33.Let $y = y_{1} (x)$ and $y = y_{2} (x)$ be two distinct solutions of the differential equation $\frac{d y}{d x} = x + y$ , with $y_{1} (0) = 0$ and $y_{2} (0) = 1$ respectively. Then, the number of points of intersection of $y = y_{1} (x)$ and $y = y_{2} (x)$ is
Mathematics · Differential Equations · MCQ
Q34.Let $a = α \hat{i} + \hat{j} + β \hat{k}$ and $b = 3 \hat{i} - 5 \hat{j} + 4 \hat{k}$ be two vectors, such that $a \times b = - \hat{i} + 9 \hat{j} + 12 \hat{k}$ . Then the projection of $b - 2 a$ on $b + a$ …
Mathematics · Vector Algebra · MCQ
Q35.Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$ , is a multiple of 7 but not divisible by 5 , then $9 p$ is equal to :
Mathematics · Probability · MCQ
Q36.Let $A (1, 1), B (- 4, 3), C (- 2, - 5)$ be vertices of a triangle $A B C, P$ be a point on side $B C$ , and $Δ_{1}$ and $Δ_{2}$ be the areas of triangles $A P B$ and $A B C$ , respectively. If $Δ_{1} : Δ_{2} = 4 : 7$ , then the area…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If the circle $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0, g, c \in R$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2 cy = 8$ , then the length of intercept made by the circle on $x$ -axis is :
Mathematics · Circle · MCQ
Q38.Let a function $f : R \to R$ be defined as : $f (x) = ⎩ ⎨ ⎧ 0 \int x (5 - ∣ t - 3∣) d t, x^{2} + b x x > 4, x \leq 4$ where $b \in R$ . If $f$ is continuous…
Mathematics · Definite Integration · MCQ
Q39.For $k \in R$ , let the solutions of the equation $cos (sin^{- 1} (x cot (tan^{- 1} (cos (sin^{- 1} x))))) = k, 0 < ∣ x ∣ < \frac{1}{2}$ be $α$ and $β$ ,…
Mathematics · Inverse Trigonometric Functions · Numerical
Q40.The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is .
Mathematics · Statistics · Numerical
Q41.An ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ passes through the vertices of the hyperbola $H : \frac{x ^{2}}{49} - \frac{y ^{2}}{64} = - 1$ . Let the major and minor axes of the ellipse $E$ coincide with the transverse and conjugate…
Mathematics · Hyperbola · Numerical
Q42.Let $y = y (x)$ be the solution curve of the differential equation $sin (2 x^{2}) lo g_{e} (tan x^{2}) d y + (4 x y - 42 x sin (x^{2} - \frac{π}{4})) d x = 0$ , $0 < x < \frac{π}{2}$ …
Mathematics · Differential Equations · Numerical
Q43.Let $f (x) = 2 x^{2} - x - 1$ and $S = {n \in Z : ∣ f (n) ∣ \leq 800}$ . Then, the value of $n \in S \sum f (n)$ is equal to .
Mathematics · Functions · Numerical
Q44.Let $S$ be the set containing all $3 \times 3$ matrices with entries from ${- 1, 0, 1}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{T} A$ is 6 is .
Mathematics · Matrices and Determinants · Numerical
Q45.If the length of the latus rectum of the ellipse $x^{2} + 4 y^{2} + 2 x + 8 y - λ = 0$ is 4 , and $l$ is the length of its major axis, then $λ + l$ is equal to .
Mathematics · Ellipse · Numerical
Q46.Let $S = {z \in C : z^{2} + \overset{z}{ˉ} = 0}$ . Then $z \in S \sum (Re (z) + Im (z))$ is equal to .
Mathematics · Complex Numbers · Numerical
Q47.A torque meter is calibrated to reference standards of mass, length and time each with $5%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :
Physics · Units and Measurements · MCQ
Q48.A bullet is shot vertically downwards with an initial velocity of $100 m / s$ from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision.…
Physics · Motion in A Straight Line · MCQ
Q49.Sand is being dropped from a stationary dropper at a rate of $0.5 kgs^{- 1}$ on a conveyor belt moving with a velocity of $5 ms^{- 1}$ . The power needed to keep the belt moving with the same velocity will be :
Physics · Work Power and Energy · MCQ
Q50.A bag is gently dropped on a conveyor belt moving at a speed of $2 m / s$ . The coefficient of friction between the conveyor belt and bag is $0.4$ . Initially, the bag slips on the belt before it stops due to friction. The…
Physics · Laws of Motion · MCQ
Q51.Two cylindrical vessels of equal cross-sectional area $16 cm^{2}$ contain water upto heights $150 cm$ and $150 cm$ respectively. The vessels are interconnected so that the water levels in them become equal.…
Physics · Properties of Matter · MCQ
Q52.Two satellites $A$ and $B$ , having masses in the ratio $4 : 3$ , are revolving in circular orbits of radii $3 r$ and $4 r$ respectively around the earth. The ratio of total mechanical energy of…
Physics · Gravitation · MCQ
Q53.If $K_{1}$ and $K_{2}$ are the thermal conductivities, $L_{1}$ and $L_{2}$ are the lengths and $A_{1}$ and $A_{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K _{2}}{K _{1}} = 9, \frac{A _{1}}{A _{2}} = 2, \frac{L _{1}}{L _{2}} = 2$ … Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q54.Read the following statements : A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice. B. Two bodies $P$ and $Q$ having equal surface areas are maintained…
Physics · Heat and Thermodynamics · MCQ
Q55.Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1 : 4$ , then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in…
Physics · Heat and Thermodynamics · MCQ
Q56.Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge $q_{0}$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the…
Physics · Electrostatics · MCQ
Q57.Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $r_{1}$ and $r_{2}$ $(r_{1} > r_{2})$ . If the potential difference…
Physics · Current Electricity · MCQ
Q58.A direct current of $4 A$ and an alternating current of peak value $3 Ω$ flow through resistance of $3 Ω$ and $2 Ω$ respectively. The ratio of heat produced in the two resistances in same interval of time…
Physics · Alternating Current · MCQ
Q59.A beam of light travelling along $X$ -axis is described by the electric field $E_{y} = 900 sin ω (t - x / c)$ . The ratio of electric force to magnetic force on a charge $q$ moving along $Y$ -axis with a speed of $3 \times 1 0^{7} ms^{- 1}$ …
Physics · Electromagnetic Waves · MCQ
Q60.A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $λ$ , calculate the change of microscope's resolving power due to oil and choose…
Physics · Geometrical Optics · MCQ
Q61.An electron (mass $m$ ) with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ is moving in an electric field $E = - E_{0} \hat{i} (E_{0} > 0)$ where $E_{0}$ is constant. If at $t = 0$ de…
Physics · Dual Nature of Radiation · MCQ
Q62.A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below. The logic gate circuit is : Includes diagram
Physics · Electronic Devices · MCQ
Q63.In a meter bridge experiment, for measuring unknown resistance 'S', the null point is obtained at a distance $5.6 k Ω$ from the left side as shown at point D. If R is $5.6 k Ω$ , then the value of unknown resistance 'S'… Includes diagram
Physics · Current Electricity · Numerical
Q64.The one division of main scale of Vernier callipers reads $1 mm$ and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to…
Physics · Units and Measurements · Numerical
Q65.Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $π /2$ and $π /3$ at points $A$ and $B$ respectively. The difference…
Physics · Wave Optics · Numerical
Q66.To light, a $50 W, 100 V$ lamp is connected, in series with a capacitor of capacitance $\frac{50}{π x} μ F$ , with $200 V, 50 Hz AC$ source. The value of $x$ will be …
Physics · Alternating Current · Numerical
Q67.A $1 A$ long copper wire carries a current of $2.0 mm^{2}$ . If the cross section of the wire is $2.0 mm^{2}$ and the resistivity of copper is $1.7 \times 1 0^{- 8} Ω m$ , the force experienced by moving…
Physics · Current Electricity · Numerical
Q68.A long cylindrical volume contains a uniformly distributed charge of density $ρ Cm^{- 3}$ . The electric field inside the cylindrical volume at a distance $x = \frac{2 ε _{0}}{ρ} m$ from its axis is … Includes diagram
Physics · Electrostatics · Numerical
Q69.A mass $A_{1}$ , attached to a horizontal spring, executes SHM with an amplitude $A_{1}$ . When this mass passes through its mean position, then a smaller mass of $124 g$ is placed over it and both masses move…
Physics · Simple Harmonic Motion · Numerical
Q70.A square aluminum (shear modulus is $25 \times 1 0^{9} Nm^{- 2}$ ) slab of side $15 cm$ and thickness $18.0 \times 1 0^{4} N$ is subjected to a shearing force (on its narrow face) of $18.0 \times 1 0^{4} N$ . The lower…
Physics · Properties of Matter · Numerical
Q71.A pulley of radius $F = (12 t - 3 t^{2}) N$ is rotated about its axis by a force $F = (12 t - 3 t^{2}) N$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of…
Physics · Rotational Motion · Numerical
Q72.A ball of mass m is thrown vertically upward. Another ball of mass $θ$ is thrown at an angle $θ$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls…
Physics · Motion in A Plane · Numerical