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2021 · 16 Mar · Shift 2

70 questions · JEE Main

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2021 · 16 Mar · Shift 2

2021 · 16 Mar · Shift 2

70 questions · JEE Main

Chemistry23 questions Mathematics22 questions Physics25 questions

Practical Organic ChemistryChemistry · 2 questions Alcohols Phenols and EthersChemistry · 1 questions HydrocarbonsChemistry · 1 questions Some Basic Concepts of ChemistryChemistry · 2 questions Periodic Table and PeriodicityChemistry · 2 questions Compounds Containing NitrogenChemistry · 2 questions BiomoleculesChemistry · 1 questions D and F Block ElementsChemistry · 2 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 1 questions Haloalkanes and HaloarenesChemistry · 1 questions Redox ReactionsChemistry · 1 questions Coordination CompoundsChemistry · 1 questions ElectrochemistryChemistry · 1 questions ThermodynamicsChemistry · 1 questions Structure of AtomChemistry · 1 questions Chemical Kinetics and Nuclear ChemistryChemistry · 1 questions Ionic EquilibriumChemistry · 1 questions SolutionsChemistry · 1 questions Differential EquationsMathematics · 2 questions Application of DerivativesMathematics · 2 questions Vector AlgebraMathematics · 1 questions 3D GeometryMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions Limits Continuity and DifferentiabilityMathematics · 3 questions Definite IntegrationMathematics · 2 questions Sets and RelationsMathematics · 1 questions Complex NumbersMathematics · 1 questions Inverse Trigonometric FunctionsMathematics · 1 questions CircleMathematics · 1 questions Straight Lines and Pair of Straight LinesMathematics · 1 questions ProbabilityMathematics · 1 questions Sequences and SeriesMathematics · 1 questions Indefinite IntegralsMathematics · 1 questions StatisticsMathematics · 1 questions Matrices and DeterminantsMathematics · 1 questions Properties of MatterPhysics · 1 questions Geometrical OpticsPhysics · 3 questions Electronic DevicesPhysics · 1 questions Circular MotionPhysics · 1 questions Center of MassPhysics · 1 questions Motion in A PlanePhysics · 2 questions Dual Nature of RadiationPhysics · 1 questions Heat and ThermodynamicsPhysics · 2 questions MagneticsPhysics · 1 questions Units and MeasurementsPhysics · 1 questions Current ElectricityPhysics · 2 questions ElectrostaticsPhysics · 1 questions Electromagnetic InductionPhysics · 1 questions Alternating CurrentPhysics · 1 questions Rotational MotionPhysics · 2 questions CapacitorPhysics · 1 questions GravitationPhysics · 1 questions Laws of MotionPhysics · 1 questions WavesPhysics · 1 questions

Q1.Match List - I with List - II : The correct match is : Includes table
Chemistry · Practical Organic Chemistry · MCQ
Q2.The structure of X is : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q3.An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammonical silver nitrate forms a bright silver mirror along the sides of the test tube. The unsaturated hydrocarbon X is :
Chemistry · Hydrocarbons · MCQ
Q4.The exact volumes of 1 M $N a O H$ solution required to neutralise 50 mL of 1 M $H_{3} P O_{3}$ solution and 100 mL of 2 M $H_{3} P O_{2}$ solution, respectively, are :
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q5.The characteristics of elements X, Y and Z with atomic numbers, respectively, 33, 53 and 83 are :
Chemistry · Periodic Table and Periodicity · MCQ
Q6.Which of the following is least basic?
Chemistry · Compounds Containing Nitrogen · MCQ
Q7.Ammonolysis of Alkyl halides followed by the treatment with NaOH solution can be used to prepare primary, secondary and tertiary amines. The purpose of NaOH in the reaction is :
Chemistry · Compounds Containing Nitrogen · MCQ
Q8.The secondary structure of protein is stabilised by:
Chemistry · Biomolecules · MCQ
Q9.Fex2 and Fey3 are known when x and y are :
Chemistry · D and F Block Elements · MCQ
Q10.Identify the elements X and Y using the ionisation energy values given below : Includes table
Chemistry · Periodic Table and Periodicity · MCQ
Q11.In the above reaction, the reagent ''A'' is : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q12.Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system. (Atomic numbers Ce = 58, Gd = 64 and Eu = 63) (a) $(N H_{4})_{2} [C e (N O_{3})_{6}]$ (b) $G d (N O_{3})_{3}$ and (c) $E u (N O_{3})_{3}$ …
Chemistry · D and F Block Elements · MCQ
Q13.Identify the reagent(s) 'A' and condition(s) for the reaction Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q14.Statement I : Sodium hydride can be used as an oxidising agent. Statement II : The lone pair of electrons on nitrogen in pyridine makes it basic. Choose the CORRECT answer from the options given below :
Chemistry · Redox Reactions · MCQ
Q15. $[T i (H_{2} O)_{6}]^{3 +}$ absorbs light of wavelength 498 nm during a d $-$ d transition. The octahedral splitting energy for the above complex is $\times$ 10 $-$ 19 J. (Round off to the Nearest Integer). h = 6.626 $\times$ …
Chemistry · Coordination Compounds · Numerical
Q16.A 5.0 m mol dm $-$ 3 aqueous solution of $K C l$ has a conductance of 0.55 mS when measured in a cell of cell constant 1.3 cm $-$ 1. The molar conductivity of this solution is mSm2 mol $-$ 1. (Round off to the…
Chemistry · Electrochemistry · Numerical
Q17.At 25 $^{\circ}$ C, 50 g of iron reacts with $H C l$ to form $F e C l_{2}$ . The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is J. (Round off to the…
Chemistry · Thermodynamics · Numerical
Q18.The number of orbitals with n = 5, m1 = +2 is . (Round off to the Nearest Integer).
Chemistry · Structure of Atom · Numerical
Q19.A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q20.In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The percentage composition of nitrogen in the compound is . (Round…
Chemistry · Practical Organic Chemistry · Numerical
Q21.When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, $\times$ 10 $-$ 5 moles of lead sulphate precipitate out. (Round off to the Nearest Integer).
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q22.Sulphurous acid ( $H_{2} S O_{3}$ ) has Ka1 = 1.7 $\times$ 10 $-$ 2 and Ka2 = 6.4 $\times$ 10 $-$ 8. The pH of 0.588 M $H_{2} S O_{3}$ is . (Round off to the Nearest Integer).
Chemistry · Ionic Equilibrium · Numerical
Q23.At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is ideal, the vapour pressure of the mixture is kPa. (Round off to the…
Chemistry · Solutions · Numerical
Q24.If y = y(x) is the solution of the differential equation $\frac{d y}{d x}$ + (tan x) y = sin x, $0 \leq x \leq \frac{π}{3}$ , with y(0) = 0, then $y (\frac{π}{4})$ equal to :
Mathematics · Differential Equations · MCQ
Q25.Let f be a real valued function, defined on R $-$ { $-$ 1, 1} and given by f(x) = 3 loge $\frac{x - 1}{x + 1} - \frac{2}{x - 1}$ . Then in which of the following intervals, function f(x) is increasing?
Mathematics · Application of Derivatives · MCQ
Q26.Let $a$ = $i$ + 2 $j -$ 3 $k$ and $b = 2 i -$ 3 $j$ + 5 $k$ . If $r \times a$ = $b \times r$ , $r$ …
Mathematics · Vector Algebra · MCQ
Q27.If the foot of the perpendicular from point (4, 3, 8) on the line $L_{1} : \frac{x - a}{l} = \frac{y - 2}{3} = \frac{z - b}{4}$ , l $e$ 0 is (3, 5, 7), then the shortest distance between the line L1 and line $L_{2} : \frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ …
Mathematics · 3D Geometry · MCQ
Q28.Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let $α$ be the number of triangles having these points from different sides as vertices and $β$ be the number of…
Mathematics · Permutations and Combinations · MCQ
Q29.Let f : S $\to$ S where S = (0, $\infty$ ) be a twice differentiable function such that f(x + 1) = xf(x). If g : S $\to$ R be defined as g(x) = loge f(x), then the value of |g''(5) $-$ g''(1)| is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.Consider the integral $I = \int_{0}^{10} \frac{[ x ] e ^{[x]}}{e ^{x - 1}} d x$ , where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :
Mathematics · Definite Integration · MCQ
Q31.Let C1 be the curve obtained by the solution of differential equation $2 x y \frac{d y}{d x} = y^{2} - x^{2}, x > 0$ . Let the curve C2 be the solution of $\frac{2 x y}{x ^{2} - y ^{2}} = \frac{d y}{d x}$ . If both the curves pass through…
Mathematics · Differential Equations · MCQ
Q32.Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P (x) d x$ = 1 and P(x) leaves remainder 5 when it is divided by (x $-$ 2). Then the value of 9(b + c) is equal to :
Mathematics · Definite Integration · MCQ
Q33.Let A = {2, 3, 4, 5, ....., 30} and ' $≃$ ' be an equivalence relation on A $\times$ A, defined by (a, b) $≃$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered…
Mathematics · Sets and Relations · MCQ
Q34.The least value of |z| where z is complex number which satisfies the inequality $exp (\frac{( ∣ z ∣ + 3 ) ( ∣ z ∣ - 1 )}{∣∣ z ∣ + 1∣} lo g_{e} 2) \geq lo g_{2} ∣5 7 + 9 i ∣, i = - 1$ , is equal to :
Mathematics · Complex Numbers · MCQ
Q35.Let $α \in$ R be such that the function $f (x) = {\frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, α, x e 0 x = 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy $sin^{- 1} (\frac{3 x}{5}) + sin^{- 1} (\frac{4 x}{5}) = sin^{- 1} x$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q37.Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2 $2$ and 2 $5$ , respectively. Then the shortest distance from origin to a tangent to this circle which is…
Mathematics · Circle · MCQ
Q38.Let A( $-$ 1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of $Δ$ ABC and $Δ$ PQC respectively, such that A1 = 3A2,…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :
Mathematics · Probability · MCQ
Q40.The maximum value of $f (x) = sin^{2} x 1 + sin^{2} x sin^{2} x 1 + cos^{2} x cos^{2} x cos^{2} x cos 2 x cos 2 x sin 2 x, x \in R$ …
Mathematics · Application of Derivatives · MCQ
Q41.Let $\frac{1}{16}$ , a and b be in G.P. and $\frac{1}{a}$ , $\frac{1}{b}$ , 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to .
Mathematics · Sequences and Series · Numerical
Q42.For real numbers $α$ , $β$ , $γ$ and $δ$ , if $\int \frac{( x ^{2} - 1 ) + t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )}{( x ^{4} + 3 x ^{2} + 1 ) t a n ^{- 1} ( \frac{x ^{2} + 1}{x} )} d x = α lo g_{e} (tan^{- 1} (\frac{x ^{2} + 1}{x})) + β tan^{- 1} (\frac{γ ( x ^{2} + 1 )}{x}) + δ tan^{- 1} (\frac{x ^{2} + 1}{x}) + C$ …
Mathematics · Indefinite Integrals · Numerical
Q43.Let f : R $\to$ R and g : R $\to$ R be defined as $f (x) = {x + a, ∣ x - 1∣, x < 0 x \geq 0$ and $g (x) = {x + 1, (x - 1)^{2} + b, x < 0 x \geq 0$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q44.Consider the statistics of two sets of observations as follows : If the variance of the combined set of these two observations is $\frac{17}{9}$ , then the value of n is equal to . Includes table
Mathematics · Statistics · Numerical
Q45.Let $A = [a_{1} a_{2}]$ and $B = [b_{1} b_{2}]$ be two 2 $\times$ 1 matrices with real entries such that A = XB, where $X = \frac{1}{3} [11 - 1 k]$ …
Mathematics · Matrices and Determinants · Numerical
Q46.What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10 $-$ 3 Pa s, respectively. (Density of water : 103…
Physics · Properties of Matter · MCQ
Q47.The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are R1 and R2 respectively.
Physics · Geometrical Optics · MCQ
Q48.The following logic gate is equivalent to : Includes diagram
Physics · Electronic Devices · MCQ
Q49.Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh $-$ 1 and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip…
Physics · Circular Motion · MCQ
Q50.A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical… Includes diagram
Physics · Center of Mass · MCQ
Q51.A mosquito is moving with a velocity $v = 0.5 t^{2} i + 3 t j + 9 k$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?
Physics · Motion in A Plane · MCQ
Q52.Red light differs from blue light as they have :
Physics · Geometrical Optics · MCQ
Q53.The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? (mp = 1.00727u me = 0.00055u)
Physics · Dual Nature of Radiation · MCQ
Q54.Calculate the value of mean free path ( $λ$ ) for oxygen molecules at temperature 27 $^{\circ}$ C and pressure 1.01 $\times$ 105 Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 $\times$ 10 $-$ 23 JK $-$ 1)
Physics · Heat and Thermodynamics · MCQ
Q55.A charge Q is moving $d l$ distance in the magnetic field $B$ . Find the value of work done by $B$ .
Physics · Magnetics · MCQ
Q56.In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least…
Physics · Units and Measurements · MCQ
Q57.A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s.
Physics · Current Electricity · MCQ
Q58.Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
Physics · Electrostatics · MCQ
Q59.The magnetic field in a region is given by $B = B_{o} (\frac{x}{a}) k$ . A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $v$ … Includes diagram
Physics · Electromagnetic Induction · MCQ
Q60.A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q61.For the given circuit, comment on the type of transformer used. Includes diagram
Physics · Alternating Current · MCQ
Q62.A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $θ$ with the horizontal. The acceleration of the disc will be $\frac{2}{b}$ g sin $θ$ where b is .… Includes diagram
Physics · Rotational Motion · Numerical
Q63.The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is $Ω$ . (Round off to the Nearest Integer)
Physics · Current Electricity · Numerical
Q64.In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig.) the… Includes diagram
Physics · Capacitor · Numerical
Q65.If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5} \frac{G M ^{2}}{R}$ where x is (Round off to the…
Physics · Gravitation · Numerical
Q66.A body of mass 2 kg moves under a force of $(2 i + 3 j + 5 k)$ N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is …
Physics · Laws of Motion · Numerical
Q67.A closed organ pipe of length L and an open organ pipe contain gases of densities $ρ$ 1 and $ρ$ 2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same…
Physics · Waves · Numerical
Q68.A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just…
Physics · Motion in A Plane · Numerical
Q69.A deviation of 2 $^{\circ}$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light…
Physics · Geometrical Optics · Numerical
Q70.A force $F$ = $4 i + 3 j + 4 k$ is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is . (Round off…
Physics · Rotational Motion · Numerical