2024 · 6 Apr · Shift 2

89 questions · JEE Main

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2024 · 6 Apr · Shift 2

2024 · 6 Apr · Shift 2

89 questions · JEE Main

Chemistry29 questions Mathematics30 questions Physics30 questions

Q1.The number of ions from the following that are expected to behave as oxidising agent is : $Sn^{4 +}, Sn^{2 +}, Pb^{2 +}, Tl^{3 +}, Pb^{4 +}, Tl^{+}$
Chemistry · Redox Reactions · MCQ
Q2.The correct arrangement for decreasing order of electrophilic substitution for above compounds is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q3.During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in $NH_{4} OH$ solution when sodium carbonate extract was first acidified with dil. $HNO_{3}$ …
Chemistry · Salt Analysis · MCQ
Q4.Consider the given reaction, identify the major product P. Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q5.Match List I with List II. Choose the correct answer from the options given below : Includes table
Chemistry · Redox Reactions · MCQ
Q6.Identify the product A in the following reaction. Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q7.The correct statement among the following, for a "chromatography" purification method is :
Chemistry · Practical Organic Chemistry · MCQ
Q8.Consider the above chemical reaction. Product "A" is : Includes diagram
Chemistry · Hydrocarbons · MCQ
Q9.How can an electrochemical cell be converted into an electrolytic cell ?
Chemistry · Electrochemistry · MCQ
Q10.Given below are two statements : Statement I : $PF_{5}$ and $BrF_{5}$ both exhibit $sp^{3} d$ hybridisation. Statement II : Both $SF_{6}$ and $[Co (NH_{3})_{6}]^{3 +}$ exhibit $sp^{3} d^{2}$ …
Chemistry · Coordination Compounds · MCQ
Q11.Match List I with List II. Choose the correct answer from the options given below : Includes table
Chemistry · Coordination Compounds · MCQ
Q12.Molality $(m)$ of $3 M$ aqueous solution of $NaCl$ is : (Given : Density of solution $= 1.25 g mL^{- 1}$ , Molar mass in $g mol^{- 1} : Na - 23, Cl - 35.5$ )
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q13.Evaluate the following statements related to group 14 elements for their correctness. (A) Covalent radius decreases down the group from $C$ to $Pb$ in a regular manner. (B) Electronegativity decreases from $C$ to…
Chemistry · P Block Elements · MCQ
Q14.Arrange the following elements in the increasing order of number of unpaired electrons in it. (A) $Sc$ (B) $Cr$ (C) $V$ (D) $Ti$ (E) $Mn$ Choose the correct answer from the options given below :
Chemistry · D and F Block Elements · MCQ
Q15.The major products formed : A and B respectively are : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q16.The incorrect statements regarding enzymes are : (A) Enzymes are biocatalysts. (B) Enzymes are non-specific and can catalyse different kinds of reactions. (C) Most Enzymes are globular proteins. (D) Enzyme - oxidase catalyses the…
Chemistry · Biomolecules · MCQ
Q17.The ratio $\frac{K _{P}}{K _{C}}$ for the reaction : $CO_{(g)} + \frac{1}{2} O_{2 (g)} ⇌ CO_{2 (g)}$ is :
Chemistry · Chemical Equilibrium · MCQ
Q18.The correct IUPAC name of $[PtBr_{2} (PMe_{3})_{2}]$ is :
Chemistry · Coordination Compounds · MCQ
Q19.The incorrect statement regarding the geometrical isomers of 2-butene is :
Chemistry · Basics of Organic Chemistry · MCQ
Q20.Consider the following reactions The number of protons that do not involve in hydrogen bonding in the product B is . Includes diagram
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q21.For the reaction at $298 K, 2 A + B \to C, Δ H = 400 kJ mol^{- 1}$ and $Δ S = 0.2 kJ mol^{- 1} K^{- 1}$ . The reaction will become…
Chemistry · Thermodynamics · Numerical
Q22.Number of carbocations from the following that are not stabilized by hyperconjugation is . Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q23.When ' $x$ ' $\times 1 0^{- 2} mL$ methanol (molar mass $= 32 g$ ' density $= 0.792 g / cm^{3}$ ) is added to $100 mL$ . water (density $= 1 g / cm^{3}$ ), the following diagram is… Includes diagram
Chemistry · Solutions · Numerical
Q24.For hydrogen atom, energy of an electron in first excited state is $- 3.4 eV, K . E$ . of the same electron of hydrogen atom is $x eV$ . Value of $x$ is $\times 1 0^{- 1} eV$ …
Chemistry · Structure of Atom · Numerical
Q25.Consider the two different first order reactions given below $A + B \to C (Reaction 1) P \to Q (Reaction 2)$ The…
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q26.An amine $(X)$ is prepared by ammonolysis of benzyl chloride. On adding p-toluenesulphonyl chloride to it the solution remains clear. Molar mass of the amine $(X)$ formed is $g mol^{- 1}$ …
Chemistry · Compounds Containing Nitrogen · Numerical
Q27.Among $VO_{2}^{+}, MnO_{4}^{-}$ and $Cr_{2} O_{7}^{2 -}$ , the spin-only magnetic moment value of the species with least oxidising ability is BM (Nearest integer). (Given atomic member $V = 23, Mn = 25, Cr = 24$ …
Chemistry · D and F Block Elements · Numerical
Q28.The ratio of number of oxygen atoms to bromine atoms in the product Q is $\times 1 0^{- 1}$ . Includes diagram
Chemistry · Haloalkanes and Haloarenes · Numerical
Q29.Total number of species from the following with central atom utilising $sp^{2}$ hybrid orbitals for bonding is . $NH_{3}, SO_{2}, SiO_{2}, BeCl_{2}, C_{2} H_{2}, C_{2} H_{4}, BCl_{3}, HCHO, C_{6} H_{6}, BF_{3}, C_{2} H_{4} Cl_{2}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q30.If the function $f (x) = (\frac{1}{x})^{2 x}; x > 0$ attains the maximum value at $x = \frac{1}{e}$ then :
Mathematics · Functions · MCQ
Q31.If $z_{1}, z_{2}$ are two distinct complex number such that $\frac{z _{1} - 2 z _{2}}{\frac{1}{2} - z _{1} z ˉ _{2}} = 2$ , then
Mathematics · Complex Numbers · MCQ
Q32.Let $A = {1, 2, 3, 4, 5}$ . Let $R$ be a relation on $A$ defined by $x R y$ if and only if $4 x \leq 5 y$ . Let $m$ be the number of elements in $R$ and $n$ be the minimum…
Mathematics · Sets and Relations · MCQ
Q33.Let $f (x) = \frac{1}{7 - s i n 5 x}$ be a function defined on $R$ . Then the range of the function $f (x)$ is equal to :
Mathematics · Functions · MCQ
Q34. $lim_{n \to \infty} \frac{( 1 ^{2} - 1 ) ( n - 1 ) + ( 2 ^{2} - 2 ) ( n - 2 ) + \dots + ( ( n - 1 ) ^{2} - ( n - 1 ) ) \cdot 1}{( 1 ^{3} + 2 ^{3} + \dots\dots + n ^{3} ) - ( 1 ^{2} + 2 ^{2} + \dots\dots + n ^{2} )}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.If $A$ is a square matrix of order 3 such that $det (A) = 3$ and $det (adj (- 4 adj (- 3 adj (3 adj ((2 A)^{- 1}))))) = 2^{m} 3^{n}$ …
Mathematics · Matrices and Determinants · MCQ
Q36.If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :
Mathematics · Probability · MCQ
Q37.Let $a = 2 \hat{i} + \hat{j} - \hat{k}, b = ((a \times (\hat{i} + \hat{j})) \times \hat{i}) \times \hat{i}$ . Then the square of the projection of $a$ on $b$ is:
Mathematics · Vector Algebra · MCQ
Q38.Let $a = 6 \hat{i} + \hat{j} - \hat{k}$ and $b = \hat{i} + \hat{j}$ . If $c$ is a is vector such that $∣ c ∣ \geq 6, a \cdot c = 6∣ c ∣, ∣ c - a ∣ = 22$ …
Mathematics · Vector Algebra · MCQ
Q39.If the area of the region ${(x, y) : \frac{a}{x ^{2}} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2, 0 < a < 1}$ is $(lo g_{e} 2) - \frac{1}{7}$ then the value of $7 a - 3$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q40.Let $P (α, β, γ)$ be the image of the point $Q (3, - 3, 1)$ in the line $\frac{x - 0}{1} = \frac{y - 3}{1} = \frac{z - 1}{- 1}$ and $R$ be the point $(2, 5, - 1)$ . If the area of the triangle $PQR$ is $λ$ …
Mathematics · 3D Geometry · MCQ
Q41.Let $A B C$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $A B C$ and the same process is repeated infinitely many times. If $P$ is the sum of perimeters and $Q$ is…
Mathematics · Sequences and Series · MCQ
Q42.Suppose the solution of the differential equation $\frac{d y}{d x} = \frac{( 2 + α ) x - β y + 2}{β x - 2 α y - ( β γ - 4 α )}$ represents a circle passing through origin. Then the radius of this circle is :
Mathematics · Differential Equations · MCQ
Q43.A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took…
Mathematics · Sequences and Series · MCQ
Q44.If $P (6, 1)$ be the orthocentre of the triangle whose vertices are $A (5, - 2), B (8, 3)$ and $C (h, k)$ , then the point $C$ lies on the circle :
Mathematics · Circle · MCQ
Q45.If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $31 5^{th}$ position in this arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q46.Suppose for a differentiable function $h, h (0) = 0, h (1) = 1$ and $h^{'} (0) = h^{'} (1) = 2$ . If $g (x) = h (e^{x}) e^{h (x)}$ , then $g^{'} (0)$ is equal to:
Mathematics · Differentiation · MCQ
Q47.Let $0 \leq r \leq n$ . If $^{n + 1} C_{r + 1} :^{n} C_{r} :^{n - 1} C_{r - 1} = 55 : 35 : 21$ , then $2 n + 5 r$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q48.If $\int \frac{1}{a ^{2} s i n ^{2} x + b ^{2} c o s ^{2} x} d x = \frac{1}{12} tan^{- 1} (3 tan x) +$ constant, then the maximum value of $a sin x + b cos x$ , is :
Mathematics · Indefinite Integrals · MCQ
Q49.If the locus of the point, whose distances from the point $(2, 1)$ and $(1, 3)$ are in the ratio $5 : 4$ , is $a x^{2} + b y^{2} + c x y + d x + ey + 170 = 0$ , then the value of $a^{2} + 2 b + 3 c + 4 d + e$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q50.Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f : [0, \infty) \to R$ be a function defined by $f (x) = [\frac{x}{2} + 3] - [x]$ . Let $S$ be the set of all points in the…
Mathematics · Limits Continuity and Differentiability · Numerical
Q51.In a triangle $ABC, BC = 7, AC = 8, AB = α \in N$ and $cos A = \frac{2}{3}$ . If $49 cos (3 C) + 42 = \frac{m}{n}$ , where $gcd (m, n) = 1$ , then $m + n$ …
Mathematics · Properties of Triangle · Numerical
Q52.Let $[t]$ denote the largest integer less than or equal to $t$ . If $0 \int 3 ([x^{2}] + [\frac{x ^{2}}{2}]) d x = a + b 2 - 3 - 5 + c 6 - 7$ , where $a, b, c \in Z$ …
Mathematics · Definite Integration · Numerical
Q53.If the solution $y (x)$ of the given differential equation $(e^{y} + 1) cos x d x + e^{y} sin x d y = 0$ passes through the point $(\frac{π}{2}, 0)$ , then the value of $e^{y (\frac{π}{6})}$ …
Mathematics · Differential Equations · Numerical
Q54.If the shortest distance between the lines $\frac{x - λ}{3} = \frac{y - 2}{- 1} = \frac{z - 1}{1}$ and $\frac{x + 2}{- 3} = \frac{y + 5}{2} = \frac{z - 4}{4}$ is $\frac{44}{30}$ , then the largest possible value of $∣ λ ∣$ is equal to …
Mathematics · 3D Geometry · Numerical
Q55.The length of the latus rectum and directrices of hyperbola with eccentricity e are 9 and $x = \pm \frac{4}{3}$ , respectively. Let the line $y - 3 x + 3 = 0$ touch this hyperbola at $(x_{0}, y_{0})$ . If $m$ …
Mathematics · Hyperbola · Numerical
Q56.Let $α, β$ be roots of $x^{2} + 2 x - 8 = 0$ . If $U_{n} = α^{n} + β^{n}$ , then $\frac{U _{10} + 2 U _{9}}{2 U _{8}}$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q57.If the system of equations $2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = - 1$ has infinitely many solutions, then $(λ - μ)$ is equal to :
Mathematics · Matrices and Determinants · Numerical
Q58.If $S (x) = (1 + x) + 2 (1 + x)^{2} + 3 (1 + x)^{3} + \dots + 60 (1 + x)^{60}, x e q 0$ , and $(60)^{2} S (60) = a (b)^{b} + b$ , where $a, b \in N$ , then $(a + b)$ equal to .
Mathematics · Sequences and Series · Numerical
Q59.From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If…
Mathematics · Probability · Numerical
Q60.A car of $800 kg$ is taking turn on a banked road of radius $300 m$ and angle of banking $3 0^{\circ}$ . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $(g = 10 m / s^{2}, 3 = 1.73)$ …
Physics · Circular Motion · MCQ
Q61.A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_{1}$ . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_{2}$ . Time required to…
Physics · Motion in A Straight Line · MCQ
Q62.Given below are two statements: Statement (I) : Dimensions of specific heat is $[L^{2} T^{- 2} K^{- 1}]$ . Statement (II) : Dimensions of gas constant is $[M L^{2} T^{- 1} K^{- 1}]$ …
Physics · Heat and Thermodynamics · MCQ
Q63.A body of weight $200 N$ is suspended from a tree branch through a chain of mass $10 kg$ . The branch pulls the chain by a force equal to (if $g = 10 m / s^{2}$ ) :
Physics · Laws of Motion · MCQ
Q64.The number of electrons flowing per second in the filament of a $110 W$ bulb operating at $220 V$ is : (Given $e = 1.6 \times 1 0^{- 19} C$ )
Physics · Current Electricity · MCQ
Q65.The acceptor level of a p-type semiconductor is $6 eV$ . The maximum wavelength of light which can create a hole would be : Given $hc = 1242 eV nm$ .
Physics · Electronic Devices · MCQ
Q66.In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{th}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49…
Physics · Units and Measurements · MCQ
Q67.In a coil, the current changes from $- 2 A$ to $+ 2 A$ in $0.2 s$ and induces an emf of $0.1 V$ . The self inductance of the coil is :
Physics · Electromagnetic Induction · MCQ
Q68.Energy of 10 non rigid diatomic molecules at temperature $T$ is :
Physics · Heat and Thermodynamics · MCQ
Q69.When UV light of wavelength $300 nm$ is incident on the metal surface having work function $2.13 eV$ , electron emission takes place. The stopping potential is : (Given hc $= 1240 eV nm$ )
Physics · Dual Nature of Radiation · MCQ
Q70.Match List I with List II: Choose the correct answer from the options given below : Includes table Includes diagram
Physics · Magnetic Properties of Matter · MCQ
Q71.For the thin convex lens, the radii of curvature are at $15 cm$ and $30 cm$ respectively. The focal length the lens is $20 cm$ . The refractive index of the material is :
Physics · Geometrical Optics · MCQ
Q72.Two identical conducting spheres P and S with charge Q on each, repel each other with a force $16 N$ . A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new…
Physics · Electrostatics · MCQ
Q73.The longest wavelength associated with Paschen series is : (Given $R_{H} = 1.097 \times 1 0^{7} SI$ unit)
Physics · Atoms and Nuclei · MCQ
Q74.A total of $48 J$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^{\circ} C$ . The work done by the gas is: Given, $R = 8.3 J K^{- 1} mol^{- 1}$ …
Physics · Heat and Thermodynamics · MCQ
Q75.When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :
Physics · Work Power and Energy · MCQ
Q76.Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $R =$ Radius of bubble, $S =$ Surface tension of bubble)
Physics · Properties of Matter · MCQ
Q77.Assuming the earth to be a sphere of uniform mass density, a body weighed $300 N$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?
Physics · Gravitation · MCQ
Q78.In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $= 49 MSD; 20$ divisions on main scale in each $cm$ For mark on paper $MSR = 8.45 cm, VC = 26$ …
Physics · Units and Measurements · MCQ
Q79.In the given electromagnetic wave $E_{y} = 600 sin (ω t - kx) Vm^{- 1}$ , intensity of the associated light beam is (in $W / m^{2}$ : (Given $ϵ_{0} = 9 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ …
Physics · Electromagnetic Waves · MCQ
Q80.For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $2.5 nF$ . If resistance of $200Ω$ and $100 mH$ inductor is being used in the given circuit. The…
Physics · Alternating Current · Numerical
Q81.Three balls of masses $2 kg, 4 kg$ and $6 kg$ respectively are arranged at centre of the edges of an equilateral triangle of side $2 m$ . The moment of inertia of the system about an axis through the…
Physics · Rotational Motion · Numerical
Q82.In the given figure an ammeter A consists of a $240Ω$ coil connected in parallel to a $10Ω$ shunt. The reading of the ammeter is $mA$ . Includes diagram
Physics · Current Electricity · Numerical
Q83.A coil having 100 turns, area of $5 \times 1 0^{- 3} m^{2}$ , carrying current of $1 mA$ is placed in uniform magnetic field of $0.20 T$ such a way that plane of coil is perpendicular to the magnetic field. The…
Physics · Magnetics · Numerical
Q84.A capacitor of $10 μ F$ capacitance whose plates are separated by $10 mm$ through air and each plate has area $4 cm^{2}$ is now filled equally with two dielectric media of $K_{1} = 2, K_{2} = 3$ respectively as shown… Includes diagram
Physics · Capacitor · Numerical
Q85.A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^{2} = 1 + t^{2}$ . Its acceleration at any time $t$ is $x^{- n}$ where $n =$ .
Physics · Motion in A Straight Line · Numerical
Q86.Two coherent monochromatic light beams of intensities I and $4 I$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $x I$ . The value of $x$ is …
Physics · Wave Optics · Numerical
Q87.Two open organ pipes of lengths $60 cm$ and $90 cm$ resonate at $6^{th}$ and $5^{th}$ harmonics respectively. The difference of frequencies for the given modes is…
Physics · Waves · Numerical
Q88.In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2 V$ . The wavelength of light emitted by hydrogen atom when excited to the first excitation level is…
Physics · Dual Nature of Radiation · Numerical
Q89.A wire of cross sectional area A, modulus of elasticity $2 \times 1 0^{11} Nm^{- 2}$ and length $2 m$ is stretched between two vertical rigid supports. When a mass of $2 kg$ is suspended at the middle it sags… Includes diagram
Physics · Properties of Matter · Numerical