2024 · 31 Jan · Shift 1

90 questions · JEE Main

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2024 · 31 Jan · Shift 1

2024 · 31 Jan · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Biomolecules · MCQ
Q2.Consider the oxides of group 14 elements $SiO_{2}, GeO_{2}, SnO_{2}, PbO_{2}, CO$ and $GeO$ . The amphoteric oxides are
Chemistry · P Block Elements · MCQ
Q3.The compound that is white in color is
Chemistry · P Block Elements · MCQ
Q4.Give below are two statements: Statement - I: Noble gases have very high boiling points. Statement - II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low…
Chemistry · P Block Elements · MCQ
Q5.A species having carbon with sextet of electrons and can act as electrophile is called
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Identify the mixture that shows positive deviations from Raoult's Law
Chemistry · Solutions · MCQ
Q7.The correct statements from following are: A. The strength of anionic ligands can be explained by crystal field theory. B. Valence bond theory does not give a quantitative interpretation of kinetic stability of coordination compounds. C.…
Chemistry · Coordination Compounds · MCQ
Q8.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Alcohols react both as nucleophiles and electrophiles. Reason R: Alcohols react with active metals such as sodium, potassium…
Chemistry · Alcohols Phenols and Ethers · MCQ
Q9.The product (C) in the below mentioned reaction is : $CH_{3} - CH_{2} - CH_{2} - Br KOH_{(alc)} Δ A HBr B Δ KOH_{(aq)} C$ …
Chemistry · Haloalkanes and Haloarenes · MCQ
Q10.Identify the factor from the following that does not affect electrolytic conductance of a solution.
Chemistry · Electrochemistry · MCQ
Q11.Integrated rate law equation for a first order gas phase reaction is given by (where $P_{i}$ is initial pressure and $P_{t}$ is total pressure at time $t$ )
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q12.For the given reaction, choose the correct expression of $K_{C}$ from the following :- $Fe_{(aq)}^{3 +} + SCN_{(aq)}^{-} ⇌ (FeSCN)_{(aq)}^{2 +}$
Chemistry · Chemical Equilibrium · MCQ
Q13.The linear combination of atomic orbitals to form molecular orbitals takes place only when the combining atomic orbitals A. have the same energy B. have the minimum overlap C. have same symmetry about the molecular axis D. have different…
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q14.Identify correct statements from below: A. The chromate ion is square planar. B. Dichromates are generally prepared from chromates. C. The green manganate ion is diamagnetic. D. Dark green coloured $K_{2} MnO_{4}$ …
Chemistry · D and F Block Elements · MCQ
Q15.The metals that are employed in the battery industries are A. $Fe$ B. $Mn$ C. $Ni$ D. $Cr$ E. $Cd$ Choose the correct answer from the options given below:
Chemistry · D and F Block Elements · MCQ
Q16.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Practical Organic Chemistry · MCQ
Q17.'Adsorption' principle is used for which of the following purification method?
Chemistry · Surface Chemistry · MCQ
Q18.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: $pK_{a}$ value of phenol is 10.0 while that of ethanol is 15.9 . Reason R: Ethanol is stronger acid than…
Chemistry · Alcohols Phenols and Ethers · MCQ
Q19.Given below are two statements: Statement I: IUPAC name of $HO - CH_{2} - (CH_{2})_{3} - CH_{2} - COCH_{3}$ is 7-hydroxyheptan-2-one. Statement II: 2-oxoheptan-7-ol is the correct IUPAC name for…
Chemistry · Basics of Organic Chemistry · MCQ
Q20.The correct sequence of electron gain enthalpy of the elements listed below is A. Ar B. Br C. F D. S Choose the most appropriate from the options given below:
Chemistry · Periodic Table and Periodicity · MCQ
Q21.Consider the following reaction at $298 K \cdot \frac{3}{2} O_{2 (g)} ⇌ O_{3 (g)} \cdot K_{P} = 2.47 \times 1 0^{- 29}$ . $Δ_{r} G^{⊖}$ for the reaction is …
Chemistry · Thermodynamics · Numerical
Q22.The product of the following reaction is P. The number of hydroxyl groups present in the product P is . Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q23.The ionization energy of sodium in $kJ mol^{- 1}$ , if electromagnetic radiation of wavelength $242 nm$ is just sufficient to ionize sodium atom is .
Chemistry · Structure of Atom · Numerical
Q24.Number of alkanes obtained on electrolysis of a mixture of $CH_{3} COONa$ and $C_{2} H_{5} COONa$ is .
Chemistry · Electrochemistry · Numerical
Q25.The 'Spin only' Magnetic moment for $[Ni (NH_{3})_{6}]^{2 +}$ is $\times 1 0^{- 1} BM$ . (given $=$ Atomic number of $Ni : 28$ )
Chemistry · Coordination Compounds · Numerical
Q26.One Faraday of electricity liberates $x \times 1 0^{- 1}$ gram atom of copper from copper sulphate. $x$ is .
Chemistry · Electrochemistry · Numerical
Q27.Number of moles of methane required to produce $22 g CO_{2 (g)}$ after combustion is $x \times 1 0^{- 2}$ moles. The value of $x$ is .
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q28.Molar mass of the salt from $NaBr, NaNO_{3}, KI$ and $CaF_{2}$ which does not evolve coloured vapours on heating with concentrated $H_{2} SO_{4}$ is $g mol^{- 1}$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q29.The total number of hydrogen atoms in product A and product B is . Includes diagram
Chemistry · Haloalkanes and Haloarenes · Numerical
Q30.The number of species from the following in which the central atom uses $sp^{3}$ hybrid orbitals in its bonding is . $NH_{3}, SO_{2}, SiO_{2}, BeCl_{2}, CO_{2}, H_{2} O, CH_{4}, BF_{3}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q31. $lim_{x \to 0} \frac{e ^{2∣ s i n x ∣} - 2∣ s i n x ∣ - 1}{x ^{2}}$
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.For $α, β, γ e q 0$ , if $sin^{- 1} α + sin^{- 1} β + sin^{- 1} γ = π$ and $(α + β + γ) (α - γ + β) = 3 α β$ , then $γ$ equals
Mathematics · Inverse Trigonometric Functions · MCQ
Q33.Let $S$ be the set of positive integral values of $a$ for which $\frac{a x ^{2} + 2 ( a + 1 ) x + 9 a + 4}{x ^{2} - 8 x + 32} < 0, \forall x \in R$ . Then, the number of elements in $S$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let $α, β, γ, δ \in Z$ and let $A (α, β), B (1, 0), C (γ, δ)$ and $D (1, 2)$ be the vertices of a parallelogram $ABCD$ . If $A B = 10$ and the points $A$ and $C$ lie…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.For $0 < c < b < a$ , let $(a + b - 2 c) x^{2} + (b + c - 2 a) x + (c + a - 2 b) = 0$ and $α \neq = 1$ be one of its root. Then, among the two statements (I) If $α \in (- 1, 0)$ , then $b$ cannot be the geometric mean of $a$ and $c$ (II) If $α \in (0, 1)$ …
Mathematics · Sequences and Series · MCQ
Q36.If $f (x) = \frac{4 x + 3}{6 x - 4}, x e q \frac{2}{3}$ and $(f \circ f) (x) = g (x)$ , where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}}$ , then $(g o g o g) (4)$ is equal to
Mathematics · Functions · MCQ
Q37.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = \frac{( t a n x ) + y}{s i n x ( s e c x - s i n x t a n x )}, x \in (0, \frac{π}{2})$ satisfying the condition $y (\frac{π}{4}) = 2$ . Then, $y (\frac{π}{3})$ …
Mathematics · Differential Equations · MCQ
Q38.Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is
Mathematics · Probability · MCQ
Q39.Let $a = 3 \hat{i} + \hat{j} - 2 \hat{k}, b = 4 \hat{i} + \hat{j} + 7 \hat{k}$ and $c = \hat{i} - 3 \hat{j} + 4 \hat{k}$ be three vectors. If a vectors $p$ satisfies $p \times b = c \times b$ and $p \cdot a = 0$ …
Mathematics · Vector Algebra · MCQ
Q40.The sum of the series $\frac{1}{1 - 3 \cdot 1 ^{2} + 1 ^{4}} + \frac{2}{1 - 3 \cdot 2 ^{2} + 2 ^{4}} + \frac{3}{1 - 3 \cdot 3 ^{2} + 3 ^{4}} + \dots$ up to 10 -terms is
Mathematics · Sequences and Series · MCQ
Q41.Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is…
Mathematics · Probability · MCQ
Q42.The distance of the point $Q (0, 2, - 2)$ form the line passing through the point $P (5, - 4, 3)$ and perpendicular to the lines $r = (- 3 \hat{i} + 2 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 5 \hat{k}), λ \in R$ and $r = (\hat{i} - 2 \hat{j} + \hat{k}) + μ (- \hat{i} + 3 \hat{j} + 2 \hat{k}), μ \in R$ …
Mathematics · Vector Algebra · MCQ
Q43.If the system of linear equations $x - 2 y + z = - 4 2 x + α y + 3 z = 5 3 x - y + β z = 3$ has infinitely many solutions, then $12 α + 13 β$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q44.Let $g (x)$ be a linear function and $f (x) = {g (x) (\frac{1 + x}{2 + x})^{\frac{1}{x}}, x \leq 0, x > 0$ , is continuous at $x = 0$ . If $f^{'} (1) = f (- 1)$ , then the value $g (3)$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.The area of the region ${(x, y) : y^{2} \leq 4 x, x 0, x e q 3}$ is
Mathematics · Area Under the Curves · MCQ
Q46.The solution curve of the differential equation $y \frac{d x}{d y} = x (lo g_{e} x - lo g_{e} y + 1), x > 0, y > 0$ passing through the point $(e, 1)$ is
Mathematics · Differential Equations · MCQ
Q47.Let $a$ be the sum of all coefficients in the expansion of $(1 - 2 x + 2 x^{2})^{2023} (3 - 4 x^{2} + 2 x^{3})^{2024}$ and $b = lim_{x \to 0} (\frac{\int _{0}^{x} \frac{l o g ( 1 + t )}{t ^{2024} + 1} d t}{x ^{2}})$ . If the…
Mathematics · Binomial Theorem · MCQ
Q48. $If f (x) = x^{3} 3 x^{2} + 2 x^{3} - x 2 x^{2} + 1 2 x 4 1 + 3 x x^{3} + 6 x^{2} - 2 for all x \in R, then 2 f (0) + f^{'} (0) is equal to$ …
Mathematics · Application of Derivatives · MCQ
Q49.If one of the diameters of the circle $x^{2} + y^{2} - 10 x + 4 y + 13 = 0$ is a chord of another circle $C$ , whose center is the point of intersection of the lines $2 x + 3 y = 12$ and $3 x - 2 y = 5$ , then the radius of the circle $C$ is :
Mathematics · Circle · MCQ
Q50.If the foci of a hyperbola are same as that of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point $(2, \frac{14}{3} \frac{2}{5})$ …
Mathematics · Hyperbola · MCQ
Q51.If $α$ denotes the number of solutions of $∣1 - i ∣^{x} = 2^{x}$ and $β = (\frac{∣ z ∣}{a r g ( z )})$ , where $$z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right],…
Mathematics · Complex Numbers · Numerical
Q52.In the expansion of $(1 + x) (1 - x^{2}) (1 + \frac{3}{x} + \frac{3}{x ^{2}} + \frac{1}{x ^{3}})^{5}, x e q 0$ , the sum of the coefficients of $x^{3}$ and $x^{- 13}$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q53.Let $a$ and $b$ be two vectors such that $∣ a ∣ = 1, ∣ b ∣ = 4$ , and $a \cdot b = 2$ . If $c = (2 a \times b) - 3 b$ and the angle between $b$ and $c$ is $α$ , then $192 sin^{2} α$ …
Mathematics · Vector Algebra · Numerical
Q54.If the integral $525 0 \int \frac{π}{2} sin 2 x cos^{\frac{11}{2}} x (1 + cos^{\frac{5}{2}} x)^{\frac{1}{2}} d x$ is equal to $(n 2 - 64)$ , then $n$ is equal to .
Mathematics · Definite Integration · Numerical
Q55.Let $S = (- 1, \infty)$ and $f : S \to R$ be defined as $f (x) = \int_{- 1}^{x} (e^{t} - 1)^{11} (2 t - 1)^{5} (t - 2)^{7} (t - 3)^{12} (2 t - 10)^{61} d t,$ Let $p =$ Sum of squares of the values of $x$ , where $f (x)$ …
Mathematics · Definite Integration · Numerical
Q56.Let $Q$ and $R$ be the feet of perpendiculars from the point $P (a, a, a)$ on the lines $x = y, z = 1$ and $x = - y, z = - 1$ respectively. If $∠ QPR$ is a right angle, then $12 a^{2}$ is equal to …
Mathematics · 3D Geometry · Numerical
Q57.Let the foci and length of the latus rectum of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > bb e (\pm 5, 0)$ and $50$ , respectively. Then, the square of the eccentricity of the hyperbola $\frac{x ^{2}}{b ^{2}} - \frac{y ^{2}}{a ^{2} b ^{2}} = 1$ …
Mathematics · Hyperbola · Numerical
Q58.The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .
Mathematics · Permutations and Combinations · Numerical
Q59.Let $A = {1, 2, 3, 4}$ and $R = {(1, 2), (2, 3), (1, 4)}$ be a relation on $A$ . Let $S$ be the equivalence relation on $A$ such that $R \subset S$ and the number of elements in $S$ is $n$ . Then, the…
Mathematics · Sets and Relations · Numerical
Q60.Let $f : R \to R$ be a function defined by $f (x) = \frac{4 ^{x}}{4 ^{x} + 2}$ and $M = \int_{f (a)}^{f (1 - a)} x sin^{4} (x (1 - x)) d x, N = \int_{f (a)}^{f (1 - a)} sin^{4} (x (1 - x)) d x; a e q \frac{1}{2}$ . If $α M = β N, α, β \in N$ …
Mathematics · Definite Integration · Numerical
Q61.Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $(\frac{2 2 + 1}{32}) \frac{Gm ^{2}}{L ^{2}}$ , the length of…
Physics · Gravitation · MCQ
Q62.Two charges $q$ and $3 q$ are separated by a distance ' $r$ ' in air. At a distance $x$ from charge $q$ , the resultant electric field is zero. The value of $x$ is :
Physics · Electrostatics · MCQ
Q63.The given figure represents two isobaric processes for the same mass of an ideal gas, then Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q64.In the given arrangement of a doubly inclined plane two blocks of masses $M$ and $m$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane… Includes diagram
Physics · Laws of Motion · MCQ
Q65.The relation between time ' $t$ ' and distance ' $x$ ' is $t = α x^{2} + β x$ , where $α$ and $β$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is :
Physics · Motion in A Straight Line · MCQ
Q66.An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:
Physics · Center of Mass · MCQ
Q67.The parameter that remains the same for molecules of all gases at a given temperature is :
Physics · Heat and Thermodynamics · MCQ
Q68.A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B = B_{0} \hat{k}$ as shown in figure. The magnetic force on the wire if it has a… Includes diagram
Physics · Magnetics · MCQ
Q69.When a metal surface is illuminated by light of wavelength $λ$ , the stopping potential is $8 V$ . When the same surface is illuminated by light of wavelength $3 λ$ , stopping potential is $2 V$ . The threshold…
Physics · Dual Nature of Radiation · MCQ
Q70.The refractive index of a prism with apex angle $A$ is $cot A /2$ . The angle of minimum deviation is :
Physics · Geometrical Optics · MCQ
Q71.The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60 cm$ , the length of the closed pipe will be:
Physics · Waves · MCQ
Q72.If the wavelength of the first member of Lyman series of hydrogen is $λ$ . The wavelength of the second member will be
Physics · Atoms and Nuclei · MCQ
Q73.A coil is places perpendicular to a magnetic field of $5000 T$ . When the field is changed to $3000 T$ in $2 s$ , an induced emf of $22 V$ is produced in the coil. If the diameter of the coil is $0.02 m$ …
Physics · Electromagnetic Induction · MCQ
Q74.A coin is placed on a disc. The coefficient of friction between the coin and the disc is $μ$ . If the distance of the coin from the center of the disc is $r$ , the maximum angular velocity which can be given to the disc, so that the coin…
Physics · Circular Motion · MCQ
Q75.Two conductors have the same resistances at $0^{\circ} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2}$ . The respective temperature coefficients for their series and parallel combinations are :
Physics · Current Electricity · MCQ
Q76.If the percentage errors in measuring the length and the diameter of a wire are $0.1%$ each. The percentage error in measuring its resistance will be:
Physics · Units and Measurements · MCQ
Q77.A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?
Physics · Properties of Matter · MCQ
Q78.A force is represented by $F = a x^{2} + b t^{\frac{1}{2}}$ where $x =$ distance and $t =$ time. The dimensions of $b^{2} / a$ are:
Physics · Units and Measurements · MCQ
Q79.In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 1 0^{10} Hz$ and an amplitude of $50 Vm^{- 1}$ . The total average energy density of the electromagnetic field of the wave is :…
Physics · Electromagnetic Waves · MCQ
Q80.Identify the logic operation performed by the given circuit. Includes diagram
Physics · Electronic Devices · MCQ
Q81.A solid circular disc of mass $50 kg$ rolls along a horizontal floor so that its center of mass has a speed of $0.4 m / s$ . The absolute value of work done on the disc to stop it is J.
Physics · Center of Mass · Numerical
Q82.An electron moves through a uniform magnetic field $B = B_{0} \hat{i} + 2 B_{0} \hat{j} T$ . At a particular instant of time, the velocity of electron is $u = 3 \hat{i} + 5 \hat{j} m / s$ . If the magnetic force acting…
Physics · Magnetics · Numerical
Q83.A parallel plate capacitor with plate separation $5 mm$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2 mm$ , while keeping the battery connections intact, the capacitor…
Physics · Capacitor · Numerical
Q84.The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02%$ is $m$ . (Take density of sea water $= 1 0^{3} kgm^{- 3}$ , Bulk modulus of rubber $= 9 \times 1 0^{8} Nm^{- 2}$ …
Physics · Properties of Matter · Numerical
Q85.A body starts falling freely from height $H$ hits an inclined plane in its path at height $h$ . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which…
Physics · Center of Mass · Numerical
Q86.A particle performs simple harmonic motion with amplitude $A$ . Its speed is increased to three times at an instant when its displacement is $\frac{2 A}{3}$ . The new amplitude of motion is $\frac{n A}{3}$ . The value of $n$ is …
Physics · Simple Harmonic Motion · Numerical
Q87.The mass defect in a particular reaction is $0.4 g$ . The amount of energy liberated is $n \times 1 0^{7} kWh$ , where $n =$ . (speed of light $= 3 \times 1 0^{8} m / s)$
Physics · Atoms and Nuclei · Numerical
Q88.A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L (L = l^{2})$ . The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $x \times 1 0^{- 7} H$ …
Physics · Electromagnetic Induction · Numerical
Q89.Equivalent resistance of the following network is $Ω$ . Includes diagram
Physics · Current Electricity · Numerical
Q90.Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_{1}$ (b) Waves are coherent is $I_{2}$ and differ in phase by $6 0^{\circ}$ . If $\frac{I _{1}}{I _{2}} = \frac{10}{x}$ …
Physics · Wave Optics · Numerical