2024 · 30 Jan · Shift 2

90 questions · JEE Main

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2024 · 30 Jan · Shift 2

2024 · 30 Jan · Shift 2

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.The products A and B formed in the following reaction scheme are respectively Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q2.The correct stability order of carbocations is
Chemistry · Basics of Organic Chemistry · MCQ
Q3.Which among the following purification methods is based on the principle of "Solubility" in two different solvents?
Chemistry · Basics of Organic Chemistry · MCQ
Q4.IUPAC name of following compound is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q5.The solution from the following with highest depression in freezing point/lowest freezing point is
Chemistry · Solutions · MCQ
Q6.Given below are two statements: Statement - I: Since Fluorine is more electronegative than nitrogen, the net dipole moment of $NF_{3}$ is greater than $NH_{3}$ . Statement - II: In $NH_{3}$ , the orbital dipole due to…
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q7.A and B formed in the following reactions are: $CrO_{2} Cl_{2} + 4 NaOH \to A + 2 NaCl + 2 H_{2} O, A + 2 HCl + 2 H_{2} O_{2} \to B + 3 H_{2} O$ …
Chemistry · P Block Elements · MCQ
Q8.If a substance ' $A$ ' dissolves in solution of a mixture of ' $B$ ' and ' $C$ ' with their respective number of moles as $n_{A}, n_{B}$ and $n_{C_{3}}$ . Mole fraction of $C$ in the…
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q9.The molecule / ion with square pyramidal shape is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q10.Given below are two statements: Statement - I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow $S_{N}^{2}$ mechanism. Statement - II: A…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q11.Choose the correct statements about the hydrides of group 15 elements. A. The stability of the hydrides decreases in the order $NH_{3} > PH_{3} > AsH_{3} > SbH_{3} > BiH_{3}$ . B. The reducing…
Chemistry · P Block Elements · MCQ
Q12.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: $H_{2} Te$ is more acidic than $H_{2} S$ . Reason R: Bond dissociation enthalpy of $H_{2} Te$ …
Chemistry · Periodic Table and Periodicity · MCQ
Q13.Alkaline oxidative fusion of $MnO_{2}$ gives "A" which on electrolytic oxidation in alkaline solution produces B. A and B respectively are
Chemistry · Electrochemistry · MCQ
Q14.Salicylaldehyde is synthesized from phenol, when reacted with
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q15.m-chlorobenzaldehyde on treatment with 50% KOH solution yields :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q16.Products A and B formed in the following set of reactions are Includes diagram
Chemistry · Hydrocarbons · MCQ
Q17.The orange colour of $K_{2} Cr_{2} O_{7}$ and purple colour of $KMnO_{4}$ is due to
Chemistry · D and F Block Elements · MCQ
Q18.The coordination geometry around the manganese in decacarbonyldimanganese $(0)$ is
Chemistry · Coordination Compounds · MCQ
Q19.Reduction potential of ions are given below: $ClO_{4}^{-} E^{\circ} = 1.19 V IO_{4}^{-} E^{\circ} = 1.65 V BrO_{4}^{-} E^{\circ} = 1.74 V$ …
Chemistry · Electrochemistry · MCQ
Q20.Given below are two statements: Statement - I: Along the period, the chemical reactivity of the elements gradually increases from group 1 to group 18 . Statement - II: The nature of oxides formed by group 1 elements is basic while that of…
Chemistry · Periodic Table and Periodicity · MCQ
Q21.The total number of correct statements, regarding the nucleic acids is . A. RNA is regarded as the reserve of genetic information B. DNA molecule self-duplicates during cell division C. DNA synthesizes proteins in…
Chemistry · Biomolecules · Numerical
Q22.Number of metal ions characterized by flame test among the following is . $Sr^{2 +}, Ba^{2 +}, Ca^{2 +}, Cu^{2 +}, Zn^{2 +}, Co^{2 +}, Fe^{2 +}$
Chemistry · D and F Block Elements · Numerical
Q23.Number of spectral lines obtained in $He^{+}$ spectra, when an electron makes transition from fifth excited state to first excited state will be
Chemistry · Structure of Atom · Numerical
Q24.Total number of species from the following which can undergo disproportionation reaction is . $H_{2} O_{2}, ClO_{3}^{-}, P_{4}, Cl_{2}, Ag, Cu^{+ 1}, F_{2}, NO_{2}, K^{+}$ …
Chemistry · Redox Reactions · Numerical
Q25.Number of geometrical isomers possible for the given structure is/are . Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q26.The $pH$ of an aqueous solution containing $1 M$ benzoic acid $(pK_{a} = 4.20)$ and $1 M$ sodium benzoate is 4.5. The volume of benzoic acid solution in $300 mL$ of this…
Chemistry · Ionic Equilibrium · Numerical
Q27. $NO_{2}$ required for a reaction is produced by decomposition of $N_{2} O_{5}$ in $CCl_{4}$ as by equation $2 N_{2} O_{5 (g)} \to 4 NO_{2 (g)} + O_{2 (g)}$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q28.Number of complexes which show optical isomerism among the following is . $cis- [Cr (ox)_{2} Cl_{2}]^{3 -}, [Co (en)_{3}]^{3 +}, cis- [Pt (en)_{2} Cl_{2}]^{2 +}, cis- [Co (en)_{2} Cl_{2}]^{+}, trans- [Pt (en)_{2} Cl_{2}]^{2 +}, trans- [Cr (ox)_{2} Cl_{2}]^{3 -}$ …
Chemistry · Coordination Compounds · Numerical
Q29.2-chlorobutane $+ Cl_{2} \to C_{4} H_{8} Cl_{2}$ (isomers) Total number of optically active isomers shown by $C_{4} H_{8} Cl_{2}$ , obtained in the above reaction is …
Chemistry · Haloalkanes and Haloarenes · Numerical
Q30.Two reactions are given below: $2 Fe_{(s)} + \frac{3}{2} O_{2 (g)} \to Fe_{2} O_{3 (s)}, Δ H^{\circ} = - 822 kJ / mol C_{(s)} + \frac{1}{2} O_{2 (g)} \to CO_{(g)}, Δ H^{\circ} = - 110 kJ / mol$ …
Chemistry · Thermodynamics · Numerical
Q31.Let $f : R \to R$ be a function defined by $f (x) = \frac{x}{( 1 + x ^{4} ) ^{1/4}}$ , and $g (x) = f (f (f (f (x))))$ . Then, $18 \int_{0}^{25} x^{2} g (x) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q32.Let $a$ and $b$ be be two distinct positive real numbers. Let $1 1^{th}$ term of a GP, whose first term is $a$ and third term is $b$ , is equal to $p^{th}$ term of another GP, whose first term is $a$ and fifth term is $b$ .…
Mathematics · Sequences and Series · MCQ
Q33.Let $y = f (x)$ be a thrice differentiable function in $(- 5, 5)$ . Let the tangents to the curve $y = f (x)$ at $(1, f (1))$ and $(3, f (3))$ make angles $π /6$ and $π /4$ , respectively with positive $x$ -axis. If $27 1 \int 3 ((f^{'} (t))^{2} + 1) f^{''} (t) d t = α + β 3$ …
Mathematics · Definite Integration · MCQ
Q34.For $α, β \in (0, π /2)$ , let $3 sin (α + β) = 2 sin (α - β)$ and a real number $k$ be such that $tan α = k tan β$ . Then, the value of $k$ is equal to
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35.If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^{3} + 2 z^{2} + 2 z + 1 = 0$ , is equal to
Mathematics · Complex Numbers · MCQ
Q36.Let $f : R - {0} \to R$ be a function satisfying $f (\frac{x}{y}) = \frac{f ( x )}{f ( y )}$ for all $x, y, f (y) e q 0$ . If $f^{'} (1) = 2024$ , then
Mathematics · Differentiation · MCQ
Q37.Let $R = x 00 0 y 0 00 z$ be a non-zero $3 \times 3$ matrix, where $x sin θ = y sin (θ + \frac{2 π}{3}) = z sin (θ + \frac{4 π}{3}) e q 0, θ \in (0, 2 π)$ …
Mathematics · Matrices and Determinants · MCQ
Q38.If $x^{2} - y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ is the locus of a point, which moves such that it is always equidistant from the lines $x + 2 y + 7 = 0$ and $2 x - y + 8 = 0$ , then the value of $g + c + h - f$ equals
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Let $a$ and $b$ be real constants such that the function $f$ defined by $f (x) = {x^{2} + 3 x + a b x + 2, x \leq 1, x > 1$ be differentiable on $R$ . Then, the value of $\int_{- 2}^{2} f (x) d x$ …
Mathematics · Definite Integration · MCQ
Q40.Let $f : R \to R$ be defined as $f (x) = a e^{2 x} + b e^{x} + c x$ . If $f (0) = - 1, f^{'} (lo g_{e} 2) = 21$ and $\int_{0}^{l o g_{e} 4} (f (x) - c x) d x = \frac{39}{2}$ , then the value of $∣ a + b + c ∣$ equals
Mathematics · Definite Integration · MCQ
Q41.Let $L_{1} : r = (\hat{i} - \hat{j} + 2 \hat{k}) + λ (\hat{i} - \hat{j} + 2 \hat{k}), λ \in R$ , $L_{2} : r = (\hat{j} - \hat{k}) + μ (3 \hat{i} + \hat{j} + p \hat{k}), μ \in R, and L_{3} : r = δ (ℓ \hat{i} + m \hat{j} + n \hat{k}), δ \in R$ …
Mathematics · 3D Geometry · MCQ
Q42.Let $a = \hat{i} + α \hat{j} + β \hat{k}, α, β \in R$ . Let a vector $b$ be such that the angle between $a$ and $b$ is $\frac{π}{4}$ and $∣ b ∣^{2} = 6$ . If $\vec{a} \cdot \vec{b}=3…
Mathematics · Vector Algebra · MCQ
Q43.Let $P$ be a point on the hyperbola $H : \frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ , in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $213$ . Then, the square of the distance of $P$ from the origin is
Mathematics · Hyperbola · MCQ
Q44.Let $f (x) = (x + 3)^{2} (x - 2)^{3}, x \in [- 4, 4]$ . If $M$ and $m$ are the maximum and minimum values of $f$ , respectively in $[- 4, 4]$ , then the value of $M - m$ is
Mathematics · Application of Derivatives · MCQ
Q45.Suppose $2 - p, p, 2 - α, α$ are the coefficients of four consecutive terms in the expansion of $(1 + x)^{n}$ . Then the value of $p^{2} - α^{2} + 6 α + 2 p$ equals
Mathematics · Binomial Theorem · MCQ
Q46.Consider the system of linear equations $x + y + z = 5, x + 2 y + λ^{2} z = 9, x + 3 y + λ z = μ$ , where $λ, μ \in R$ . Then, which of the following statement is NOT correct?
Mathematics · Matrices and Determinants · MCQ
Q47.Let $a$ and $b$ be two vectors such that $∣ b ∣ = 1$ and $∣ b \times a ∣ = 2$ . Then $∣ (b \times a) - b ∣^{2}$ is equal to
Mathematics · Vector Algebra · MCQ
Q48.If the domain of the function $f (x) = lo g_{e} (\frac{2 x + 3}{4 x ^{2} + x - 3}) + cos^{- 1} (\frac{2 x - 1}{x + 2})$ is $(α, β]$ , then the value of $5 β - 4 α$ is equal to
Mathematics · Functions · MCQ
Q49.Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is
Mathematics · Probability · MCQ
Q50.Let $A (α, 0)$ and $B (0, β)$ be the points on the line $5 x + 7 y = 50$ . Let the point $P$ divide the line segment $A B$ internally in the ratio $7 : 3$ . Let $3 x - 25 = 0$ be a directrix of the ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ …
Mathematics · Ellipse · MCQ
Q51.In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $A, B$ and $C$ . A student is required to attempt total 15 questions taking at least 4 questions from each…
Mathematics · Permutations and Combinations · Numerical
Q52.Let $Y = Y (X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y^{'} (x) (X - x)$ and the co-ordinate axes, where $(x, y)$ is any point on the curve, is always $\frac{- y ^{2}}{2 Y ^{'} ( x )} + 1, Y^{'} (x) e q 0$ …
Mathematics · Differential Equations · Numerical
Q53.The number of real solutions of the equation $x (x^{2} + 3∣ x ∣ + 5∣ x - 1∣ + 6∣ x - 2∣) = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q54.Consider two circles $C_{1} : x^{2} + y^{2} = 25$ and $C_{2} : (x - α)^{2} + y^{2} = 16$ , where $α \in (5, 9)$ . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_{1}$ and $C_{2}$ be $sin^{- 1} (\frac{63}{8})$ …
Mathematics · Circle · Numerical
Q55.Let a line passing through the point $(- 1, 2, 3)$ intersect the lines $L_{1} : \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z + 1}{- 2}$ at $M (α, β, γ)$ and $L_{2} : \frac{x + 2}{- 3} = \frac{y - 2}{- 2} = \frac{z - 1}{4}$ at $N (a, b, c)$ . Then, the value of $\frac{( α + β + γ ) ^{2}}{( a + b + c ) ^{2}}$ …
Mathematics · 3D Geometry · Numerical
Q56.The variance $σ^{2}$ of the data is . Includes table
Mathematics · Statistics · Numerical
Q57.The area of the region enclosed by the parabola $(y - 2)^{2} = x - 1$ , the line $x - 2 y + 4 = 0$ and the positive coordinate axes is .
Mathematics · Area Under the Curves · Numerical
Q58.The number of symmetric relations defined on the set ${1, 2, 3, 4}$ which are not reflexive is .
Mathematics · Sets and Relations · Numerical
Q59.Let $α = \sum_{k = 0}^{n} (\frac{( ^{n} C _{k} ) ^{2}}{k + 1})$ and $β = \sum_{k = 0}^{n - 1} (\frac{^{n} C _{k} ^{n} C _{k + 1}}{k + 2})$ If $5 α = 6 β$ , then $n$ equals .
Mathematics · Binomial Theorem · Numerical
Q60.Let $S_{n}$ be the sum to $n$ -terms of an arithmetic progression $3, 7, 11$ , If $40 < (\frac{6}{n ( n + 1 )} \sum_{k = 1}^{n} S_{k}) < 42$ , then $n$ equals .
Mathematics · Sequences and Series · Numerical
Q61.If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $0.5 mm$ , the Vernier constant of traveling microscope is
Physics · Units and Measurements · MCQ
Q62.An electron revolving in $n^{th}$ Bohr orbit has magnetic moment $μ_{n}$ . If $μ_{n} \propto n^{x}$ , the value of $x$ is
Physics · Atoms and Nuclei · MCQ
Q63.In the given circuit, the voltage across load resistance (R $_{L}$ ) is : Includes diagram
Physics · Electronic Devices · MCQ
Q64.An alternating voltage $V (t) = 220 sin 100 π t$ volt is applied to a purely resistive load of $50Ω$ . The time taken for the current to rise from half of the peak value to the peak value is:
Physics · Alternating Current · MCQ
Q65.Choose the correct statement for processes A & B shown in figure. Includes diagram
Physics · Heat and Thermodynamics · Multiple correct
Q66.A block of mass $m$ is placed on a surface having vertical crossection given by $y = x^{2} /4$ . If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:
Physics · Laws of Motion · MCQ
Q67.A block of ice at $- 1 0^{\circ} C$ is slowly heated and converted to steam at $10 0^{\circ} C$ . Which of the following curves represent the phenomenon qualitatively:
Physics · Heat and Thermodynamics · MCQ
Q68.When a potential difference $V$ is applied across a wire of resistance $R$ , it dissipates energy at a rate $W$ . If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy…
Physics · Current Electricity · MCQ
Q69.Match List I with List II Choose the correct answer from the options given below: Includes table
Physics · Electromagnetic Induction · MCQ
Q70.In a nuclear fission reaction of an isotope of mass $M$ , three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $Δ M$ will be :
Physics · Atoms and Nuclei · MCQ
Q71.For the photoelectric effect, the maximum kinetic energy $(E_{k})$ of the photoelectrons is plotted against the frequency $(v)$ of the incident photons as shown in figure. The slope of the graph gives Includes diagram
Physics · Dual Nature of Radiation · MCQ
Q72.A beam of unpolarised light of intensity $I_{0}$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $4 5^{\circ}$ relative to that of $A$ . The intensity of…
Physics · Wave Optics · MCQ
Q73.If three moles of monoatomic gas $(γ = \frac{5}{3})$ is mixed with two moles of a diatomic gas $(γ = \frac{7}{5})$ , the value of adiabatic exponent $γ$ for the mixture is
Physics · Heat and Thermodynamics · MCQ
Q74.Three blocks $A, B$ and $C$ are pulled on a horizontal smooth surface by a force of $80 N$ as shown in figure The tensions T $_{1}$ and T $_{2}$ in the string are respectively : Includes diagram
Physics · Laws of Motion · MCQ
Q75.A particle of charge ' $- q$ ' and mass ' $m$ ' moves in a circle of radius ' $r$ ' around an infinitely long line charge of linear charge density ' $+ λ$ '. Then time period will be given as : (Consider $k$ as Coulomb's constant)
Physics · Electrostatics · MCQ
Q76.Escape velocity of a body from earth is $11.2 km / s$ . If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :
Physics · Gravitation · MCQ
Q77.Projectiles A and B are thrown at angles of $4 5^{\circ}$ and $6 0^{\circ}$ with vertical respectively from top of a $400 m$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $v_{A} : v_{B}$ …
Physics · Motion in A Plane · MCQ
Q78.If the total energy transferred to a surface in time $t$ is $6.48 \times 1 0^{5} J$ , then the magnitude of the total momentum delivered to this surface for complete absorption will be:
Physics · Dual Nature of Radiation · MCQ
Q79.If mass is written as $m = k c^{P} G^{- 1/2} h^{1/2}$ then the value of $P$ will be : (Constants have their usual meaning with $k a$ dimensionless constant)
Physics · Units and Measurements · MCQ
Q80.A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of $6 0^{\circ}$ by a force of $10 N$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10 m$ … Includes diagram
Physics · Work Power and Energy · MCQ
Q81.A big drop is formed by coalescing 1000 small identical drops of water. If $E_{1}$ be the total surface energy of 1000 small drops of water and $E_{2}$ be the surface energy of single big drop of water, then $E_{1} : E_{2}$ is $x : 1$ where $x =$ …
Physics · Properties of Matter · Numerical
Q82.A power transmission line feeds input power at $2.3 kV$ to a step down transformer with its primary winding having 3000 turns. The output power is delivered at $230 V$ by the transformer. The current in the primary of…
Physics · Alternating Current · Numerical
Q83.The current of $5 A$ flows in a square loop of sides $1 m$ is placed in air. The magnetic field at the centre of the loop is $X 2 \times 1 0^{- 7} T$ . The value of $X$ is .
Physics · Magnetics · Numerical
Q84.Two discs of moment of inertia $I_{1} = 4 kg m^{2}$ and $I_{2} = 2 kg m^{2}$ , about their central axes & normal to their planes, rotating with angular speeds $10 rad / s$ & $4 rad / s$ …
Physics · Rotational Motion · Numerical
Q85.A point source is emitting sound waves of intensity $16 \times 1 0^{- 8} Wm^{- 2}$ at the origin. The difference in intensity (magnitude only) at two points located at a distances of $2 m$ and $4 m$ from the origin respectively will…
Physics · Waves · Numerical
Q86.Two resistance of $100Ω$ and $200Ω$ are connected in series with a battery of $4 V$ and negligible internal resistance. A voltmeter is used to measure voltage across $100Ω$ resistance, which gives reading as $1 V$ …
Physics · Current Electricity · Numerical
Q87.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $3 7^{\circ}$ with each other. When suspended in a liquid of density $0.7 g / cm^{3}$ , the angle remains same. If density…
Physics · Electrostatics · Numerical
Q88.A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 m$ , then the time period of small oscillations will be s.…
Physics · Gravitation · Numerical
Q89.In an experiment to measure the focal length $(f)$ of a convex lens, the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y$ - $x$ plot is shown in figure. The… Includes diagram
Physics · Geometrical Optics · Numerical
Q90.A vector has magnitude same as that of $A = 3 \hat{i} + 4 \hat{j}$ and is parallel to $B = 4 \hat{i} + 3 \hat{j}$ . The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively where…
Physics · Vector Algebra · Numerical