2024 · 29 Jan · Shift 1

90 questions · JEE Main

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2024 · 29 Jan · Shift 1

2024 · 29 Jan · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Identify the incorrect pair from the following :
Chemistry · P Block Elements · MCQ
Q2.Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$ : Assertion A : The first ionisation enthalpy decreases across a period. Reason $R$ : The increasing…
Chemistry · Periodic Table and Periodicity · MCQ
Q3.The major product(P) in the following reaction is Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q4.Identify product A and product B : Includes diagram
Chemistry · Hydrocarbons · MCQ
Q5.the arenium ion which is not involved in the bromination of Aniline is .
Chemistry · Compounds Containing Nitrogen · MCQ
Q6.Given below are two statements : Statement I : The electronegativity of group 14 elements from $Si$ to $Pb$ , gradually decreases. Statement II : Group 14 contains non-metallic, metallic, as well as metalloid elements. In…
Chemistry · Periodic Table and Periodicity · MCQ
Q7.Chlorine undergoes disproportionation in alkaline medium as shown below : $aCl_{2 (g)} + b OH_{(aq)}^{-} \to c ClO_{(aq)}^{-} + d Cl_{(aq)}^{-} + e H_{2} O_{(l)}$ …
Chemistry · Redox Reactions · MCQ
Q8.In chromyl chloride test for confirmation of $Cl^{-}$ ion, a yellow solution is obtained. Acidification of the solution and addition of amyl alcohol and $10% H_{2} O_{2}$ turns organic layer blue indicating…
Chemistry · Practical Organic Chemistry · MCQ
Q9.Type of amino acids obtained by hydrolysis of proteins is :
Chemistry · Biomolecules · MCQ
Q10.The correct set of four quantum numbers for the valence electron of rubidium atom $(Z = 37)$ is :
Chemistry · Structure of Atom · MCQ
Q11.The difference in energy between the actual structure and the lowest energy resonance structure for the given compound is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q12.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Coordination Compounds · MCQ
Q13.The final product A formed in the following multistep reaction sequence is Includes diagram
Chemistry · Hydrocarbons · MCQ
Q14.Which of the following is not correct?
Chemistry · Thermodynamics · MCQ
Q15.The interaction between $π$ bond and lone pair of electrons present on an adjacent atom is responsible for
Chemistry · Basics of Organic Chemistry · MCQ
Q16.In which one of the following metal carbonyls, $CO$ forms a bridge between metal atoms?
Chemistry · Coordination Compounds · MCQ
Q17. $KMnO_{4}$ decomposes on heating at $513 K$ to form $O_{2}$ along with
Chemistry · D and F Block Elements · MCQ
Q18.Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with $FeSO_{4}$ in presence of concentrated $H_{2} SO_{4}$ indicates the presence of element/s
Chemistry · Salt Analysis · MCQ
Q19.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : Aryl halides cannot be prepared by replacement of hydroxyl group of phenol by halogen atom. Reason R : Phenols react with…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q20.In alkaline medium, $MnO_{4}^{-}$ oxidises $I^{-}$ to
Chemistry · Redox Reactions · MCQ
Q21.The mass of zinc produced by the electrolysis of zine sulphate solution with a steady current of $0.015 A$ for 15 minutes is $\times 1 0^{- 4} g$ . (Atomic mass of zinc $= 65.4 amu$ )
Chemistry · Electrochemistry · Numerical
Q22.A solution of $H_{2} SO_{4}$ is $31.4% H_{2} SO_{4}$ by mass and has a density of $1.25 g / mL$ . The molarity of the $H_{2} SO_{4}$ solution is $M$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q23.Consider the given reaction. The total number of oxygen atom/s present per molecule of the product $(P)$ is . Includes diagram
Chemistry · Hydrocarbons · Numerical
Q24.For the reaction $N_{2} O_{4 (g)} ⇄ 2 NO_{2 (g)}, K_{p} = 0.492 atm$ at $300 K . K_{c}$ for the reaction at same temperature…
Chemistry · Chemical Equilibrium · Numerical
Q25.The number of species from the following which are paramagnetic and with bond order equal to one is . $H_{2}, He_{2}^{+}, O_{2}^{+}, N_{2}^{2 -}, O_{2}^{2 -}, F_{2}, Ne_{2}^{+}, B_{2}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q26.For a reaction taking place in three steps at same temperature, overall rate constant $K = \frac{K _{1} K _{2}}{K _{3}}$ . If $Ea_{1}, Ea_{2}$ and $Ea_{3}$ are 40, 50 and $60 kJ / mol$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q27.From the compounds given below, number of compounds which give positive Fehling's test is . Benzaldehyde, Acetaldehyde, Acetone, Acetophenone, Methanal, 4nitrobenzaldehyde, cyclohexane carbaldehyde.
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q28.Number of compounds with one lone pair of electrons on central atom amongst following is . $O_{3}, H_{2} O, SF_{4}, ClF_{3}, NH_{3}, BrF_{5}, XeF_{4}$
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q29.Number of compounds among the following which contain sulphur as heteroatom is . Furan, Thiophene, Pyridine, Pyrrole, Cysteine, Tyrosine
Chemistry · Biomolecules · Numerical
Q30.The osmotic pressure of a dilute solution is $7 \times 1 0^{5} Pa$ at $273 K$ . Osmotic pressure of the same solution at $283 K$ is $\times 1 0^{4} Nm^{- 2}$ .
Chemistry · Solutions · Numerical
Q31.Suppose $f (x) = \frac{( 2 ^{x} + 2 ^{- x} ) t a n x t a n ^{- 1} ( x ^{2} - x + 1 )}{( 7 x ^{2} + 3 x + 1 ) ^{3}}$ . Then the value of $f^{'} (0)$ is equal to
Mathematics · Differentiation · MCQ
Q32.Let $a, b$ and $c$ be three non-zero vectors such that $b$ and $c$ are non-collinear. If $a + 5 b$ is collinear with $c, b + 6 c$ is collinear with $a$ and $a + α b + β c = 0$ …
Mathematics · Vector Algebra · MCQ
Q33.Let $(5, \frac{a}{4})$ be the circumcenter of a triangle with vertices $A (a, - 2), B (a, 6)$ and $C (\frac{a}{4}, - 2)$ . Let $α$ denote the circumradius, $β$ denote the area and $γ$ …
Mathematics · Properties of Triangle · MCQ
Q34.If $α, - \frac{π}{2} < α < \frac{π}{2}$ is the solution of $4 cos θ + 5 sin θ = 1$ , then the value of $tan α$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q35.If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to
Mathematics · Sequences and Series · MCQ
Q36.A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is
Mathematics · Probability · MCQ
Q37.In an A.P., the sixth term $a_{6} = 2$ . If the product $a_{1} a_{4} a_{5}$ is the greatest, then the common difference of the A.P. is equal to
Mathematics · Sequences and Series · MCQ
Q38. $Let A = 100 0 α β 0 β α and ∣2 A ∣^{3} = 2^{21} where α, β \in Z, Then a value of α is$ …
Mathematics · Matrices and Determinants · MCQ
Q39.Let $R$ be a relation on $Z \times Z$ defined by $(a, b) R (c, d)$ if and only if $a d - b c$ is divisible by 5. Then $R$ is
Mathematics · Sets and Relations · MCQ
Q40.If $f (x) = {2 + 2 x, 1 - \frac{x}{3}, - 1 \leq x < 0 0 \leq x \leq 3; g (x) = {- x, x, - 3 \leq x \leq 0 0 < x \leq 1$ , then range…
Mathematics · Functions · MCQ
Q41.Let $O$ be the origin and the position vectors of $A$ and $B$ be $2 \hat{i} + 2 \hat{j} + \hat{k}$ and $2 \hat{i} + 4 \hat{j} + 4 \hat{k}$ respectively. If the internal bisector of $∠ AOB$ meets the line $AB$ at…
Mathematics · 3D Geometry · MCQ
Q42.In a $△ A B C$ , suppose $y = x$ is the equation of the bisector of the angle $B$ and the equation of the side $A C$ is $2 x - y = 2$ . If $2 A B = B C$ and the points $A$ and $B$ are respectively $(4, 6)$ and $(α, β)$ , then $α + 2 β$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q43.For $x \in (- \frac{π}{2}, \frac{π}{2})$ , if $y (x) = \int \frac{cosec x + s i n x}{cosec x s e c x + t a n x s i n ^{2} x} d x$ , and $lim_{x \to (\frac{π}{2})^{-}} y (x) = 0$ then $y (\frac{π}{4})$ …
Mathematics · Indefinite Integrals · MCQ
Q44.Let $A$ be a square matrix such that $AA^{T} = I$ . Then $\frac{1}{2} A [(A + A^{T})^{2} + (A - A^{T})^{2}]$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q45.If $z = \frac{1}{2} - 2 i$ is such that $∣ z + 1∣ = α z + β (1 + i), i = - 1$ and $α, β \in R$ , then $α + β$ is equal to
Mathematics · Complex Numbers · MCQ
Q46.Consider the function $f : [\frac{1}{2}, 1] \to R$ defined by $f (x) = 42 x^{3} - 32 x - 1$ . Consider the statements (I) The curve $y = f (x)$ intersects the $x$ -axis exactly at one point. (II) The curve $y = f (x)$ …
Mathematics · Application of Derivatives · MCQ
Q47.Let $P QR$ be a triangle with $R (- 1, 4, 2)$ . Suppose $M (2, 1, 2)$ is the mid point of $PQ$ . The distance of the centroid of $△ PQR$ from the point of intersection of the lines $\frac{x - 2}{0} = \frac{y}{2} = \frac{z + 3}{- 1}$ …
Mathematics · 3D Geometry · MCQ
Q48. $x \to \frac{π}{2} lim \frac{1}{( x - \frac{π}{2} ) ^{2}} x^{3} \int (\frac{π}{2})^{3} cos (t^{\frac{1}{3}}) d t$ is equal to
Mathematics · Definite Integration · MCQ
Q49.A function $y = f (x)$ satisfies $f (x) sin 2 x + sin x - (1 + cos^{2} x) f^{'} (x) = 0$ with condition $f (0) = 0$ . Then, $f (\frac{π}{2})$ is equal to
Mathematics · Differential Equations · MCQ
Q50.If the value of the integral $\int_{- \frac{π}{2}}^{\frac{π}{2}} (\frac{x ^{2} c o s x}{1 + π ^{x}} + \frac{1 + s i n ^{2} x}{1 + e ^{s i n x^{2123}}}) d x = \frac{π}{4} (π + a) - 2$ , then the value of $a$ is
Mathematics · Definite Integration · MCQ
Q51.The area (in sq. units) of the part of the circle $x^{2} + y^{2} = 169$ which is below the line $5 x - y = 13$ is $\frac{π α}{2 β} - \frac{65}{2} + \frac{α}{β} sin^{- 1} (\frac{12}{13})$ , where $α, β$ are coprime…
Mathematics · Area Under the Curves · Numerical
Q52.If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, α, β, 60$ where $α > β$ , are 56 and 66.2 respectively, then $α^{2} + β^{2}$ is equal to .
Mathematics · Statistics · Numerical
Q53.Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P (α, β)$ . Then, $17 β - α$ …
Mathematics · Circle · Numerical
Q54.A line with direction ratios $2, 1, 2$ meets the lines $x = y + 2 = z$ and $x + 2 = 2 y = 2 z$ respectively at the points $P$ and $Q$ . If the length of the perpendicular from the point $(1, 2, 12)$ to the line $PQ$ is $l$ , then $l^{2}$ …
Mathematics · 3D Geometry · Numerical
Q55. $If \frac{^{11} C _{1}}{2} + \frac{^{11} C _{2}}{3} + \dots + \frac{^{11} C _{9}}{10} = \frac{n}{m} with gcd (n, m) = 1, then n + m is equal to$ .
Mathematics · Binomial Theorem · Numerical
Q56.If the points of intersection of two distinct conics $x^{2} + y^{2} = 4 b$ and $\frac{x ^{2}}{16} + \frac{y ^{2}}{b ^{2}} = 1$ lie on the curve $y^{2} = 3 x^{2}$ , then $33$ times the area of the rectangle formed by the intersection points is …
Mathematics · Area Under the Curves · Numerical
Q57.All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is .
Mathematics · Permutations and Combinations · Numerical
Q58.Let $α, β$ be the roots of the equation $x^{2} - x + 2 = 0$ with $Im (α) > Im (β)$ . Then $α^{6} + α^{4} + β^{4} - 5 α^{2}$ is equal to .
Mathematics · Complex Numbers · Numerical
Q59.Let $f (x) = 2^{x} - x^{2}, x \in R$ . If $m$ and $n$ are respectively the number of points at which the curves $y = f (x)$ and $y = f^{'} (x)$ intersect the $x$ -axis, then the value of $m + n$ is .
Mathematics · Application of Derivatives · Numerical
Q60.If the solution curve $y = y (x)$ of the differential equation $(1 + y^{2}) (1 + lo g_{e} x) d x + x d y = 0, x > 0$ passes through the point $(1, 1)$ and $y (e) = \frac{α - t a n ( \frac{3}{2} )}{β + t a n ( \frac{3}{2} )}$ …
Mathematics · Differential Equations · Numerical
Q61.The resistance $R = \frac{V}{I}$ where $V = (200 \pm 5) V$ and $I = (20 \pm 0.2) A$ , the percentage error in the measurement of $R$ is :
Physics · Units and Measurements · MCQ
Q62.The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $25%$ of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:
Physics · Dual Nature of Radiation · MCQ
Q63.A convex mirror of radius of curvature $30 cm$ forms an image that is half the size of the object. The object distance is :
Physics · Geometrical Optics · MCQ
Q64.The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $24Ω$ is applied. The resistance of galvanometer coil will be :
Physics · Current Electricity · MCQ
Q65.A capacitor of capacitance $100 μ F$ is charged to a potential of $12 V$ and connected to a $6.4 mH$ inductor to produce oscillations. The maximum current in the circuit would be :
Physics · Alternating Current · MCQ
Q66.At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $R$ .)
Physics · Gravitation · MCQ
Q67.A galvanometer having coil resistance $10Ω$ shows a full scale deflection for a current of $3 mA$ . For it to measure a current of $8 A$ , the value of the shunt should be:
Physics · Current Electricity · MCQ
Q68.A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as shown in the figure. It's volume is then reduced to the original value from $B$ to $C$ by an isobaric… Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q69.Two charges of $5 Q$ and $- 2 Q$ are situated at the points $(3 a, 0)$ and $(- 5 a, 0)$ respectively. The electric flux through a sphere of radius ' $4 a$ ' having center at origin is :
Physics · Electrostatics · MCQ
Q70.A biconvex lens of refractive index 1.5 has a focal length of $20 cm$ in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:
Physics · Geometrical Optics · MCQ
Q71.A block of mass $100 kg$ slides over a distance of $10 m$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $(in J$ ) is :
Physics · Work Power and Energy · MCQ
Q72.Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in…
Physics · Properties of Matter · MCQ
Q73.If the radius of curvature of the path of two particles of same mass are in the ratio $3 : 4$ , then in order to have constant centripetal force, their velocities will be in the ratio of :
Physics · Circular Motion · MCQ
Q74.Match List I with List II Choose the correct answer from the options given below: Includes table
Physics · Electromagnetic Induction · MCQ
Q75.Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains $1 g$ of hydrogen and $B$ contains $1 g$ of oxygen. $P_{A}$ and $P_{B}$ are the pressures of the…
Physics · Heat and Thermodynamics · MCQ
Q76.In the given circuit, the breakdown voltage of the Zener diode is $3.0 V$ . What is the value of $I_{z}$ ? Includes diagram
Physics · Electronic Devices · MCQ
Q77.A body starts moving from rest with constant acceleration covers displacement $S_{1}$ in first $(p - 1)$ seconds and $S_{2}$ in first $p$ seconds. The displacement $S_{1} + S_{2}$ will be made in time :
Physics · Motion in A Straight Line · MCQ
Q78.The electric current through a wire varies with time as $I = I_{0} + β t$ , where $I_{0} = 20 A$ and $β = 3 A / s$ . The amount of electric charge crossed through a section of the wire in $20 s$ is :
Physics · Current Electricity · MCQ
Q79.The potential energy function (in $J$ ) of a particle in a region of space is given as $U = (2 x^{2} + 3 y^{3} + 2 z)$ . Here $x, y$ and $z$ are in meter. The magnitude of $x$ -component of force (in $N$ ) acting on the particle at point $P (1, 2, 3) m$ …
Physics · Work Power and Energy · MCQ
Q80.The explosive in a Hydrogen bomb is a mixture of $_{1} H^{2},_{1} H^{3}$ and $_{3} Li^{6}$ in some condensed form. The chain reaction is given by $_{3} Li^{6} +_{0} n^{1} \to_{2} He^{4} +_{1} H^{3}_{1} H^{2} +_{1} H^{3} \to_{2} He^{4} +_{0} n^{1}$ …
Physics · Atoms and Nuclei · MCQ
Q81.In a double slit experiment shown in figure, when light of wavelength $400 nm$ is used, dark fringe is observed at $P$ . If $D = 0.2 m$ , the minimum distance between the slits $S_{1}$ and $S_{2}$ is … Includes diagram
Physics · Wave Optics · Numerical
Q82.A cylinder is rolling down on an inclined plane of inclination $6 0^{\circ}$ . It's acceleration during rolling down will be $\frac{x}{3} m / s^{2}$ , where $x =$ (use $g = 10 m / s^{2}$ ).
Physics · Rotational Motion · Numerical
Q83.An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+ σ$ . The electron at $t = 0$ is at a distance of $1 m$ from $S$ and has a…
Physics · Electrostatics · Numerical
Q84.When a hydrogen atom going from $n = 2$ to $n = 1$ emits a photon, its recoil speed is $\frac{x}{5} m / s$ . Where $x =$ . (Use, mass of hydrogen atom $= 1.6 \times 1 0^{- 27} kg$ )
Physics · Atoms and Nuclei · Numerical
Q85.A square loop of side $10 cm$ and resistance $0.7Ω$ is placed vertically in east-west plane. A uniform magnetic field of $0.20 T$ is set up across the plane in north east direction. The magnetic field is decreased to zero…
Physics · Electromagnetic Induction · Numerical
Q86.The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 cm$ from its center is $1.5 \times 1 0^{- 5} T m$ . The magnetic moment of the dipole is $A m^{2}$ …
Physics · Magnetic Properties of Matter · Numerical
Q87.A $16Ω$ wire is bend to form a square loop. A $9 V$ battery with internal resistance $1Ω$ is connected across one of its sides. If a $4 μ F$ capacitor is connected across one of its diagonals, the energy stored by…
Physics · Capacitor · Numerical
Q88.When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$ , where $x =$ .
Physics · Simple Harmonic Motion · Numerical
Q89.A ball rolls off the top of a stairway with horizontal velocity $u$ . The steps are $0.1 m$ high and $0.1 m$ wide. The minimum velocity $u$ with which that ball just hits the step 5 of the stairway will be $x ms^{- 1}$ …
Physics · Motion in A Plane · Numerical
Q90.In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70 ms^{- 1}$ and $65 ms^{- 1}$ respectively. If the wing area is $2 m^{2}$ , the lift of…
Physics · Properties of Matter · Numerical