2024 · 6 Apr · Shift 1

90 questions · JEE Main

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2024 · 6 Apr · Shift 1

2024 · 6 Apr · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.The number of element from the following that do not belong to lanthanoids is $Eu, Cm, Er, Tb, Yb$ and $Lu$
Chemistry · D and F Block Elements · MCQ
Q2.A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will - Includes diagram
Chemistry · Electrochemistry · MCQ
Q3.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Chemistry in Everyday Life · MCQ
Q4.At $- 2 0^{\circ} C$ and $1 atm$ pressure, a cylinder is filled with equal number of $H_{2}, I_{2}$ and $HI$ molecules for the reaction $H_{2} (g) + I_{2} (g) ⇌ 2 HI (g)$ …
Chemistry · Chemical Equilibrium · MCQ
Q5.The electron affinity value are negative for A. $Be \to Be^{-}$ B. $N \to N^{-}$ C. $O \to O^{2 -}$ D. $Na \to Na^{-}$ E. $Al \to Al^{-}$ …
Chemistry · Periodic Table and Periodicity · MCQ
Q6.Consider the following complexes (A) $[CoCl (NH_{3})_{5}]^{2 +}$ , (B) $[Co (CN)_{6}]^{3 -}$ , (C) $[Co (NH_{3})_{5} (H_{2} O)]^{3 +}$ …
Chemistry · Coordination Compounds · MCQ
Q7.Functional group present in sulphonic acids is :
Chemistry · Basics of Organic Chemistry · MCQ
Q8.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Salt Analysis · MCQ
Q9.Given below are two statements : Statement I : Gallium is used in the manufacturing of thermometers. Statement II : A thermometer containing gallium is useful for measuring the freezing point $(256 K)$ of brine solution. In the…
Chemistry · P Block Elements · MCQ
Q10.The density of ' $x$ ' $M$ solution (' $x$ ' molar) of $NaOH$ is $1.12 g mL^{- 1}$ , while in molality, the concentration of the solution is $3 m$ ( 3 molal). Then $x$ is (Given : Molar mass of $NaOH$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q11.Match List I with List II Choose the correct answer from the options given below: Includes table
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 · Chemical Bonding and Molecular Structure · MCQ
Q13.Which of the following statements are correct? A. Glycerol is purified by vacuum distillation because it decomposes at its normal boiling point. B. Aniline can be purified by steam distillation as aniline is miscible in water. C. Ethanol…
Chemistry · Practical Organic Chemistry · MCQ
Q14.Which of the following material is not a semiconductor.
Chemistry · P Block Elements · MCQ
Q15.Which of the following is metamer of the given compound (X) ? Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q16.In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of intermediate is .
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.Which among the following aldehydes is most reactive towards nucleophilic addition reactions?
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q18.DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorrect base structure.
Chemistry · Biomolecules · MCQ
Q19.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Coordination Compounds · MCQ
Q20.Given below are two statements : Statement I : Piciric acid is 2,4,6 - trinitrotoluene. Statement II : Phenol - 2,4 - disulphonic acid is treated with Conc. $HNO_{3}$ to get picric acid. In the light of the above statements, choose…
Chemistry · Compounds Containing Nitrogen · MCQ
Q21.The major product of the following reaction is P. $CH_{3} C \equiv C - CH_{3} (i) Na /liq. NH_{3} (ii) dil. KMnO_{4} 273 K$ …
Chemistry · Hydrocarbons · Numerical
Q22.Time required for $99.9%$ completion of a first order reaction is times the time required for completion of $90%$ reaction.(nearest integer)
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q23.Consider the dissociation of the weak acid HX as given below $HX (aq) ⇌ H^{+} (aq) + X^{-} (aq), Ka = 1.2 \times 1 0^{- 5}$ [ $K_{a}$ : dissociation…
Chemistry · Ionic Equilibrium · Numerical
Q24.An ideal gas, $\overline{C}_{v} = \frac{5}{2} R$ , is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $298 K$ and $5 atm$ …
Chemistry · Thermodynamics · Numerical
Q25.The major products from the following reaction sequence are product A and product B. The total sum of $π$ electrons in product A and product B are (nearest integer) Includes diagram
Chemistry · Hydrocarbons · Numerical
Q26.The difference in the 'spin-only' magnetic moment values of $KMnO_{4}$ and the manganese product formed during titration of $KMnO_{4}$ against oxalic acid in acidic medium is $BM$ . (nearest…
Chemistry · Coordination Compounds · Numerical
Q27. $9.3 g$ of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100% yield/conversion) is g. (nearest integer)
Chemistry · Compounds Containing Nitrogen · Numerical
Q28.Number of molecules from the following which can exhibit hydrogen bonding is . (nearest integer) Includes diagram
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q29.Among $CrO, Cr_{2} O_{3}$ and $CrO_{3}$ , the sum of spin-only magnetic moment values of basic and amphoteric oxides is $1 0^{- 2} BM$ (nearest integer). (Given atomic number of $Cr$ …
Chemistry · D and F Block Elements · Numerical
Q30.Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is $\times 1 0^{13} Hz$ (nearest integer). [Given : $R_{H}$ (Rydberg constant) $= 2.18 \times 1 0^{- 18} J, h$ …
Chemistry · Structure of Atom · Numerical
Q31.A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are $m$ and $n$ , respectively, then $m + n^{2}$ is equal to
Mathematics · Circle · MCQ
Q32.Let a variable line of slope $m > 0$ passing through the point $(4, - 9)$ intersect the coordinate axes at the points $A$ and $B$ . The minimum value of the sum of the distances of $A$ and $B$ from the origin is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Let $A = {n \in [100, 700] \cap N : n$ is neither a multiple of 3 nor a multiple of 4 $}$ . Then the number of elements in $A$ is
Mathematics · Sets and Relations · MCQ
Q34.Let $C$ be the circle of minimum area touching the parabola $y = 6 - x^{2}$ and the lines $y = 3 ∣ x ∣$ . Then, which one of the following points lies on the circle $C$ ?
Mathematics · Parabola · MCQ
Q35.If $A (3, 1, - 1), B (\frac{5}{3}, \frac{7}{3}, \frac{1}{3}), C (2, 2, 1)$ and $D (\frac{10}{3}, \frac{2}{3}, \frac{- 1}{3})$ are the vertices of a quadrilateral $A B C D$ , then its area is
Mathematics · 3D Geometry · MCQ
Q36.Let the relations $R_{1}$ and $R_{2}$ on the set $X = {1, 2, 3, \dots, 20}$ be given by $R_{1} = {(x, y) : 2 x - 3 y = 2}$ and $R_{2} = {(x, y) : - 5 x + 4 y = 0}$ . If $M$ and $N$ be the minimum number of elements required to be added in $R_{1}$ and $R_{2}$ ,…
Mathematics · Sets and Relations · MCQ
Q37.Let the area of the region enclosed by the curves $y = 3 x, 2 y = 27 - 3 x$ and $y = 3 x - x x$ be $A$ . Then $10 A$ is equal to
Mathematics · Area Under the Curves · MCQ
Q38. $If f (x) = {x^{3} sin (\frac{1}{x}), 0 x e q 0, x = 0, then$
Mathematics · Differentiation · MCQ
Q39.The shortest distance between the lines $\frac{x - 3}{2} = \frac{y + 15}{- 7} = \frac{z - 9}{5}$ and $\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{- 3}$ is
Mathematics · 3D Geometry · MCQ
Q40.Let $y = y (x)$ be the solution of the differential equation $(2 x lo g_{e} x) \frac{d y}{d x} + 2 y = \frac{3}{x} lo g_{e} x, x > 0$ and $y (e^{- 1}) = 0$ . Then, $y (e)$ is equal to
Mathematics · Differential Equations · MCQ
Q41.Let $α, β$ be the distinct roots of the equation $x^{2} - (t^{2} - 5 t + 6) x + 1 = 0, t \in R$ and $a_{n} = α^{n} + β^{n}$ . Then the minimum value of $\frac{a _{2023} + a _{2025}}{a _{2024}}$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.For $α, β \in R$ and a natural number $n$ , let $A_{r} = r 2 r 3 r - 2 123 \frac{n ^{2}}{2} + α n^{2} - β \frac{n ( 3 n - 1 )}{2}$ . Then $2 A_{10} - A_{8}$ …
Mathematics · Matrices and Determinants · MCQ
Q43.Let $f : (- \infty, \infty) - {0} \to R$ be a differentiable function such that $f^{'} (1) = lim_{a \to \infty} a^{2} f (\frac{1}{a})$ . Then $lim_{a \to \infty} \frac{a ( a + 1 )}{2} tan^{- 1} (\frac{1}{a}) + a^{2} - 2 lo g_{e} a$ …
Mathematics · Differentiation · MCQ
Q44. $0 \int π /4 \frac{c o s ^{2} x s i n ^{2} x}{( c o s ^{3} x + s i n ^{3} x ) ^{2}} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q45.The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is
Mathematics · Statistics · MCQ
Q46.Let $y = y (x)$ be the solution of the differential equation $(1 + x^{2}) \frac{d y}{d x} + y = e^{t a n^{- 1} x}$ , $y (1) = 0$ . Then $y (0)$ is
Mathematics · Differential Equations · MCQ
Q47.The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Mathematics · Permutations and Combinations · MCQ
Q48.The function $f (x) = \frac{x ^{2} + 2 x - 15}{x ^{2} - 4 x + 9}, x \in R$ is
Mathematics · Functions · MCQ
Q49.The interval in which the function $f (x) = x^{x}, x > 0$ , is strictly increasing is
Mathematics · Application of Derivatives · MCQ
Q50.A company has two plants $A$ and $B$ to manufacture motorcycles. $60%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B .80%$ of the motorcycles manufactured at plant $A$ are rated of the…
Mathematics · Probability · MCQ
Q51.Let $x_{1}, x_{2}, x_{3}, x_{4}$ be the solution of the equation $4 x^{4} + 8 x^{3} - 17 x^{2} - 12 x + 9 = 0$ and $(4 + x_{1}^{2}) (4 + x_{2}^{2}) (4 + x_{3}^{2}) (4 + x_{4}^{2}) = \frac{125}{16} m$ . Then the value of $m$ is …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q52.Let a conic $C$ pass through the point $(4, - 2)$ and $P (x, y), x \geq 3$ , be any point on $C$ . Let the slope of the line touching the conic $C$ only at a single point $P$ be half the slope of the line joining the points $P$ and $(3, - 5)$ . If…
Mathematics · Parabola · Numerical
Q53.If the second, third and fourth terms in the expansion of $(x + y)^{n}$ are 135, 30 and $\frac{10}{3}$ , respectively, then $6 (n^{3} + x^{2} + y)$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q54.Let $α β γ = 45; α, β, γ \in R$ . If $x (α, 1, 2) + y (1, β, 2) + z (2, 3, γ) = (0, 0, 0)$ for some $x, y, z \in R, x y z e q 0$ , then $6 α + 4 β + γ$ is equal to …
Mathematics · Matrices and Determinants · Numerical
Q55.Let $P$ be the point $(10, - 2, - 1)$ and $Q$ be the foot of the perpendicular drawn from the point $R (1, 7, 6)$ on the line passing through the points $(2, - 5, 11)$ and $(- 6, 7, - 5)$ . Then the length of the line segment $P Q$ is equal to …
Mathematics · 3D Geometry · Numerical
Q56.Let the first term of a series be $T_{1} = 6$ and its $r^{th}$ term $T_{r} = 3 T_{r - 1} + 6^{r}, r = 2, 3$ , ............ $n$ . If the sum of the first $n$ terms of this series is $\frac{1}{5} (n^{2} - 12 n + 39) (4 \cdot 6^{n} - 5 \cdot 3^{n} + 1)$ …
Mathematics · Sequences and Series · Numerical
Q57.For $n \in N$ , if $cot^{- 1} 3 + cot^{- 1} 4 + cot^{- 1} 5 + cot^{- 1} n = \frac{π}{4}$ , then $n$ is equal to .
Mathematics · Inverse Trigonometric Functions · Numerical
Q58.Let $r_{k} = \frac{\int _{0}^{1} ( 1 - x ^{7} ) ^{k} d x}{\int _{0}^{1} ( 1 - x ^{7} ) ^{k + 1} d x}, k \in N$ . Then the value of $\sum_{k = 1}^{10} \frac{1}{7 ( r _{k} - 1 )}$ is equal to .
Mathematics · Definite Integration · Numerical
Q59.Let $a = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, b = 3 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and a vector $c$ be such that $a \times (b + c) + b \times c = \hat{i} + 8 \hat{j} + 13 \hat{k}$ . If $\vec{a} \cdot…
Mathematics · Vector Algebra · Numerical
Q60.Let $L_{1}, L_{2}$ be the lines passing through the point $P (0, 1)$ and touching the parabola $9 x^{2} + 12 x + 18 y - 14 = 0$ . Let $Q$ and $R$ be the points on the lines $L_{1}$ and $L_{2}$ such that the $△ P QR$ is an isosceles triangle with base $QR$ …
Mathematics · Parabola · Numerical
Q61.A bullet of mass $50 g$ is fired with a speed $100 m / s$ on a plywood and emerges with $40 m / s$ . The percentage loss of kinetic energy is :
Physics · Work Power and Energy · MCQ
Q62.The specific heat at constant pressure of a real gas obeying $P V^{2} = R T$ equation is:
Physics · Heat and Thermodynamics · MCQ
Q63.The correct truth table for the following logic circuit is : Includes diagram
Physics · Electronic Devices · MCQ
Q64.Electromagnetic waves travel in a medium with speed of $1.5 \times 1 0^{8} m s^{- 1}$ . The relative permeability of the medium is 2.0. The relative permittivity will be:
Physics · Electromagnetic Waves · MCQ
Q65.To find the spring constant $(k)$ of a spring experimentally, a student commits $2%$ positive error in the measurement of time and $1%$ negative error in measurement of mass. The percentage error in determining value of $k$ is :
Physics · Units and Measurements · MCQ
Q66.The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is : Includes diagram
Physics · Current Electricity · MCQ
Q67.A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2} ($ where $m_{2} > m_{1})$ . If the acceleration of the system is $\frac{g}{2}$ , then the ratio of the masses $\frac{m _{1}}{m _{2}}$ …
Physics · Laws of Motion · MCQ
Q68.To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_{E}, g =$ acceleration due to gravity on the surface of earth):
Physics · Gravitation · MCQ
Q69.Match List I with List II Choose the correct answer from the options given below: Includes table
Physics · Units and Measurements · MCQ
Q70.Which of the following phenomena does not explain by wave nature of light. A. reflection B. diffraction C. photoelectric effect D. interference E. polarization Choose the most appropriate answer from the options given below:
Physics · Dual Nature of Radiation · MCQ
Q71.Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2 m, 4 m$ , have same momentum, respectively. The particle with maximum kinetic energy is :
Physics · Work Power and Energy · MCQ
Q72.In photoelectric experiment energy of $2.48 eV$ irradiates a photo sensitive material. The stopping potential was measured to be $0.5 V$ . Work function of the photo sensitive material is :
Physics · Dual Nature of Radiation · MCQ
Q73.While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 mm$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $1 mm$ and it has 100…
Physics · Units and Measurements · MCQ
Q74.Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same…
Physics · Alternating Current · MCQ
Q75. $σ$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :
Physics · Electrostatics · MCQ
Q76.An element $Δ l = Δ x \hat{i}$ is placed at the origin and carries a large current $I = 10 A$ . The magnetic field on the $y$ -axis at a distance of $0.5 m$ from the elements $Δ x$ of $1 cm$ length is: Includes diagram
Physics · Magnetics · MCQ
Q77.A small ball of mass $m$ and density $ρ$ is dropped in a viscous liquid of density $ρ_{0}$ . After sometime, the ball falls with constant velocity. The viscous force on the ball is :
Physics · Properties of Matter · MCQ
Q78.A train starting from rest first accelerates uniformly up to a speed of $80 km / h$ for time $t$ , then it moves with a constant speed for time $3 t$ . The average speed of the train for this duration of journey will be…
Physics · Motion in A Straight Line · MCQ
Q79.A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
Physics · Heat and Thermodynamics · MCQ
Q80.The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
Physics · Atoms and Nuclei · MCQ
Q81.A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$ . The value of $x$ is .
Physics · Properties of Matter · Numerical
Q82.If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be hours 30 minutes.
Physics · Gravitation · Numerical
Q83.A particle is doing simple harmonic motion of amplitude $0.06 m$ and time period $3.14 s$ . The maximum velocity of the particle is $cm / s$ .
Physics · Simple Harmonic Motion · Numerical
Q84.Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x σ}{ϵ _{0}}$ . The value of $x$ is (all quantities are measured in SI… Includes diagram
Physics · Electrostatics · Numerical
Q85.Radius of a certain orbit of hydrogen atom is 8.48 $A o$ . If energy of electron in this orbit is $E / x$ . then $x =$ (Given $a_{0} = 0.529 A o$ , $E =$ energy of electron in ground…
Physics · Atoms and Nuclei · Numerical
Q86.For three vectors $A = (- x \hat{i} - 6 \hat{j} - 2 \hat{k}), B = (- \hat{i} + 4 \hat{j} + 3 \hat{k})$ and $C = (- 8 \hat{i} - \hat{j} + 3 \hat{k})$ , if $A \cdot (B \times C) = 0$ , then value of $x$ is …
Physics · Vector Algebra · Numerical
Q87.The refractive index of prism is $μ = 3$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is $^{\circ}$ .
Physics · Geometrical Optics · Numerical
Q88.A wire of resistance $R$ and radius $r$ is stretched till its radius became $r /2$ . If new resistance of the stretched wire is $x R$ , then value of $x$ is .
Physics · Current Electricity · Numerical
Q89.When a $d c$ voltage of $100 V$ is applied to an inductor, a $d c$ current of $5 A$ flows through it. When an ac voltage of $200 V$ peak value is connected to inductor, its inductive reactance is found to be $203 Ω$ …
Physics · Alternating Current · Numerical
Q90.A circular coil having 200 turns, $2.5 \times 1 0^{- 4} m^{2}$ area and carrying $100 μ A$ current is placed in a uniform magnetic field of $1 T$ . Initially the magnetic dipole moment $(M)$ was directed…
Physics · Magnetics · Numerical