2024 · 9 Apr · Shift 1

90 questions · JEE Main

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2024 · 9 Apr · Shift 1

2024 · 9 Apr · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Identify the product A and product B in the following set of reactions. Includes diagram
Chemistry · Hydrocarbons · MCQ
Q2.The molar conductivity for electrolytes $A$ and $B$ are plotted against $C^{3/2}$ as shown below. Electrolytes $A$ and $B$ respectively are: Includes diagram
Chemistry · Electrochemistry · MCQ
Q3.Given below are two statements : Statement (I) : The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule. Statement…
Chemistry · Periodic Table and Periodicity · MCQ
Q4. $0.05 M CuSO_{4}$ when treated with $0.01 M K_{2} Cr_{2} O_{7}$ gives green colour solution of $Cu_{2} Cr_{2} O_{7}$ . The two solutions are separated as shown below :… Includes diagram
Chemistry · Solutions · MCQ
Q5.Identify major product "X" formed in the following reaction : Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q6.The $F^{-}$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula.
Chemistry · Biomolecules · MCQ
Q7.Identify the incorrect statements regarding primary standard of titrimetric analysis. (A) It should be purely available in dry form. (B) It should not undergo chemical change in air. (C) It should be hygroscopic and should react with…
Chemistry · Practical Organic Chemistry · MCQ
Q8.What is the structure of C? Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q9.The electronic configuration of $Cu (II)$ is $3 d^{9}$ whereas that of $Cu (I)$ is $3 d^{10}$ . Which of the following is correct?
Chemistry · D and F Block Elements · MCQ
Q10.In which one of the following pairs the central atoms exhibit $sp^{2}$ hybridization ?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q11.Relative stability of the contributing structures is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q12.Correct order of basic strength of Pyrrole , Pyridine and Piperidine is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q13.For the given compounds, the correct order of increasing $pK_{a}$ value : Choose the correct answer from the options given below : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q14.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Both rhombic and monoclinic sulphur exist as $S_{8}$ while oxygen exists as $O_{2}$ . Reason (R) :…
Chemistry · P Block Elements · MCQ
Q15.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The total number of geometrical isomers shown by $[Co (en)_{2} Cl_{2}]^{+}$ complex ion is…
Chemistry · Coordination Compounds · MCQ
Q16.Methods used for purification of organic compounds are based on :
Chemistry · Basics of Organic Chemistry · MCQ
Q17.Compare the energies of following sets of quantum numbers for multielectron system. (A) $n = 4, 1 = 1$ (B) $n = 4, 1 = 2$ (C) $n = 3, l = 1$ (D) $n = 3, 1 = 2$ (E) $n = 4, 1 = 0$ Choose the correct answer from the…
Chemistry · Structure of Atom · MCQ
Q18.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $S_{N} 2$ reaction of $C_{6} H_{5} CH_{2} Br$ occurs more readily…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q19.On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed?
Chemistry · P Block Elements · MCQ
Q20.In the following sequence of reaction, the major products B and C respectively are : Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q21.The standard reduction potentials at $298 K$ for the following half cells are given below : $Cr_{2} O_{7}^{2 -} + 14 H^{+} + 6 e^{-} \to 2 Cr^{3 +} + 7 H_{2} O, E^{\circ} = 1.33 V Fe^{3 +} (aq) + 3 e^{-} \to Fe Ni^{2 +} (aq) + 2 e^{-} \to Ni Ag^{+} (aq) + e^{-} \to Ag Au^{3 +} (aq) + 3 e^{-} \to Au E^{\circ} = - 0.04 V E^{\circ} = - 0.25 V E^{\circ} = 0.80 V E^{\circ} = 1.40 V$ …
Chemistry · Electrochemistry · Numerical
Q22.Total number of essential amino acid among the given list of amino acids is . Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline
Chemistry · Biomolecules · Numerical
Q23.Number of ambidentate ligands among the following is . $NO_{2}^{-}, SCN^{-}, C_{2} O_{4}^{2 -}, NH_{3}, CN^{-}, SO_{4}^{2 -}, H_{2} O .$
Chemistry · Coordination Compounds · Numerical
Q24.Number of colourless lanthanoid ions among the following is . $Eu^{3 +}, Lu^{3 +}, Nd^{3 +}, La^{3 +}, Sm^{3 +}$
Chemistry · D and F Block Elements · Numerical
Q25.The total number of species from the following in which one unpaired electron is present, is . $N_{2}, O_{2}, C_{2}^{-}, O_{2}^{-}, O_{2}^{2 -}, H_{2}^{+}, CN^{-}, He_{2}^{+}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q26.Given below are two statements : Statement I : The rate law for the reaction $A + B \to C$ is rate $(r) = k [A]^{2} [B]$ . When the concentration of both $A$ and $B$ is doubled, the reaction rate is increased " $x$ "… Includes diagram
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q27.How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects? Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q28.When equal volume of $1 M HCl$ and $1 M H_{2} SO_{4}$ are separately neutralised by excess volume of $1 M NaOH$ solution. $x$ and $y kJ$ of heat is liberated…
Chemistry · Thermodynamics · Numerical
Q29.The heat of solution of anhydrous $CuSO_{4}$ and $CuSO_{4} \cdot 5 H_{2} O$ are $- 70 kJ mol^{- 1}$ and $+ 12 kJ mol^{- 1}$ respectively. The heat of hydration of $CuSO_{4}$ …
Chemistry · Thermodynamics · Numerical
Q30.Molarity $(M)$ of an aqueous solution containing $x g$ of anhyd. $CuSO_{4}$ in $500 mL$ solution at $3 2^{\circ} C$ is $2 \times 1 0^{- 1} M$ . Its molality will be $\times 1 0^{- 3} m$ …
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q31.If the domain of the function $f (x) = sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$ , then $12 α β$ is equal to :
Mathematics · Functions · MCQ
Q32.Let three vectors , $a = α \hat{i} + 4 \hat{j} + 2 \hat{k}, b = 5 \hat{i} + 3 \hat{j} + 4 \hat{k}, c = x \hat{i} + y \hat{j} + z \hat{k}$ form a triangle such that $c = a - b$ …
Mathematics · Vector Algebra · MCQ
Q33.Let $f (x) = a x^{3} + b x^{2} + c x + 41$ be such that $f (1) = 40, f^{'} (1) = 2$ and $f^{''} (1) = 4$ . Then $a^{2} + b^{2} + c^{2}$ is equal to:
Mathematics · Differentiation · MCQ
Q34.The parabola $y^{2} = 4 x$ divides the area of the circle $x^{2} + y^{2} = 5$ in two parts. The area of the smaller part is equal to :
Mathematics · Area Under the Curves · MCQ
Q35.The solution of the differential equation $(x^{2} + y^{2}) d x - 5 x y d y = 0, y (1) = 0$ , is :
Mathematics · Differential Equations · MCQ
Q36.Let $∣ cos θ cos (60 - θ) cos (60 + θ) ∣ \leq \frac{1}{8}, θ ϵ [0, 2 π]$ . Then, the sum of all $θ \in [0, 2 π]$ , where $cos 3 θ$ attains its maximum value, is :
Mathematics · Trigonometric Functions and Equations · MCQ
Q37.If the sum of the series $\frac{1}{1 \cdot ( 1 + d )} + \frac{1}{( 1 + d ) ( 1 + 2 d )} + \dots + \frac{1}{( 1 + 9 d ) ( 1 + 10 d )}$ is equal to 5, then $50 d$ is equal to :
Mathematics · Sequences and Series · MCQ
Q38.The coefficient of $x^{70}$ in $x^{2} (1 + x)^{98} + x^{3} (1 + x)^{97} + x^{4} (1 + x)^{96} + \dots + x^{54} (1 + x)^{46}$ is $^{99} C_{p} -^{46} C_{q}$ . Then a possible value of $p + q$ is :
Mathematics · Binomial Theorem · MCQ
Q39.The frequency distribution of the age of students in a class of 40 students is given below. If the mean deviation about the median is 1.25, then $4 x + 5 y$ is equal to : Includes table
Mathematics · Statistics · MCQ
Q40.Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$ . Let $(x_{c}, y_{c})$ be the point of intersection of the lines $3 x + 5 y = 1$ and $(2 + c) x + 5 c^{2} y = 1$ . If $h = lim_{c \to 1} x_{c}$ …
Mathematics · Circle · MCQ
Q41.Let $\int \frac{2 - t a n x}{3 + t a n x} d x = \frac{1}{2} (α x + lo g_{e} ∣ β sin x + γ cos x ∣) + C$ , where $C$ is the constant of integration. Then $α + \frac{γ}{β}$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q42.Let $α, β$ be the roots of the equation $x^{2} + 22 x - 1 = 0$ . The quadratic equation, whose roots are $α^{4} + β^{4}$ and $\frac{1}{10} (α^{6} + β^{6})$ , is:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q43.Let $f (x) = x^{2} + 9, g (x) = \frac{x}{x - 9}$ and $a = f \circ g (10), b = g \circ f (3)$ . If $e$ and $l$ denote the eccentricity and the length of the latus rectum of the ellipse $\frac{x ^{2}}{a} + \frac{y ^{2}}{b} = 1$ …
Mathematics · Ellipse · MCQ
Q44.The shortest distance between the lines $\frac{x - 3}{4} = \frac{y + 7}{- 11} = \frac{z - 1}{5}$ and $\frac{x - 5}{3} = \frac{y - 9}{- 6} = \frac{z + 2}{1}$ is:
Mathematics · 3D Geometry · MCQ
Q45.A variable line $L$ passes through the point $(3, 5)$ and intersects the positive coordinate axes at the points $A$ and $B$ . The minimum area of the triangle $OAB$ , where $O$ is the origin, is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q46.The solution curve, of the differential equation $2 y \frac{d y}{d x} + 3 = 5 \frac{d y}{d x}$ , passing through the point $(0, 1)$ is a conic, whose vertex lies on the line :
Mathematics · Differential Equations · MCQ
Q47.Let $λ, μ \in R$ . If the system of equations $3 x + 5 y + λ z = 3 7 x + 11 y - 9 z = 2 97 x + 155 y - 189 z = μ$ has infinitely many solutions, then $μ + 2 λ$ is equal to…
Mathematics · Matrices and Determinants · MCQ
Q48.A ray of light coming from the point $P (1, 2)$ gets reflected from the point $Q$ on the $x$ -axis and then passes through the point $R (4, 3)$ . If the point $S (h, k)$ is such that $P QR S$ is a parallelogram, then $h k^{2}$ is…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q49.Let the line $L$ intersect the lines $x - 2 = - y = z - 1, 2 (x + 1) = 2 (y - 1) = z + 1$ and be parallel to the line $\frac{x - 2}{3} = \frac{y - 1}{1} = \frac{z - 2}{2}$ . Then which of the following points lies on $L$ ?
Mathematics · 3D Geometry · MCQ
Q50.Let $O A = 2 a, O B = 6 a + 5 b$ and $O C = 3 b$ , where $O$ is the origin. If the area of the parallelogram with adjacent sides $O A$ and $O C$ …
Mathematics · Vector Algebra · MCQ
Q51.Let $A = {2, 3, 6, 7}$ and $B = {4, 5, 6, 8}$ . Let $R$ be a relation defined on $A \times B$ by $(a_{1}, b_{1}) R (a_{2}, b_{2})$ if and only if $a_{1} + a_{2} = b_{1} + b_{2}$ . Then the number of elements in $R$ is .
Mathematics · Sets and Relations · Numerical
Q52.Let $lim_{n \to \infty} (\frac{n}{n ^{4} + 1} - \frac{2 n}{( n ^{2} + 1 ) n ^{4} + 1} + \frac{n}{n ^{4} + 16} - \frac{8 n}{( n ^{2} + 4 ) n ^{4} + 16} + \dots + \frac{n}{n ^{4} + n ^{4}} - \frac{2 n \cdot n ^{2}}{( n ^{2} + n ^{2} ) n ^{4} + n ^{4}})$ …
Mathematics · Definite Integration · Numerical
Q53.Let $f : (0, π) \to R$ be a function given by $f (x) = ⎩ ⎨ ⎧ (\frac{8}{7})^{\frac{t a n 8 x}{t a n 7 x}}, a - 8, (1 + ∣ cot x ∣)^{\frac{b}{a} ∣ t a n x ∣}, 0 < x < \frac{π}{2} x = \frac{π}{2} \frac{π}{2} < x < π$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q54.The remainder when $42 8^{2024}$ is divided by 21 is .
Mathematics · Binomial Theorem · Numerical
Q55.If a function $f$ satisfies $f (m + n) = f (m) + f (n)$ for all $m, n \in N$ and $f (1) = 1$ , then the largest natural number $λ$ such that $\sum_{k = 1}^{2022} f (λ + k) \leq (2022)^{2}$ …
Mathematics · Functions · Numerical
Q56.Let the centre of a circle, passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ , be $(h, k)$ . Then for all possible values of the coordinates of the centre $(h, k), 4 (h^{2} + k^{2})$ is equal to …
Mathematics · Circle · Numerical
Q57.The sum of the square of the modulus of the elements in the set ${z = a + ib : a, b \in Z, z \in C, ∣ z - 1∣ \leq 1, ∣ z - 5∣ \leq ∣ z - 5 i ∣}$ is .
Mathematics · Complex Numbers · Numerical
Q58.Let the set of all positive values of $λ$ , for which the point of local minimum of the function $(1 + x (λ^{2} - x^{2}))$ satisfies $\frac{x ^{2} + x + 2}{x ^{2} + 5 x + 6} < 0$ , be $(α, β)$ . Then $α^{2} + β^{2}$ is equal to …
Mathematics · Application of Derivatives · Numerical
Q59.Let $A$ be a non-singular matrix of order 3. If $det (3 adj (2 adj ((det A) A))) = 3^{- 13} \cdot 2^{- 10}$ and $det (3 adj (2 A)) = 2^{m} \cdot 3^{n}$ …
Mathematics · Matrices and Determinants · Numerical
Q60.Let $a, b$ and $c$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1, 2, 3, 4$ . If the probability that $a x^{2} + b x + c = 0$ has all real roots is $\frac{m}{n}, gcd (m, n) = 1$ …
Mathematics · Probability · Numerical
Q61.A plane EM wave is propagating along $x$ direction. It has a wavelength of $4 mm$ . If electric field is in $y$ direction with the maximum magnitude of $60 Vm^{- 1}$ , the equation for magnetic field is :
Physics · Electromagnetic Waves · MCQ
Q62.A galvanometer has a coil of resistance $200Ω$ with a full scale deflection at $20 μ A$ . The value of resistance to be added to use it as an ammeter of range $(0 - 20) mA$ is :
Physics · Current Electricity · MCQ
Q63.The dimensional formula of latent heat is :
Physics · Units and Measurements · MCQ
Q64.A sphere of relative density $σ$ and diameter $D$ has concentric cavity of diameter $d$ . The ratio of $\frac{D}{d}$ , if it just floats on water in a tank is :
Physics · Properties of Matter · MCQ
Q65.The volume of an ideal gas $(γ = 1.5)$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :
Physics · Heat and Thermodynamics · MCQ
Q66.A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $1.42 eV$ . The wavelength of light emitted from the LED is :
Physics · Electronic Devices · MCQ
Q67.A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v = α x$ , where $α$ is a constant. The total work done by all the forces applied on the particle during…
Physics · Work Power and Energy · MCQ
Q68.Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account Statement (II) : Ampere's circuital law does not depend…
Physics · Magnetics · MCQ
Q69.A particle moving in a straight line covers half the distance with speed $6 m / s$ . The other half is covered in two equal time intervals with speeds $9 m / s$ and $15 m / s$ …
Physics · Motion in A Straight Line · MCQ
Q70.Given below are two statements : Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side. Statement (II) : Concave lens always forms a…
Physics · Geometrical Optics · MCQ
Q71.A sample of 1 mole gas at temperature $T$ is adiabatically expanded to double its volume. If adiab constant for the gas is $γ = \frac{3}{2}$ , then the work done by the gas in the process is :
Physics · Heat and Thermodynamics · MCQ
Q72.A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$ , the capacitance of the arrangement is : Includes diagram
Physics · Capacitor · MCQ
Q73.One main scale division of a vernier caliper is equal to $m$ units. If $n^{th}$ division of main scale coincides with $(n + 1)^{th}$ division of vernier scale, the least count of the vernier caliper is :
Physics · Units and Measurements · MCQ
Q74.A heavy iron bar, of weight $W$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $θ$ with the horizontal. The weight experienced by the person is :
Physics · Laws of Motion · MCQ
Q75.A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m _{2}}{m _{1}}$ is :
Physics · Laws of Motion · MCQ
Q76.The energy equivalent of $1 g$ of substance is :
Physics · Atoms and Nuclei · MCQ
Q77.The equivalent resistance between A and B is : Includes diagram
Physics · Current Electricity · MCQ
Q78.An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 km$ . From earth's surface to the orbit, the change in total mechanical energy of the ball is…
Physics · Gravitation · MCQ
Q79.A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :
Physics · Alternating Current · MCQ
Q80.A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :
Physics · Dual Nature of Radiation · MCQ
Q81.A square loop of edge length $2 m$ carrying current of $2 A$ is placed with its edges parallel to the $x$ - $y$ axis. A magnetic field is passing through the $x$ - $y$ plane and expressed as $B = B_{0} (1 + 4 x) \hat{k}$ ,…
Physics · Magnetics · Numerical
Q82.At the centre of a half ring of radius $R = 10 cm$ and linear charge density $4 nC m^{- 1}$ , the potential is $x π V$ . The value of $x$ is .
Physics · Electrostatics · Numerical
Q83.In a Young's double slit experiment, the intensity at a point is $(\frac{1}{4})^{th}$ of the maximum intensity, the minimum distance of the point from the central maximum is $μ m$ .…
Physics · Wave Optics · Numerical
Q84.If $a$ and $b$ makes an angle $cos^{- 1} (\frac{5}{9})$ with each other, then $∣ a + b ∣ = 2 ∣ a - b ∣$ for $∣ a ∣ = n ∣ b ∣$ The integer value of $n$ is .
Physics · Vector Algebra · Numerical
Q85.Two persons pull a wire towards themselves. Each person exerts a force of $200 N$ on the wire. Young's modulus of the material of wire is $1 \times 1 0^{11} N m^{- 2}$ . Original length of the wire is $2 m$ …
Physics · Properties of Matter · Numerical
Q86.The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 m, 2 ms^{- 1}$ and $16 ms^{- 2}$ at a certain instant. The amplitude of the motion is $x, m$ …
Physics · Simple Harmonic Motion · Numerical
Q87.A star has $100%$ helium composition. It starts to convert three $^{4} He$ into one $^{12} C$ via triple alpha process as $^{4} He +^{4} He +^{4} He \to^{12} C + Q$ …
Physics · Atoms and Nuclei · Numerical
Q88.A string is wrapped around the rim of a wheel of moment of inertia $0.40 kgm^{2}$ and radius $10 cm$ . The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $40 N$ …
Physics · Rotational Motion · Numerical
Q89.When a coil is connected across a $20 V$ dc supply, it draws a current of $5 A$ . When it is connected across $20 V, 50 Hz$ ac supply, it draws a current of $4 A$ . The self inductance of the…
Physics · Alternating Current · Numerical
Q90.The current flowing through the $1Ω$ resistor is $\frac{n}{10}$ A. The value of $n$ is . Includes diagram
Physics · Current Electricity · Numerical