2024 · 4 Apr · Shift 2

90 questions · JEE Main

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2024 · 4 Apr · Shift 2

2024 · 4 Apr · Shift 2

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Fuel cell, using hydrogen and oxygen as fuels, A. has been used in spaceship B. has as efficiency of $40%$ to produce electricity C. uses aluminum as catalysts D. is eco-friendly E. is actually a type of Galvanic cell only Choose the…
Chemistry · Electrochemistry · MCQ
Q2.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Biomolecules · MCQ
Q3.If an iron (III) complex with the formula $[Fe (NH_{3})_{x} (CN)_{y}]^{-}$ has no electron in its $e_{g}$ orbital, then the value of $x + y$ is
Chemistry · Coordination Compounds · MCQ
Q4.The number of unpaired d-electrons in $[Co (H_{2} O)_{6}]^{3 +}$ is .
Chemistry · Coordination Compounds · MCQ
Q5.Correct order of stability of carbanion is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Product P is Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.The correct order of the first ionization enthalpy is
Chemistry · Periodic Table and Periodicity · MCQ
Q8.Given below are two statements : Statement I : The correct order of first ionization enthalpy values of $Li, Na, F$ and $Cl$ is $Na S t a t e m e n t I I : T h ecor r ec t or d er o f n e g a t i v ee l ec t r o n g ain e n t ha l p y v a l u eso f$ …
Chemistry · Periodic Table and Periodicity · MCQ
Q9.For a strong electrolyte, a plot of molar conductivity against (concentration) $^{1/2}$ is a straight line, with a negative slope, the correct unit for the slope is
Chemistry · Electrochemistry · MCQ
Q10.When $MnO_{2}$ and $H_{2} SO_{4}$ is added to a salt $(A)$ , the greenish yellow gas liberated as salt (A) is :
Chemistry · Redox Reactions · MCQ
Q11.The correct statement/s about Hydrogen bonding is/are A. Hydrogen bonding exists when $H$ is covalently bonded to the highly electro negative atom. B. Intermolecular $H$ bonding is present in $o$ -nitro phenol C. Intramolecular $H$ …
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q12.Choose the Incorrect Statement about Dalton's Atomic Theory
Chemistry · Structure of Atom · MCQ
Q13. $CH_{3} - CH_{2} - CH_{2} - Br + NaOH C_{2} H_{5} OH Product ’A’$ Consider the above reactions, identify product B and product C. Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q14.The number of species from the following that have pyramidal geometry around the central atom is $S_{2} O_{3}^{2 -}, SO_{4}^{2 -}, SO_{3}^{2 -}, S_{2} O_{7}^{2 -}$
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q15.A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of $3.86 BM$ . The atomic number of the metal is
Chemistry · Coordination Compounds · MCQ
Q16.Common name of Benzene - 1,2 - diol is -
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.The equilibrium constant for the reaction $SO_{3} (g) ⇌ SO_{2} (g) + \frac{1}{2} O_{2} (g)$ is $K_{c} = 4.9 \times 1 0^{- 2}$ . The value of $K_{c}$ …
Chemistry · Chemical Equilibrium · MCQ
Q18.Find out the major product formed from the following reaction. $[Me : - CH_{3}]$ Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q19.The adsorbent used in adsorption chromatography is/are - A. silica gel B. alumina C. quick lime D. magnesia Choose the most appropriate answer from the options given below :
Chemistry · Surface Chemistry · MCQ
Q20.In the above chemical reaction sequence " $A$ " and " $B$ " respectively are Includes diagram
Chemistry · Hydrocarbons · MCQ
Q21.The maximum number of orbitals which can be identified with $n = 4$ and $m_{l} = 0$ is .
Chemistry · Structure of Atom · Numerical
Q22.Number of compounds / species from the following with non-zero dipole moment is . $BeCl_{2}, BCl_{3}, NF_{3}, XeF_{4}, CCl_{4}, H_{2} O, H_{2} S, HBr, CO_{2}, H_{2}, HCl$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q23.The total number of 'sigma' and 'pi' bonds in 2-oxohex-4-ynoic acid is .
Chemistry · Basics of Organic Chemistry · Numerical
Q24.From $6.55 g$ of aniline, the maximum amount of acetanilide that can be prepared will be $\times 1 0^{- 1} g$ .
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q25. $2.7 kg$ of each of water and acetic acid are mixed. The freezing point of the solution will be $- x^{\circ} C$ . Consider the acetic acid does not dimerise in water, nor dissociates in water.…
Chemistry · Solutions · Numerical
Q26.Consider the following reaction, the rate expression of which is given below $A + B \to C rate = k [A]^{1/2} [B]^{1/2}$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q27.Three moles of an ideal gas are compressed isothermally from $60 L$ to $20 L$ using constant pressure of $5 atm$ . Heat exchange $Q$ for the compression is - Lit. atm.
Chemistry · Thermodynamics · Numerical
Q28.Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and $π$ electrons is .
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q29.Phthalimide is made to undergo following sequence of reactions. Total number of $π$ bonds present in product 'P' is/are . Includes diagram
Chemistry · Compounds Containing Nitrogen · Numerical
Q30.A first row transition metal with highest enthalpy of atomisation, upon reaction with oxygen at high temperature forms oxides of formula $M_{2} O_{n}$ (where $n = 3, 4, 5$ ). The 'spin-only' magnetic moment…
Chemistry · D and F Block Elements · Numerical
Q31.Consider a hyperbola $H$ having centre at the origin and foci on the $x$ -axis. Let $C_{1}$ be the circle touching the hyperbola $H$ and having the centre at the origin. Let $C_{2}$ be the circle…
Mathematics · Hyperbola · MCQ
Q32.If the coefficients of $x^{4}, x^{5}$ and $x^{6}$ in the expansion of $(1 + x)^{n}$ are in the arithmetic progression, then the maximum value of $n$ is:
Mathematics · Binomial Theorem · MCQ
Q33.The value of $\frac{1 \times 2 ^{2} + 2 \times 3 ^{2} + \dots + 100 \times ( 101 ) ^{2}}{1 ^{2} \times 2 + 2 ^{2} \times 3 + \dots . + 10 0 ^{2} \times 101}$ is
Mathematics · Sequences and Series · MCQ
Q34.If the function $f (x) = {\frac{7 2 ^{x} - 9 ^{x} - 8 ^{x} + 1}{2 - 1 + c o s x}, a lo g_{e} 2 lo g_{e} 3 x e q 0, x = 0$ is continuous at $x = 0$ , then the value of $a^{2}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Let $P$ be the point of intersection of the lines $\frac{x - 2}{1} = \frac{y - 4}{5} = \frac{z - 2}{1}$ and $\frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 3}{2}$ . Then, the shortest distance of $P$ from the line $4 x = 2 y = z$ is
Mathematics · 3D Geometry · MCQ
Q36.Let $f (x) = 3 x - 2 + 4 - x$ be a real valued function. If $α$ and $β$ are respectively the minimum and the maximum values of $f$ , then $α^{2} + 2 β^{2}$ is equal to
Mathematics · Application of Derivatives · MCQ
Q37.Let $f (x) = \int_{0}^{x} (t + sin (1 - e^{t})) d t, x \in R$ . Then, $lim_{x \to 0} \frac{f ( x )}{x ^{3}}$ is equal to
Mathematics · Definite Integration · MCQ
Q38.The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x, and y \geq 4 x - 1}$ is
Mathematics · Area Under the Curves · MCQ
Q39.Given that the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[- 1, 1]$ such that $cos^{- 1} x - sin^{- 1} y = α, \frac{- π}{2} \leq α \leq π$ . Then, the minimum value of $x^{2} + y^{2} + 2 x y sin α$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q40.For $λ > 0$ , let $θ$ be the angle between the vectors $a = \hat{i} + λ \hat{j} - 3 \hat{k}$ and $b = 3 \hat{i} - \hat{j} + 2 \hat{k}$ . If the vectors $a + b$ and $a - b$ are mutually perpendicular,…
Mathematics · Vector Algebra · MCQ
Q41.Let $y = y (x)$ be the solution of the differential equation $(x^{2} + 4)^{2} d y + (2 x^{3} y + 8 x y - 2) d x = 0$ . If $y (0) = 0$ , then $y (2)$ is equal to
Mathematics · Differential Equations · MCQ
Q42.If the mean of the following probability distribution of a radam variable $X$ : is $\frac{46}{9}$ , then the variance of the distribution is Includes table
Mathematics · Probability · MCQ
Q43.Let $P Q$ be a chord of the parabola $y^{2} = 12 x$ and the midpoint of $P Q$ be at $(4, 1)$ . Then, which of the following point lies on the line passing through the points $P$ and $Q$ ?
Mathematics · Parabola · MCQ
Q44.Let $C$ be a circle with radius $10$ units and centre at the origin. Let the line $x + y = 2$ intersects the circle $C$ at the points $P$ and $Q$ . Let $MN$ be a chord of $C$ of…
Mathematics · Circle · MCQ
Q45.The area (in sq. units) of the region $S = {z \in C : ∣ z - 1∣ \leq 2; (z + \overset{z}{ˉ}) + i (z - \overset{z}{ˉ}) \leq 2, lm (z) \geq 0}$ is
Mathematics · Complex Numbers · MCQ
Q46.If the value of the integral $- 1 \int 1 \frac{c o s α x}{1 + 3 ^{x}} d x$ is $\frac{2}{π}$ .Then, a value of $α$ is
Mathematics · Definite Integration · MCQ
Q47.Let three real numbers $a, b, c$ be in arithmetic progression and $a + 1, b, c + 3$ be in geometric progression. If $a > 10$ and the arithmetic mean of $a, b$ and $c$ is 8, then the cube of the geometric mean of $a, b$ and $c$ is
Mathematics · Sequences and Series · MCQ
Q48.Let a relation $R$ on $N \times N$ be defined as: $(x_{1}, y_{1}) R (x_{2}, y_{2})$ if and only if $x_{1} \leq x_{2}$ or $y_{1} \leq y_{2}$ . Consider the two statements: (I) $R$ is…
Mathematics · Sets and Relations · MCQ
Q49.Let $A = [1021]$ and $B = I + adj (A) + (adj A)^{2} + \dots + (adj A)^{10}$ . Then, the sum of all the elements of the matrix $B$ is:
Mathematics · Matrices and Determinants · MCQ
Q50.Let $a = \hat{i} + \hat{j} + \hat{k}, b = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $c = x \hat{i} + 2 \hat{j} + 3 \hat{k}, x \in R$ . If $d$ is the unit vector in the direction of $b + c$ such that $a \cdot d = 1$ …
Mathematics · Vector Algebra · MCQ
Q51.Let $S = {sin^{2} 2 θ : (sin^{4} θ + cos^{4} θ) x^{2} + (sin 2 θ) x + (sin^{6} θ + cos^{6} θ) = 0$ has real roots $}$ . If $α$ and $β$ be the smallest and largest elements of the…
Mathematics · Trigonometric Functions and Equations · Numerical
Q52.If $\int cosec^{5} x d x = α cot x cosec x (cosec^{2} x + \frac{3}{2}) + β lo g_{x} tan \frac{x}{2} + C$ where $α, β \in R$ and $C$ is…
Mathematics · Indefinite Integrals · Numerical
Q53.Let $A$ be a $2 \times 2$ symmetric matrix such that $A [11] = [37]$ and the determinant of $A$ be 1 . If $A^{- 1} = α A + β I$ , where $I$ is an…
Mathematics · Matrices and Determinants · Numerical
Q54.Consider a triangle $ABC$ having the vertices $A (1, 2), B (α, β)$ and $C (γ, δ)$ and angles $∠ A B C = \frac{π}{6}$ and $∠ B A C = \frac{2 π}{3}$ . If the points $B$ and…
Mathematics · Properties of Triangle · Numerical
Q55.In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that the team wins, and $y$ be the number of matches that team…
Mathematics · Probability · Numerical
Q56.Consider the function $f : R \to R$ defined by $f (x) = \frac{2 x}{1 + 9 x ^{2}}$ . If the composition of $f, 10 times (f \circ f \circ f \circ \dots \circ f) (x) = \frac{2 ^{10} x}{1 + 9 α x ^{2}}$ …
Mathematics · Functions · Numerical
Q57.Let $y = y (x)$ be the solution of the differential equation $(x + y + 2)^{2} d x = d y, y (0) = - 2$ . Let the maximum and minimum values of the function $y = y (x)$ in $[0, \frac{π}{3}]$ be $α$ and $β$ , respectively. If $(3 α + π)^{2} + β^{2} = γ + δ 3, γ, δ \in Z$ …
Mathematics · Differential Equations · Numerical
Q58.Let $f : R \to R$ be a thrice differentiable function such that $f (0) = 0, f (1) = 1, f (2) = - 1, f (3) = 2$ and $f (4) = - 2$ . Then, the minimum number of zeros of $(3 f^{'} f^{''} + f f^{'''}) (x)$ …
Mathematics · Differentiation · Numerical
Q59.Consider a line $L$ passing through the points $P (1, 2, 1)$ and $Q (2, 1, - 1)$ . If the mirror image of the point $A (2, 2, 2)$ in the line $L$ is $(α, β, γ)$ , then $α + β + 6 γ$ …
Mathematics · 3D Geometry · Numerical
Q60.There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .
Mathematics · Permutations and Combinations · Numerical
Q61.Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.
Physics · Units and Measurements · MCQ
Q62.A $2 kg$ brick begins to slide over a surface which is inclined at an angle of $4 5^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:
Physics · Laws of Motion · MCQ
Q63.Match List I with List II Choose the correct answer from the options given below: Includes table Includes diagram
Physics · Alternating Current · MCQ
Q64.Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :
Physics · Electronic Devices · MCQ
Q65.A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $γ = 3/2$ . The work done by the gas in the process is: $(μ = 1 mole)$
Physics · Heat and Thermodynamics · MCQ
Q66.The magnetic moment of a bar magnet is $0.5 Am^{2}$ . It is suspended in a uniform magnetic field of $8 \times 1 0^{- 2} T$ . The work done in rotating it from its most stable to most unstable position is:
Physics · Magnetic Properties of Matter · MCQ
Q67.In simple harmonic motion, the total mechanical energy of given system is $E$ . If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is: Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q68.Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason R. Assertion A: Number of photons increases with increase in frequency of light. Reason R: Maximum kinetic energy of emitted…
Physics · Dual Nature of Radiation · MCQ
Q69.A $90 kg$ body placed at $2 R$ distance from surface of earth experiences gravitational pull of : ( $R =$ Radius of earth, $g = 10 m s^{- 2}$ )
Physics · Gravitation · MCQ
Q70.According to Bohr's theory, the moment of momentum of an electron revolving in $4^{th}$ orbit of hydrogen atom is:
Physics · Atoms and Nuclei · MCQ
Q71.A cyclist starts from the point $P$ of a circular ground of radius $2 km$ and travels along its circumference to the point $S$ . The displacement of a cyclist is: Includes diagram
Physics · Circular Motion · MCQ
Q72.A body of $m kg$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is: (given, $R = 14 m, g = 10 m / s^{2}$ and $2 = 1.4$ ) Includes diagram
Physics · Work Power and Energy · MCQ
Q73.The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:
Physics · Wave Optics · MCQ
Q74.The translational degrees of freedom $(f_{t})$ and rotational degrees of freedom $(f_{r})$ of $CH_{4}$ molecule are:
Physics · Heat and Thermodynamics · MCQ
Q75.A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:
Physics · Electrostatics · MCQ
Q76.Correct formula for height of a satellite from earths surface is :
Physics · Gravitation · MCQ
Q77.Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the…
Physics · Properties of Matter · MCQ
Q78.An electric bulb rated $50 W - 200 V$ is connected across a $100 V$ supply. The power dissipation of the bulb is:
Physics · Current Electricity · MCQ
Q79.Arrange the following in the ascending order of wavelength: A. Gamma rays $(λ_{1})$ B. $x$ - rays $(λ_{2})$ C. Infrared waves $(λ_{3})$ D. Microwaves $(λ_{4})$ Choose the…
Physics · Electromagnetic Waves · MCQ
Q80.Identify the logic gate given in the circuit : Includes diagram
Physics · Electronic Devices · MCQ
Q81.In a system two particles of masses $m_{1} = 3 kg$ and $m_{2} = 2 kg$ are placed at certain distance from each other. The particle of mass $m_{1}$ is moved towards the center of mass of the system through a distance $2 cm$ …
Physics · Center of Mass · Numerical
Q82.Two parallel long current carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$ . The value of $x$ is . Includes diagram
Physics · Magnetics · Numerical
Q83.A bus moving along a straight highway with speed of $72 km / h$ is brought to halt within $4 s$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is …
Physics · Motion in A Straight Line · Numerical
Q84.A rod of length $60 cm$ rotates with a uniform angular velocity $20 rad s^{- 1}$ about its perpendicular bisector, in a uniform magnetic filed $0.5 T$ . The direction of magnetic field is parallel to the axis of…
Physics · Magnetics · Numerical
Q85.The disintegration energy $Q$ for the nuclear fission of $^{235} U \to^{140} Ce +^{94} Zr + n$ is $MeV$ . Given atomic masses of $^{235} U : 235.0439 u;^{140} Ce : 139.9054 u,^{94} Zr : 93.9063 u; n : 1.0086 u$ …
Physics · Atoms and Nuclei · Numerical
Q86.Mercury is filled in a tube of radius $2 cm$ up to a height of $30 cm$ . The force exerted by mercury on the bottom of the tube is N. (Given, atmospheric pressure $= 1 0^{5} Nm^{- 2}$ ,…
Physics · Properties of Matter · Numerical
Q87.A light ray is incident on a glass slab of thickness $43 cm$ and refractive index $2$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing…
Physics · Geometrical Optics · Numerical
Q88.Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0 mm$ and wire $B$ has radius of $4.0 mm$ . The resistance of wire $B$ is $2Ω$ . The resistance of wire $A$ is…
Physics · Current Electricity · Numerical
Q89.The displacement of a particle executing SHM is given by $x = 10 sin (w t + \frac{π}{3}) m$ . The time period of motion is $3.14 s$ . The velocity of the particle at $t = 0$ is $m / s$ …
Physics · Simple Harmonic Motion · Numerical
Q90.A parallel plate capacitor of capacitance $12.5 pF$ is charged by a battery connected between its plates to potential difference of $12.0 V$ . The battery is now disconnected and a dielectric slab $(ϵ_{r} = 6)$ …
Physics · Capacitor · Numerical