2024 · 29 Jan · Shift 2

90 questions · JEE Main

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2024 · 29 Jan · Shift 2

2024 · 29 Jan · Shift 2

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.On passing a gas, ' $X$ ', through Nessler's regent, a brown precipitate is obtained. The gas ' $X$ ' is
Chemistry · P Block Elements · MCQ
Q2.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Biomolecules · MCQ
Q3.Which of the following acts as a strong reducing agent? (Atomic number: $Ce = 58, Eu = 63, Gd = 64, Lu = 71$ )
Chemistry · D and F Block Elements · MCQ
Q4.Given below are two statements: Statement I : Fluorine has most negative electron gain enthalpy in its group. Statement II : Oxygen has least negative electron gain enthalpy in its group. In the light of the above statements, choose the…
Chemistry · Periodic Table and Periodicity · MCQ
Q5.According to IUPAC system, the compound is named as Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Structure of Atom · MCQ
Q7.The element having the highest first ionization enthalpy is
Chemistry · Periodic Table and Periodicity · MCQ
Q8.Which of the following statements are correct about $Zn, Cd$ and $Hg$ ? A. They exhibit high enthalpy of atomization as the d-subshell is full. B. $Zn$ and $Cd$ do not show variable oxidation…
Chemistry · D and F Block Elements · MCQ
Q9.The ascending acidity order of the following H atoms is Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q10.The correct IUPAC name of $K_{2} MnO_{4}$ is
Chemistry · D and F Block Elements · MCQ
Q11.Identify the reagents used for the following conversion Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q12.Chromatographic technique/s based on the principle of differential adsorption is / are A. Column chromatography B. Thin layer chromatography C. Paper chromatography Choose the most appropriate answer from the options given below:
Chemistry · Practical Organic Chemistry · MCQ
Q13.Which of the following reaction is correct?
Chemistry · Compounds Containing Nitrogen · MCQ
Q14.Anomalous behavior of oxygen is due to its
Chemistry · Periodic Table and Periodicity · MCQ
Q15.Which one of the following will show geometrical isomerism?
Chemistry · Basics of Organic Chemistry · MCQ
Q16.A reagent which gives brilliant red precipitate with Nickel ions in basic medium is
Chemistry · Coordination Compounds · MCQ
Q17.Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid results
Chemistry · Alcohols Phenols and Ethers · MCQ
Q18.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Alcohols Phenols and Ethers · MCQ
Q19.The product A formed in the following reaction is Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q20.Alkyl halide is converted into alkyl isocyanide by reaction with
Chemistry · Haloalkanes and Haloarenes · MCQ
Q21.The total number of molecules with zero dipole moment among $CH_{4}, BF_{3}, H_{2} O, HF, NH_{3}, CO_{2}$ and $SO_{2}$ is .
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q22.Standard enthalpy of vapourisation for $CCl_{4}$ is $30.5 kJ mol^{- 1}$ . Heat required for vapourisation of $284 g$ of $CCl_{4}$ at constant temperature is $kJ$ .…
Chemistry · Thermodynamics · Numerical
Q23.If $50 mL$ of $0.5 M$ oxalic acid is required to neutralise $25 mL$ of $NaOH$ solution, the amount of $NaOH$ in $50 mL$ of given $NaOH$ solution is…
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q24.The following concentrations were observed at $500 K$ for the formation of $NH_{3}$ from $N_{2}$ and $H_{2}$ . At equilibrium ; $[N_{2}] = 2 \times 1 0^{- 2} M, [H_{2}] = 3 \times 1 0^{- 2} M$ …
Chemistry · Chemical Equilibrium · Numerical
Q25.A constant current was passed through a solution of $AuCl_{4}^{-}$ ion between gold electrodes. After a period of 10.0 minutes, the increase in mass of cathode was $1.314 g$ . The total charge passed through the solution is…
Chemistry · Electrochemistry · Numerical
Q26.The total number of anti bonding molecular orbitals, formed from $2 s$ and $2 p$ atomic orbitals in a diatomic molecule is .
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q27.The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is $\times 1 0^{- 2}$ . (Given antilog $0.2006 = 1.587$ )
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q28.The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is .
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q29.The oxidation number of iron in the compound formed during brown ring test for NO $_{3}^{-}$ iron is .
Chemistry · Redox Reactions · Numerical
Q30.Molality of 0.8 M H $_{2}$ SO $_{4}$ solution (density 1.06 g cm $^{- 3}$ ) is $\times 1 0^{- 3}$ m.
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q31.Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
Mathematics · Permutations and Combinations · MCQ
Q32.Let $A$ be the point of intersection of the lines $3 x + 2 y = 14, 5 x - y = 6$ and $B$ be the point of intersection of the lines $4 x + 3 y = 8, 6 x + y = 5$ . The distance of the point $P (5, - 2)$ from the line $AB$ is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.If $\int \frac{s i n ^{\frac{3}{2}} x + c o s ^{\frac{3}{2}} x}{s i n ^{3} x c o s ^{3} x s i n ( x - θ )} d x = A cos θ tan x - sin θ + B cos θ - sin θ cot x + C$ , where $C$ is the integration constant, then $A B$ …
Mathematics · Indefinite Integrals · MCQ
Q34.The distance of the point $(2, 3)$ from the line $2 x - 3 y + 28 = 0$ , measured parallel to the line $3 x - y + 1 = 0$ , is equal to
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.Let a unit vector $\overset{u}{^} = x \hat{i} + y \hat{j} + z \hat{k}$ make angles $\frac{π}{2}, \frac{π}{3}$ and $\frac{2 π}{3}$ with the vectors $\frac{1}{2} \hat{i} + \frac{1}{2} \hat{k}, \frac{1}{2} \hat{j} + \frac{1}{2} \hat{k}$ …
Mathematics · Vector Algebra · MCQ
Q36.The function $f (x) = \frac{x}{x ^{2} - 6 x - 16}, x \in R - {- 2, 8}$
Mathematics · Application of Derivatives · MCQ
Q37.If R is the smallest equivalence relation on the set ${1, 2, 3, 4}$ such that ${(1, 2), (1, 3)} \subset R$ , then the number of elements in $R$ is .
Mathematics · Sets and Relations · MCQ
Q38.If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of the first four observations is $\frac{7}{2}$ , then the variance of the first four observations in equal to
Mathematics · Statistics · MCQ
Q39.Let $P (3, 2, 3), Q (4, 6, 2)$ and $R (7, 3, 2)$ be the vertices of $△ PQR$ . Then, the angle $∠ QPR$ is
Mathematics · 3D Geometry · MCQ
Q40. $Let y = lo g_{e} (\frac{1 - x ^{2}}{1 + x ^{2}}), - 1 < x < 1 . Then at x = \frac{1}{2}, the value of 225 (y^{'} - y^{''}) is equal to$
Mathematics · Differentiation · MCQ
Q41.If $lo g_{e} a, lo g_{e} b, lo g_{e} c$ are in an A.P. and $lo g_{e} a - lo g_{e} 2 b, lo g_{e} 2 b - lo g_{e} 3 c, lo g_{e} 3 c - lo g_{e}$ a are also in an A.P, then $a : b : c$ …
Mathematics · Sequences and Series · MCQ
Q42.If $sin (\frac{y}{x}) = lo g_{e} ∣ x ∣ + \frac{α}{2}$ is the solution of the differential equation $x cos (\frac{y}{x}) \frac{d y}{d x} = y cos (\frac{y}{x}) + x$ and $y (1) = \frac{π}{3}$ , then $α^{2}$ …
Mathematics · Differential Equations · MCQ
Q43.An integer is chosen at random from the integers $1, 2, 3, \dots, 50$ . The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is
Mathematics · Probability · MCQ
Q44.Let $O A = a, O B = 12 a + 4 b and O C = b$ , where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then $\frac{area of the quadrilateral OA BC}{area of S}$ …
Mathematics · Vector Algebra · MCQ
Q45.The function $f (x) = 2 x + 3 (x)^{\frac{2}{3}}, x \in R$ , has
Mathematics · Application of Derivatives · MCQ
Q46.If each term of a geometric progression $a_{1}, a_{2}, a_{3}, \dots$ with $a_{1} = \frac{1}{8}$ and $a_{2} e q a_{1}$ , is the arithmetic mean of the next two terms and $S_{n} = a_{1} + a_{2} + \dots .. + a_{n}$ , then $S_{20} - S_{18}$ is equal to
Mathematics · Sequences and Series · MCQ
Q47.Let $r$ and $θ$ respectively be the modulus and amplitude of the complex number $z = 2 - i (2 tan \frac{5 π}{8})$ , then $(r, θ)$ is equal to
Mathematics · Complex Numbers · MCQ
Q48.The sum of the solutions $x \in R$ of the equation $\frac{3 c o s 2 x + c o s ^{3} 2 x}{c o s ^{6} x - s i n ^{6} x} = x^{3} - x^{2} + 6$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q49.Let $x = \frac{m}{n}$ ( $m, n$ are co-prime natural numbers) be a solution of the equation $cos (2 sin^{- 1} x) = \frac{1}{9}$ and let $α, β (α > β)$ be the roots of the equation $m x^{2} - n x - m + n = 0$ . Then the…
Mathematics · Inverse Trigonometric Functions · MCQ
Q50.Let $A = 2631232112$ and $P = 157201025$ . The sum of…
Mathematics · Matrices and Determinants · MCQ
Q51.Let O be the origin, and M and $N$ be the points on the lines $\frac{x - 5}{4} = \frac{y - 4}{1} = \frac{z - 5}{3}$ and $\frac{x + 8}{12} = \frac{y + 2}{5} = \frac{z + 11}{9}$ respectively such that $MN$ is the shortest distance between the…
Mathematics · 3D Geometry · Numerical
Q52.Let the area of the region ${(x, y) : 0 \leq x \leq 3, 0 \leq y \leq min {x^{2} + 2, 2 x + 2}}$ be A. Then $12 A$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q53.Let the set $C = {(x, y) ∣ x^{2} - 2^{y} = 2023, x, y \in N}$ . Then $\sum_{(x, y) \in C} (x + y)$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q54.Let the slope of the line $45 x + 5 y + 3 = 0$ be $27 r_{1} + \frac{9 r _{2}}{2}$ for some $r_{1}, r_{2} \in R$ . Then $lim_{x \to 3} (\int_{3}^{x} \frac{8 t ^{2}}{\frac{3 r _{2} x}{2} - r _{2} x ^{2} - r _{1} x ^{3} - 3 x} d t)$ is equal to …
Mathematics · Definite Integration · Numerical
Q55.Let $α, β$ be the roots of the equation $x^{2} - 6 x + 3 = 0$ such that $Im (α) > Im (β)$ . Let $a, b$ be integers not divisible by 3 and $n$ be a natural number such that $\frac{α ^{99}}{β} + α^{98} = 3^{n} (a + ib), i = - 1$ …
Mathematics · Complex Numbers · Numerical
Q56.Let for any three distinct consecutive terms $a, b, c$ of an A.P, the lines $a x + b y + c = 0$ be concurrent at the point $P$ and $Q (α, β)$ be a point such that the system of equations $x + y + z = 6, 2 x + 5 y + α z = β and$ …
Mathematics · Matrices and Determinants · Numerical
Q57.Let $P (α, β)$ be a point on the parabola $y^{2} = 4 x$ . If $P$ also lies on the chord of the parabola $x^{2} = 8 y$ whose mid point is $(1, \frac{5}{4})$ , then $(α - 28) (β - 8)$ is equal to .
Mathematics · Parabola · Numerical
Q58.Remainder when $6 4^{3 2^{32}}$ is divided by 9 is equal to .
Mathematics · Binomial Theorem · Numerical
Q59.Let $f (x) = lim_{r \to x} {\frac{2 r ^{2} [ ( f ( r ) ) ^{2} - f ( x ) f ( r ) ]}{r ^{2} - x ^{2}} - r^{3} e^{\frac{f ( r )}{r}}}$ be differentiable in $(- \infty, 0) \cup (0, \infty)$ and $f (1) = 1$ . Then the value of ea, such that…
Mathematics · Limits Continuity and Differentiability · Numerical
Q60.If $\int_{\frac{π}{6}}^{\frac{π}{3}} 1 - sin 2 x d x = α + β 2 + γ 3$ , where $α, β$ and $γ$ are rational numbers, then $3 α + 4 β - γ$ is equal to .
Mathematics · Definite Integration · Numerical
Q61.A small liquid drop of radius $R$ is divided into 27 identical liquid drops. If the surface tension is $T$ , then the work done in the process will be:
Physics · Properties of Matter · MCQ
Q62.In the given circuit, the current in resistance R $_{3}$ is : Includes diagram
Physics · Current Electricity · MCQ
Q63.A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a ^{4} b ^{3}}{c ^{2}}$ . The percentage error in $a, b$ and $c$ are $3%, 4%$ and $5%$ respectively. Then, the percentage error in $Q$ is :
Physics · Units and Measurements · MCQ
Q64.A stone of mass $900 g$ is tied to a string and moved in a vertical circle of radius $1 m$ making $10 rpm$ . The tension in the string, when the stone is at the lowest point is (if $π^{2} = 9.8$ and $g = 9.8 m / s^{2}$ …
Physics · Circular Motion · MCQ
Q65.The truth table for this given circuit is : Includes diagram
Physics · Electronic Devices · MCQ
Q66.A bob of mass ' $m$ ' is suspended by a light string of length ' $L$ '. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position B. The ratio of kinetic… Includes diagram
Physics · Work Power and Energy · MCQ
Q67.An electric field is given by $(6 \hat{i} + 5 \hat{j} + 3 \hat{k}) N / C$ . The electric flux through a surface area $30 \hat{i} m^{2}$ lying in YZ-plane (in SI unit) is :
Physics · Electrostatics · MCQ
Q68.A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution :
Physics · Gravitation · MCQ
Q69.A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$ , its length increases by $l$ . If the radius of the wire and the applied force both are reduced to half of their original values keeping…
Physics · Properties of Matter · MCQ
Q70.The temperature of a gas having $2.0 \times 1 0^{25}$ molecules per cubic meter at $1.38 atm$ (Given, $k = 1.38 \times 1 0^{- 23} JK^{- 1}$ ) is :
Physics · Heat and Thermodynamics · MCQ
Q71.If the distance between object and its two times magnified virtual image produced by a curved mirror is $15 cm$ , the focal length of the mirror must be:
Physics · Geometrical Optics · MCQ
Q72.A plane electromagnetic wave of frequency $35 MHz$ travels in free space along the $X$ -direction. At a particular point (in space and time) $E = 9.6 \hat{j} V / m$ . The value of magnetic field at this point…
Physics · Electromagnetic Waves · MCQ
Q73.In an a.c. circuit, voltage and current are given by: $V = 100 sin (100 t) V$ and $I = 100 sin (100 t + \frac{π}{3}) mA$ respectively. The average power dissipated in one cycle is:
Physics · Alternating Current · MCQ
Q74.A particle is moving in a straight line. The variation of position ' $x$ ' as a function of time ' $t$ ' is given as $x = (t^{3} - 6 t^{2} + 20 t + 15) m$ . The velocity of the body when its acceleration becomes zero is :
Physics · Motion in A Straight Line · MCQ
Q75.The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 m$ . If it dissipates $10%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point…
Physics · Simple Harmonic Motion · MCQ
Q76. $N$ moles of a polyatomic gas $(f = 6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is :
Physics · Heat and Thermodynamics · MCQ
Q77.In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $7 λ /4$ . The ratio of intensity of fringe at this…
Physics · Wave Optics · MCQ
Q78.Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. Statement II : An atom is a spherical…
Physics · Atoms and Nuclei · MCQ
Q79.Two sources of light emit with a power of $200 W$ . The ratio of number of photons of visible light emitted by each source having wavelengths $300 nm$ and $500 nm$ respectively, will be :
Physics · Dual Nature of Radiation · MCQ
Q80.Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ …
Physics · Magnetics · MCQ
Q81.In the given circuit, the current flowing through the resistance $20Ω$ is $0.3 A$ , while the ammeter reads $0.9 A$ . The value of $R_{1}$ is $Ω$ . Includes diagram
Physics · Current Electricity · Numerical
Q82.In the given figure, the charge stored in $6 μ F$ capacitor, when points $A$ and $B$ are joined by a connecting wire is $μ C$ . Includes diagram
Physics · Capacitor · Numerical
Q83.In a single slit diffraction pattern, a light of wavelength 6000 $A o$ is used. The distance between the first and third minima in the diffraction pattern is found to be $3 mm$ when the screen in placed $50 cm$ …
Physics · Wave Optics · Numerical
Q84.A body of mass $5 kg$ moving with a uniform speed $32 ms^{- 1}$ in $X - Y$ plane along the line $y = x + 4$ . The angular momentum of the particle about the origin will be $kg m^{2} s^{- 1}$ …
Physics · Rotational Motion · Numerical
Q85.Hydrogen atom is bombarded with electrons accelerated through a potential difference of $V$ , which causes excitation of hydrogen atoms. If the experiment is being performed at $T = 0 K$ , the minimum potential…
Physics · Atoms and Nuclei · Numerical
Q86.A simple harmonic oscillator has an amplitude $A$ and time period $6 π$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x =$ A to $x = \frac{3}{2}$ A will be $\frac{π}{x} s$ …
Physics · Simple Harmonic Motion · Numerical
Q87.Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4 : 1$ and force $F_{1}$ is applied to $P$ , an extension of $Δ l$ is produced. The force which is…
Physics · Properties of Matter · Numerical
Q88.A particle is moving in a circle of radius $50 cm$ in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at $t = 0$ is $4 m / s$ , the time…
Physics · Circular Motion · Numerical
Q89.A charge of $4.0 μ C$ is moving with a velocity of $4.0 \times 1 0^{6} ms^{- 1}$ along the positive $y$ axis under a magnetic field $B$ of strength $(2 \hat{k}) T$ . The force acting on the charge is $x \hat{i} N$ …
Physics · Magnetics · Numerical
Q90.A horizontal straight wire $5 m$ long extending from east to west falling freely at right angle to horizontal component of earths magnetic field $0.60 \times 1 0^{- 4} Wbm^{- 2}$ . The instantaneous value of emf induced in…
Physics · Electromagnetic Induction · Numerical