2024 · 31 Jan · Shift 2

90 questions · JEE Main

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2024 · 31 Jan · Shift 2

2024 · 31 Jan · Shift 2

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Major product of the following reaction is - Includes diagram
Chemistry · Hydrocarbons · MCQ
Q2. $A_{(g)} ⇌ B_{(g)} + \frac{C}{2} (g)$ The correct relationship between $K_{P}, α$ and equilibrium pressure $P$ is
Chemistry · Chemical Equilibrium · MCQ
Q3.Identify major product 'P' formed in the following reaction. Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.Given below are two statements: Statement I : Group 13 trivalent halides get easily hydrolyzed by water due to their covalent nature. Statement II : $AlCl_{3}$ upon hydrolysis in acidified aqueous solution forms octahedral $[Al (H_{2} O)_{6}]^{3 +}$ …
Chemistry · P Block Elements · MCQ
Q5.The azo-dye $(Y)$ formed in the following reactions is Sulphanilic acid $+ NaNO_{2} + CH_{3} COOH \to X$ . Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q6.Given below are two statements: Statement I : $S_{8}$ solid undergoes disproportionation reaction under alkaline conditions to form $S^{2 -}$ and $S_{2} O_{3}^{2 -}$ . Statement II : $ClO_{4}^{-}$ can…
Chemistry · P Block Elements · MCQ
Q7.Identify structure of 2,3-dibromo-1-phenylpentane.
Chemistry · Basics of Organic Chemistry · MCQ
Q8.Choose the correct statements from the following A. All group 16 elements form oxides of general formula $EO_{2}$ and $EO_{3}$ , where $E = S, Se, Te$ and $Po$ . Both the types of…
Chemistry · P Block Elements · MCQ
Q9.The correct order of reactivity in electrophilic substitution reaction of the following compounds is : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q10.Choose the correct statements from the following A. $Mn_{2} O_{7}$ is an oil at room temperature B. $V_{2} O_{4}$ reacts with acid to give $VO_{2}^{2 +}$ C. $CrO$ is a basic oxide D. $V_{2} O_{5}$ …
Chemistry · D and F Block Elements · MCQ
Q11.Select the option with correct property -
Chemistry · Coordination Compounds · MCQ
Q12.Which of the following is least ionic?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q13.The four quantum numbers for the electron in the outer most orbital of potassium (atomic no. 19) are
Chemistry · Structure of Atom · MCQ
Q14.Identify the name reaction. Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q15.Consider the following elements. Which of the following is/are true about $A^{'}, B^{'}, C^{'}$ and $D^{'}$ ? A. Order of atomic radii: $B^{'} < A^{'} < D^{'} < C^{'}$ … Includes diagram
Chemistry · Periodic Table and Periodicity · MCQ
Q16.The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. A suitable…
Chemistry · Practical Organic Chemistry · MCQ
Q17.Identify A and B in the following reaction sequence. Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q18.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Coordination Compounds · MCQ
Q19.Given below are two statements : Statement I : Aniline reacts with con. $H_{2} SO_{4}$ , followed by heating at $453 - 473 K$ gives $p$ -aminobenzene sulphonic acid, which gives blood red colour in the…
Chemistry · Compounds Containing Nitrogen · MCQ
Q20.A sample of $CaCO_{3}$ and $MgCO_{3}$ weighed $2.21 g$ is ignited to constant weight of $1.152 g$ . The composition of mixture is : (Given molar mass in $g mol^{- 1} CaCO_{3} : 100, MgCO_{3} : 84$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q21.From the vitamins $A, B_{1}, B_{6}, B_{12}, C, D, E$ and $K$ , the number of vitamins that can be stored in our body is .
Chemistry · Biomolecules · Numerical
Q22.A diatomic molecule has a dipole moment of $1.2 D$ . If the bond distance is $1 A^{\circ}$ , then fractional charge on each atom is $\times 1 0^{- 1}$ esu. (Given $1 D = 1 0^{- 18}$ esucm)
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q23.Number of isomeric products formed by monochlorination of 2-methylbutane in presence of sunlight is .
Chemistry · Basics of Organic Chemistry · Numerical
Q24.In the reaction of potassium dichromate, potassium chloride and sulfuric acid (conc.), the oxidation state of the chromium in the product is $(+)$ .
Chemistry · Redox Reactions · Numerical
Q25.The values of conductivity of some materials at $298.15 K^{- 1} in Sm^{- 1}$ are $2.1 \times 1 0^{3}$ , $1.0 \times 1 0^{- 16}, 1.2 \times 10, 3.91, 1.5 \times 1 0^{- 2}, 1 \times 1 0^{- 7}, 1.0 \times 1 0^{3}$ . The number of…
Chemistry · Electrochemistry · Numerical
Q26.A compound $(x)$ with molar mass $108 g mol^{- 1}$ undergoes acetylation to give product with molar mass $192 g mol^{- 1}$ . The number of amino groups in the compound $(x)$ is…
Chemistry · Compounds Containing Nitrogen · Numerical
Q27.Number of moles of $H^{+}$ ions required by $1 mole$ of $MnO_{4}^{-}$ to oxidise oxalate ion to $CO_{2}$ is .
Chemistry · Redox Reactions · Numerical
Q28.If 5 moles of an ideal gas expands from $10 L$ to a volume of $100 L$ at $300 K$ under isothermal and reversible condition then work, $w$ , is $- x J$ . The value of $x$ is …
Chemistry · Thermodynamics · Numerical
Q29.The molarity of $1 L$ orthophosphoric acid $(H_{3} PO_{4})$ having $70%$ purity by weight (specific gravity $1.54 g cm^{- 3}$ ) is $M$ . (Molar mass…
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q30. $r = k [A]$ for a reaction, $50%$ of $A$ is decomposed in 120 minutes. The time taken for $90%$ decomposition of $A$ is minutes.
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q31.The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
Mathematics · Permutations and Combinations · MCQ
Q32.A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is
Mathematics · Probability · MCQ
Q33.Let $A$ be a $3 \times 3$ real matrix such that $A 101 = 2101, A - 1 01 = 4 - 1 01, A 010 = 2010 .$ …
Mathematics · Matrices and Determinants · MCQ
Q34.Let $(α, β, γ)$ be the mirror image of the point $(2, 3, 5)$ in the line $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ . Then, $2 α + 3 β + 4 γ$ is equal to
Mathematics · 3D Geometry · MCQ
Q35.If $a = sin^{- 1} (sin (5))$ and $b = cos^{- 1} (cos (5))$ , then $a^{2} + b^{2}$ is equal to
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let $P$ be a parabola with vertex $(2, 3)$ and directrix $2 x + y = 6$ . Let an ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ , of eccentricity $\frac{1}{2}$ pass through the focus of the parabola $P$ . Then, the square of the…
Mathematics · Ellipse · MCQ
Q37.The number of solutions, of the equation $e^{s i n x} - 2 e^{- s i n x} = 2$ , is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q38.The shortest distance, between lines $L_{1}$ and $L_{2}$ , where $L_{1} : \frac{x - 1}{2} = \frac{y + 1}{- 3} = \frac{z + 4}{2}$ and $L_{2}$ is the line, passing through the points $A (- 4, 4, 3), B (- 1, 6, 3)$ and perpendicular to the line $\frac{x - 3}{- 2} = \frac{y}{3} = \frac{z - 1}{1}$ …
Mathematics · 3D Geometry · MCQ
Q39.The area of the region enclosed by the parabolas $y = 4 x - x^{2}$ and $3 y = (x - 4)^{2}$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q40.Let $f, g : (0, \infty) \to R$ be two functions defined by $f (x) = - x \int x (∣ t ∣ - t^{2}) e^{- t^{2}} d t$ and $g (x) = 0 \int x^{2} t^{1/2} e^{- t} d t$ . Then, the value of $9 (f (lo g_{e} 9) + g (lo g_{e} 9))$ …
Mathematics · Definite Integration · MCQ
Q41.Let $f :\to R \to (0, \infty)$ be strictly increasing function such that $lim_{x \to \infty} \frac{f ( 7 x )}{f ( x )} = 1$ . Then, the value of $lim_{x \to \infty} [\frac{f ( 5 x )}{f ( x )} - 1]$ …
Mathematics · Application of Derivatives · MCQ
Q42.The temperature $T (t)$ of a body at time $t = 0$ is $16 0^{\circ} F$ and it decreases continuously as per the differential equation $\frac{d T}{d t} = - K (T - 80)$ , where $K$ is a positive constant. If $T (15) = 12 0^{\circ} F$ , then…
Mathematics · Differential Equations · MCQ
Q43.If the function $f : (- \infty, - 1] \to (a, b]$ defined by $f (x) = e^{x^{3} - 3 x + 1}$ is one - one and onto, then the distance of the point $P (2 b + 4, a + 2)$ from the line $x + e^{- 3} y = 4$ is :
Mathematics · Application of Derivatives · MCQ
Q44.Let $2^{nd}, 8^{th}$ and $4 4^{th}$ terms of a non-constant A. P. be respectively the $1^{st}, 2^{nd}$ and $3^{rd}$ terms of a G. P. If the first term of the A. P. is 1, then the sum of…
Mathematics · Sequences and Series · MCQ
Q45.Let $z_{1}$ and $z_{2}$ be two complex numbers such that $z_{1} + z_{2} = 5$ and $z_{1}^{3} + z_{2}^{3} = 20 + 15 i$ Then, $z_{1}^{4} + z_{2}^{4}$ equals -
Mathematics · Complex Numbers · MCQ
Q46.If for some $m, n;^{6} C_{m} + 2 (^{6} C_{m + 1}) +^{6} C_{m + 2} >^{8} C_{3}$ and $^{n - 1} P_{3} :^{n} P_{4} = 1 : 8$ , then $^{n} P_{m + 1} +^{n + 1} C_{m}$ is equal to
Mathematics · Permutations and Combinations · MCQ
Q47.Consider the function $f : (0, \infty) \to R$ defined by $f (x) = e^{- ∣ l o g_{e} x ∣}$ . If $m$ and $n$ be respectively the number of points at which $f$ is not continuous and $f$ is not differentiable, then $m + n$ is
Mathematics · Limits Continuity and Differentiability · MCQ
Q48.Let a variable line passing through the centre of the circle $x^{2} + y^{2} - 16 x - 4 y = 0$ , meet the positive co-ordinate axes at the points $A$ and $B$ . Then the minimum value of $O A + O B$ , where $O$ is the origin, is equal to
Mathematics · Circle · MCQ
Q49.Let $A (a, b), B (3, 4)$ and $C (- 6, - 8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P (2 a + 3, 7 b + 5)$ from the line $2 x + 3 y - 4 = 0$ measured parallel to the line $x - 2 y - 1 = 0$ is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q50.Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be $55$ and $194$ , respectively. If $a > b$ , then $a + 3 b$ is
Mathematics · Statistics · MCQ
Q51.Let $a = 3 \hat{i} + 2 \hat{j} + \hat{k}, b = 2 \hat{i} - \hat{j} + 3 \hat{k}$ and $c$ be a vector such that $(a + b) \times c = 2 (a \times b) + 24 \hat{j} - 6 \hat{k}$ and $(a - b + \hat{i}) \cdot c = - 3$ …
Mathematics · Vector Algebra · Numerical
Q52.Let $y = y (x)$ be the solution of the differential equation $sec^{2} x d x + (e^{2 y} tan^{2} x + tan x) d y = 0, 0 < x < \frac{π}{2}, y (π /4) = 0$ . If $y (π /6) = α$ , then $e^{8 α}$ is equal to …
Mathematics · Differential Equations · Numerical
Q53. $\frac{120}{π ^{3}} 0 \int π \frac{x ^{2} s i n x c o s x}{s i n ^{4} x + c o s ^{4} x} d x$ is equal to .
Mathematics · Definite Integration · Numerical
Q54.Let $A (- 2, - 1), B (1, 0), C (α, β)$ and $D (γ, δ)$ be the vertices of a parallelogram $A B C D$ . If the point $C$ lies on $2 x - y = 5$ and the point $D$ lies on $3 x - 2 y = 6$ , then the value of $∣ α + β + γ + δ ∣$ is…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q55.Let $a, b, c$ be the lengths of three sides of a triangle satistying the condition $(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0$ . If the set of all possible values of $x$ is the interval $(α, β)$ , then $12 (α^{2} + β^{2})$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q56.If $lim_{x \to 0} \frac{a x ^{2} e ^{x} - b l o g _{e} ( 1 + x ) + c x e ^{- x}}{x ^{2} s i n x} = 1$ , then $16 (a^{2} + b^{2} + c^{2})$ is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q57.Let $A = {1, 2, 3, \dots\dots\dots\dots, 100}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2 x = 3 y$ . Let $R_{1}$ be a symmetric relation on $A$ such that $R \subset R_{1}$ and the number of elements in…
Mathematics · Sets and Relations · Numerical
Q58.Let the coefficient of $x^{r}$ in the expansion of $(x + 3)^{n - 1} + (x + 3)^{n - 2} (x + 2) + (x + 3)^{n - 3} (x + 2)^{2} + \dots\dots\dots . + (x + 2)^{n - 1}$ be $α_{r}$ . If $\sum_{r = 0}^{n} α_{r} = β^{n} - γ^{n}, β, γ \in N$ , then the…
Mathematics · Binomial Theorem · Numerical
Q59.Let A be a $3 \times 3$ matrix and $det (A) = 2$ . If $n = det (2024 - times adj (adj (\dots .. (adj A))))$ , then the remainder when $n$ is divided…
Mathematics · Matrices and Determinants · Numerical
Q60.A line passes through $A (4, - 6, - 2)$ and $B (16, - 2, 4)$ . The point $P (a, b, c)$ , where $a, b, c$ are non-negative integers, on the line $A B$ lies at a distance of 21 units, from the point $A$ . The distance between the points $P (a, b, c)$ and $Q (4, - 12, 3)$ …
Mathematics · 3D Geometry · Numerical
Q61.Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface,…
Physics · Electromagnetic Waves · MCQ
Q62.Consider two physical quantities $A$ and $B$ related to each other as $E = \frac{B - x ^{2}}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
Physics · Units and Measurements · MCQ
Q63.In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons…
Physics · Dual Nature of Radiation · MCQ
Q64.The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :
Physics · Atoms and Nuclei · MCQ
Q65.A uniform magnetic field of $2 \times 1 0^{- 3} T$ acts along positive $Y$ -direction. A rectangular loop of sides $20 cm$ and $10 cm$ with current of $5 A$ is in $Y - Z$ plane. The current is in…
Physics · Magnetics · MCQ
Q66.A block of mass $5 kg$ is placed on a rough inclined surface as shown in the figure. If $F_{1}$ is the force required to just move the block up the inclined plane and $F_{2}$ is the force required to… Includes diagram
Physics · Laws of Motion · MCQ
Q67.If two vectors $A$ and $B$ having equal magnitude $R$ are inclined at angle $θ$ , then
Physics · Vector Algebra · MCQ
Q68.By what percentage will the illumination of the lamp decrease if the current drops by 20%?
Physics · Current Electricity · MCQ
Q69.The speed of sound in oxygen at S.T.P. will be approximately: (given, $R = 8.3 JK^{- 1}, γ = 1.4$ )
Physics · Heat and Thermodynamics · MCQ
Q70.A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $g /8$ , then the ratio of masses is: Includes diagram
Physics · Laws of Motion · MCQ
Q71.A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:
Physics · Heat and Thermodynamics · MCQ
Q72.A small spherical ball of radius $r$ , falling through a viscous medium of negligible density has terminal velocity ' $v$ '. Another ball of the same mass but of radius $2 r$ , falling through the same viscous medium will have terminal…
Physics · Properties of Matter · MCQ
Q73.The measured value of the length of a simple pendulum is $20 cm$ with $2 mm$ accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the…
Physics · Units and Measurements · MCQ
Q74.When unpolarized light is incident at an angle of $6 0^{\circ}$ on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is:
Physics · Wave Optics · MCQ
Q75.The resistance per centimeter of a meter bridge wire is $r$ , with $X Ω$ resistance in left gap. Balancing length from left end is at $40 cm$ with $25Ω$ resistance in right gap. Now the wire is replaced by another wire…
Physics · Current Electricity · MCQ
Q76.Force between two point charges $q_{1}$ and $q_{2}$ placed in vacuum at ' $r$ ' cm apart is $F$ . Force between them when placed in a medium having dielectric constant $K = 5$ at ' $r /5$ ' $cm$ apart will be:
Physics · Electrostatics · MCQ
Q77.A body of mass $2 kg$ begins to move under the action of a time dependent force given by $F = (6 t \hat{i} + 6 t^{2} \hat{j}) N$ . The power developed by the force at the time $t$ is given by:
Physics · Work Power and Energy · MCQ
Q78.An AC voltage $V = 20 sin 200 π t$ is applied to a series LCR circuit which drives a current $I = 10 sin (200 π t + \frac{π}{3})$ . The average power dissipated is:
Physics · Alternating Current · MCQ
Q79.The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter is $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is $v$ , the escape velocity on the moon will be :
Physics · Gravitation · MCQ
Q80.The output of the given circuit diagram is - Includes diagram
Physics · Electronic Devices · MCQ
Q81.Two blocks of mass $2 kg$ and $4 kg$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 1 0^{- 5} m$ and Young's modulus of the metal is $2.0 \times 1 0^{11} N / m^{2}$ … Includes diagram
Physics · Properties of Matter · Numerical
Q82.A body of mass ' $m$ ' is projected with a speed ' $u$ ' making an angle of $4 5^{\circ}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{2 m u ^{3}}{X g}$ . The…
Physics · Rotational Motion · Numerical
Q83.In the following circuit, the battery has an emf of $2 V$ and an internal resistance of $\frac{2}{3} Ω$ . The power consumption in the entire circuit is W. Includes diagram
Physics · Current Electricity · Numerical
Q84.Two circular coils $P$ and $Q$ of 100 turns each have same radius of $π cm$ . The currents in $P$ and $R$ are $1 A$ and $2 A$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers…
Physics · Magnetics · Numerical
Q85.Two identical spheres each of mass $2 kg$ and radius $50 cm$ are fixed at the ends of a light rod so that the separation between the centers is $150 cm$ . Then, moment of inertia of the system about an axis…
Physics · Rotational Motion · Numerical
Q86.Light from a point source in air falls on a convex curved surface of radius $20 cm$ and refractive index 1.5. If the source is located at $100 cm$ from the convex surface, the image will be formed at …
Physics · Geometrical Optics · Numerical
Q87.A nucleus has mass number $A_{1}$ and volume $V_{1}$ . Another nucleus has mass number $A_{2}$ and Volume $V_{2}$ . If relation between mass number is $A_{2} = 4 A_{1}$ , then $\frac{V _{2}}{V _{1}} =$ .
Physics · Atoms and Nuclei · Numerical
Q88.The distance between charges $+ q$ and $- q$ is $2 l$ and between $+ 2 q$ and $- 2 q$ is $4 l$ . The electrostatic potential at point $P$ at a distance $r$ from center $O$ is $- α [\frac{q l}{r ^{2}}] \times 1 0^{9} V$ ,… Includes diagram
Physics · Electrostatics · Numerical
Q89.The magnetic flux $ϕ$ (in weber) linked with a closed circuit of resistance $8Ω$ varies with time (in seconds) as $ϕ = 5 t^{2} - 36 t + 1$ . The induced current in the circuit at $t = 2 s$ is A.
Physics · Electromagnetic Induction · Numerical
Q90.The time period of simple harmonic motion of mass $M$ in the given figure is $π \frac{α M}{5 k}$ , where the value of $α$ is . Includes diagram
Physics · Simple Harmonic Motion · Numerical