2024 · 1 Feb · Shift 1

90 questions · JEE Main

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2024 · 1 Feb · Shift 1

2024 · 1 Feb · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Which of the following reactions are disproportionation reactions? (A) $Cu^{+} \to Cu^{2 +} + Cu$ (B) $3 MnO_{4}^{2 -} + 4 H^{+} ⟶ 2 MnO_{4}^{-} + MnO_{2} + 2 H_{2} O$ …
Chemistry · Redox Reactions · MCQ
Q2.Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :
Chemistry · Thermodynamics · MCQ
Q3.Identify $A$ and $B$ in the following sequence of reaction Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q4.Which of the following complex is homoleptic?
Chemistry · Coordination Compounds · MCQ
Q5.In Kjeldahl's method for estimation of nitrogen, $CuSO_{4}$ acts as :
Chemistry · Practical Organic Chemistry · MCQ
Q6.Given below are two statements : Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution. Statement (II) : In this titration phenolphthalein can be used as indicator. In the light…
Chemistry · Practical Organic Chemistry · MCQ
Q7.In case of isoelectronic species the size of $F^{-}, Ne$ and $Na^{+}$ is affected by :
Chemistry · Structure of Atom · MCQ
Q8.Ionic reactions with organic compounds proceed through : (A) homolytic bond cleavage (B) heterolytic bond cleavage (C) free radical formation (D) primary free radical (E) secondary free radical Choose the correct answer from the options…
Chemistry · Basics of Organic Chemistry · MCQ
Q9.Which of the following compound will most easily be attacked by an electrophile?
Chemistry · Basics of Organic Chemistry · MCQ
Q10.Given below are two statements : Statement (I) : A solution of $[Ni (H_{2} O)_{6}]^{2 +}$ is green in colour. Statement (II) : A solution of $[Ni (CN)_{4}]^{2 -}$ is…
Chemistry · Coordination Compounds · MCQ
Q11.We have three aqueous solutions of $NaCl$ labelled as ' $A$ ', ' $B$ ' and ' $C$ ' with concentration $0.1 M$ , $0.01 M$ and $0.001 M$ , respectively. The value of van 't Hoff…
Chemistry · Solutions · MCQ
Q12.Given below are two statements : Statement (I) : The $NH_{2}$ group in Aniline is ortho and para directing and a powerful activating group. Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and…
Chemistry · Compounds Containing Nitrogen · MCQ
Q13.According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron $(λ)$ and momentum of electron $(p)$ ?
Chemistry · Structure of Atom · MCQ
Q14.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): $PH_{3}$ has lower boiling point than $NH_{3}$ . Reason (R) : In liquid state $NH_{3}$ molecules…
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q15.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with $AgCN$ form isocyanide as…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q16.If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is :
Chemistry · Biomolecules · MCQ
Q17.In acidic medium, $K_{2} Cr_{2} O_{7}$ shows oxidising action as represented in the half reaction: $Cr_{2} O_{7}^{2 -} + XH^{+} + Ye^{⊖} \to 2 A + ZH_{2} O$ …
Chemistry · Redox Reactions · MCQ
Q18.Given below are two statements : Statement (I) : Aminobenzene and aniline are same organic compounds. Statement (II) : Aminobenzene and aniline are different organic compounds. In the light of the above statements, choose the most…
Chemistry · Compounds Containing Nitrogen · MCQ
Q19.Match List - I with List - II. Choose the correct answer from the options given below : Includes table Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q20.Arrange the bonds in order of increasing ionic character in the molecules. $LiF$ , $K_{2} O, N_{2}, SO_{2}$ and $ClF_{3}$ :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q21.The number of white coloured salts, among the following is (a) $SrSO_{4}$ (b) $Mg (NH_{4}) PO_{4}$ (c) $BaCrO_{4}$ (d) $Mn (OH)_{2}$ (e) $PbSO_{4}$ (f) $PbCrO_{4}$ (g) $AgBr$ …
Chemistry · P Block Elements · Numerical
Q22.Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is . Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q23.The potential for the given half cell at $298 K$ is (-) $\times 1 0^{- 2} V$ $2 H_{(aq)}^{+} + 2 e^{-} ⟶ H_{2} (g) [H^{+}] = 1 M, P_{H_{2}} = 2 atm$ …
Chemistry · Electrochemistry · Numerical
Q24.Among the following oxides of p-block elements, number of oxides having amphoteric nature is . $Cl_{2} O_{7}, CO, PbO_{2}, N_{2} O, NO, Al_{2} O_{3}, SiO_{2}, N_{2} O_{5}, SnO_{2}$ …
Chemistry · P Block Elements · Numerical
Q25.Consider the following reaction : $3 PbCl_{2} + 2 (NH_{4})_{3} PO_{4} \to Pb_{3} (PO_{4})_{2} + 6 NH_{4} Cl$ If $72 mmol$ of $PbCl_{2}$ is mixed with…
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q26.The number of molecules/ion/s having trigonal bipyramidal shape is . $PF_{5}, BrF_{5}, PCl_{5}, [Pt Cl_{4}]^{2 -}, BF_{3}, Fe (CO)_{5}$
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q27.The lowest oxidation number of an atom in a compound $A_{2} B$ is -2 . The number of electrons in its valence shell is .
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q28. $K_{a}$ for $CH_{3} COOH$ is $1.8 \times 1 0^{- 5}$ and $K_{b}$ for $NH_{4} OH$ is $1.8 \times 1 0^{- 5}$ . The $pH$ of ammonium acetate solution will be …
Chemistry · Ionic Equilibrium · Numerical
Q29.Number of optical isomers possible for 2-chlorobutane .
Chemistry · Basics of Organic Chemistry · Numerical
Q30.The ratio of $\frac{^{14} C}{^{12} C}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of $^{14} C$ is 5730 years, the age of wood sample is years.
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q31.A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of…
Mathematics · Probability · MCQ
Q32.The value of the integral $0 \int π /4 \frac{x d x}{s i n ^{4} ( 2 x ) + c o s ^{4} ( 2 x )}$ equals :
Mathematics · Definite Integration · MCQ
Q33.If $A = [2 - 1 12], B = [1101], C = ABA^{T}$ and $X = A^{T} C^{2} A$ …
Mathematics · Matrices and Determinants · MCQ
Q34.If $tan A = \frac{1}{x ( x ^{2} + x + 1 )}, tan B = \frac{x}{x ^{2} + x + 1}$ and $tan C = (x^{- 3} + x^{- 2} + x^{- 1})^{1/2}, 0 < A, B, C < \frac{π}{2}$ , then $A + B$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35.If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q36.Let $S = ∣ z \in C : ∣ z - 1 ∣= 1$ and $(2 - 1) (z + \overset{z}{ˉ}) - i (z - \overset{z}{ˉ}) = 22 ∣$ . Let $z_{1}, z_{2} \in S$ be such that $∣ z_{1} ∣ = z \in s max ∣ z ∣$ and $∣ z_{2} ∣ = z \in S min ∣ z ∣$ …
Mathematics · Complex Numbers · MCQ
Q37.Let the median and the mean deviation about the median of 7 observation $170, 125, 230, 190, 210$ , a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :
Mathematics · Statistics · MCQ
Q38.Let $a = - 5 \hat{i} + \hat{j} - 3 \hat{k}, b = \hat{i} + 2 \hat{j} - 4 \hat{k}$ and $c = (((a \times b) \times \hat{i}) \times \hat{i}) \times \hat{i}$ …
Mathematics · Vector Algebra · MCQ
Q39.Let $S = {x \in R : (3 + 2)^{x} + (3 - 2)^{x} = 10}$ . Then the number of elements in $S$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q40.The area enclosed by the curves $x y + 4 y = 16$ and $x + y = 6$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q41.Let $f : R \to R$ and $g : R \to R$ be defined as $f (x) = {lo g_{e} x, e^{- x}, x > 0 x \leq 0$ and $g (x) = {x, e^{x}, x ⩾ 0 x < 0$ …
Mathematics · Functions · MCQ
Q42.If the system of equations $2 x + 3 y - z = 5 x + α y + 3 z = - 4 3 x - y + β z = 7$ has infinitely many solutions, then $13 α β$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q43.For $0 < θ < π /2$ , if the eccentricity of the hyperbola $x^{2} - y^{2} cosec^{2} θ = 5$ is $7$ times eccentricity of the ellipse $x^{2} cosec^{2} θ + y^{2} = 5$ , then the value of $θ$ is :
Mathematics · Hyperbola · MCQ
Q44.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = 2 x (x + y)^{3} - x (x + y) - 1, y (0) = 1$ . Then, $(\frac{1}{2} + y (\frac{1}{2}))^{2}$ equals :
Mathematics · Differential Equations · MCQ
Q45.Let $f : R \to R$ be defined as : $f (x) = {\frac{a - b c o s 2 x}{x ^{2}}; x 1$ If $f$ is continuous everywhere in $R$ and $m$ is the number of points where $f$ is NOT differential…
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.Let $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ be an ellipse, whose eccentricity is $\frac{1}{2}$ and the length of the latusrectum is $14$ . Then the square of the eccentricity of $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ …
Mathematics · Ellipse · MCQ
Q47.Let $3, a, b, c$ be in A.P. and $3, a - 1, b + 1, c + 9$ be in G.P. Then, the arithmetic mean of $a, b$ and $c$ is :
Mathematics · Sequences and Series · MCQ
Q48.Let $C : x^{2} + y^{2} = 4$ and $C^{'} : x^{2} + y^{2} - 4 λ x + 9 = 0$ be two circles. If the set of all values of $λ$ so that the circles $C$ and $C$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a},…
Mathematics · Circle · MCQ
Q49.If $5 f (x) + 4 f (\frac{1}{x}) = x^{2} - 2, \forall x e q 0$ and $y = 9 x^{2} f (x)$ , then $y$ is strictly increasing in :
Mathematics · Application of Derivatives · MCQ
Q50.If the shortest distance between the lines $\frac{x - λ}{- 2} = \frac{y - 2}{1} = \frac{z - 1}{1}$ and $\frac{x - 3}{1} = \frac{y - 1}{- 2} = \frac{z - 2}{1}$ is 1 , then the sum of all possible values of $λ$ is :
Mathematics · 3D Geometry · MCQ
Q51.If $x = x (t)$ is the solution of the differential equation $(t + 1) d x = (2 x + (t + 1)^{4}) dt, x (0) = 2$ , then, $x (1)$ equals .
Mathematics · Differential Equations · Numerical
Q52.The number of elements in the set $S = {(x, y, z) : x, y, z \in Z, x + 2 y + 3 z = 42, x, y, z ⩾ 0}$ equals .
Mathematics · Permutations and Combinations · Numerical
Q53.If the Coefficient of $x^{30}$ in the expansion of $(1 + \frac{1}{x})^{6} (1 + x^{2})^{7} (1 - x^{3})^{8}; x e q 0$ is $α$ , then $∣ α ∣$ equals .
Mathematics · Binomial Theorem · Numerical
Q54.Let $3, 7, 11, 15, \dots, 403$ and $2, 5, 8, 11, \dots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to .
Mathematics · Sequences and Series · Numerical
Q55.Let ${x}$ denote the fractional part of $x$ and $f (x) = \frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, x e q 0$ . If $L$ and $R$ respectively denotes the left hand limit and the right hand limit…
Mathematics · Limits Continuity and Differentiability · Numerical
Q56.Let the line $L : 2 x + y = α$ pass through the point of the intersection $P$ (in the first quadrant) of the circle $x^{2} + y^{2} = 3$ and the parabola $x^{2} = 2 y$ . Let the line $L$ touch two circles $C_{1}$ …
Mathematics · Parabola · Numerical
Q57.Let $P = {z \in C : ∣ z + 2 - 3 i ∣ \leq 1}$ and $Q = {z \in C : z (1 + i) + \overset{z}{ˉ} (1 - i) \leq - 8}$ . Let in $P \cap Q$ , $∣ z - 3 + 2 i ∣$ be maximum and minimum at $z_{1}$ and $z_{2}$ …
Mathematics · Complex Numbers · Numerical
Q58.If $- π /2 \int π /2 \frac{8 2 c o s x d x}{( 1 + e ^{s i n x} ) ( 1 + s i n ^{4} x )} = α π + β lo g_{e} (3 + 22)$ , where $α, β$ are integers, then $α^{2} + β^{2}$ …
Mathematics · Definite Integration · Numerical
Q59.Let the line of the shortest distance between the lines $L_{1} : r = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}) and L_{2} : r = (4 \hat{i} + 5 \hat{j} + 6 \hat{k}) + μ (\hat{i} + \hat{j} - \hat{k})$ …
Mathematics · 3D Geometry · Numerical
Q60.Let $A = {1, 2, 3, \dots, 20}$ . Let $R_{1}$ and $R_{2}$ two relation on $A$ such that $R_{1} = {(a, b) : b$ is divisible by $a} R_{2} = {(a, b) : a$ is an integral multiple of $b}$ . Then, number of elements in $R_{1} - R_{2}$ is equal to …
Mathematics · Sets and Relations · Numerical
Q61.Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in $ms^{- 2}$ is : (Consider that the string is massless… Includes diagram
Physics · Laws of Motion · MCQ
Q62.If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = π^{2} m / s^{2}$ , then the length of the second's pendulum at a height $h = 2 R$ from the surface of earth…
Physics · Gravitation · MCQ
Q63.10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :
Physics · Units and Measurements · MCQ
Q64.Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :
Physics · Heat and Thermodynamics · MCQ
Q65.The dimensional formula of angular impulse is :
Physics · Units and Measurements · MCQ
Q66.A monochromatic light of wavelength $6000 \overset{˚}{A}$ is incident on the single slit of width $0.01 mm$ . If the diffraction pattern is formed at the focus of the convex lens of focal length $20 cm$ , the linear width…
Physics · Wave Optics · MCQ
Q67.A ball of mass $0.5 kg$ is attached to a string of length $50 cm$ . The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 N$ . The…
Physics · Circular Motion · MCQ
Q68.The reading in the ideal voltmeter $(V)$ shown in the given circuit diagram is : Includes diagram
Physics · Current Electricity · MCQ
Q69.A galvanometer has a resistance of $50 Ω$ and it allows maximum current of $5 mA$ . It can be converted into voltmeter to measure upto $100 V$ by connecting in series a resistor of resistance :
Physics · Current Electricity · MCQ
Q70.The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :
Physics · Atoms and Nuclei · MCQ
Q71.A parallel plate capacitor has a capacitance $C = 200 pF$ . It is connected to $230 V$ ac supply with an angular frequency $300 rad / s$ . The rms value of conduction current in the circuit and…
Physics · Alternating Current · MCQ
Q72.The de Broglie wavelengths of a proton and an $α$ particle are $λ$ and $2 λ$ respectively. The ratio of the velocities of proton and $α$ particle will be :
Physics · Dual Nature of Radiation · MCQ
Q73.The radius $(r)$ , length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as $r = (0.35 \pm 0.05) cm R = (100 \pm 10) ohm l = (15 \pm 0.2) cm$ …
Physics · Units and Measurements · MCQ
Q74.Two identical capacitors have same capacitance $C$ . One of them is charged to the potential $V$ and other to the potential $2 V$ . The negative ends of both are connected together. When the positive ends are also joined together,…
Physics · Capacitor · MCQ
Q75.A simple pendulum of length $1 m$ has a wooden bob of mass $1 kg$ . It is struck by a bullet of mass $1 0^{- 2} kg$ moving with a speed of $2 \times 1 0^{2} ms^{- 1}$ . The bullet gets embedded into the bob.…
Physics · Simple Harmonic Motion · MCQ
Q76.The pressure and volume of an ideal gas are related as $PV^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is :
Physics · Heat and Thermodynamics · MCQ
Q77.In series LCR circuit, the capacitance is changed from $C$ to $4 C$ . To keep the resonance frequency unchanged, the new inductance should be:
Physics · Alternating Current · MCQ
Q78.A particle moving in a circle of radius $R$ with uniform speed takes time $T$ to complete one revolution. If this particle is projected with the same speed at an angle $θ$ to the horizontal, the maximum height…
Physics · Circular Motion · MCQ
Q79.With rise in temperature, the Young's modulus of elasticity :
Physics · Properties of Matter · MCQ
Q80.In the given circuit if the power rating of Zener diode is $10 mW$ , the value of series resistance $R_{s}$ to regulate the input unregulated supply is : Includes diagram
Physics · Electronic Devices · MCQ
Q81.A rectangular loop of sides $12 cm$ and $5 cm$ , with its sides parallel to the $x$ -axis and $y$ -axis respectively, moves with a velocity of $5 cm / s$ in the positive $x$ axis direction, in a space…
Physics · Electromagnetic Induction · Numerical
Q82.A plane is in level flight at constant speed and each of its two wings has an area of $40 m^{2}$ . If the speed of the air is $180 km / h$ over the lower wing surface and $252 km / h$ over the…
Physics · Properties of Matter · Numerical
Q83.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $θ$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 g / cc$ …
Physics · Electrostatics · Numerical
Q84.A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 m$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16…
Physics · Motion in A Straight Line · Numerical
Q85.The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$ , where $x$ is .
Physics · Atoms and Nuclei · Numerical
Q86.A regular polygon of 6 sides is formed by bending a wire of length $4 π$ meter. If an electric current of $4 π 3$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 1 0^{- 7} T$ …
Physics · Magnetics · Numerical
Q87.The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20 cm$ . The focal length of the lens used is $cm$ .
Physics · Geometrical Optics · Numerical
Q88.Three identical spheres each of mass $2 M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 m$ each. Taking point of intersection of these two sides as origin, the…
Physics · Center of Mass · Numerical
Q89.A tuning fork resonates with a sonometer wire of length $1 m$ stretched with a tension of $6 N$ . When the tension in the wire is changed to $54 N$ , the same tuning fork produces 12 beats per second with it.…
Physics · Waves · Numerical
Q90.The current in a conductor is expressed as $I = 3 t^{2} + 4 t^{3}$ , where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 s$ to $t = 2 s$ is …
Physics · Current Electricity · Numerical