2024 · 8 Apr · Shift 1

90 questions · JEE Main

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2024 · 8 Apr · Shift 1

2024 · 8 Apr · Shift 1

90 questions · JEE Main

Chemistry30 questions Mathematics30 questions Physics30 questions

Q1.Combustion of glucose $(C_{6} H_{12} O_{6})$ produces $CO_{2}$ and water. The amount of oxygen (in $g$ ) required for the complete combustion of $900 g$ of glucose is : [Molar mass of glucose…
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q2.Thiosulphate reacts differently with iodine and bromine in the reactions given below: $2 S_{2} O_{3}^{2 -} + I_{2} \to S_{4} O_{6}^{2 -} + 2 I^{-} S_{2} O_{3}^{2 -} + 5 Br_{2} + 5 H_{2} O \to 2 SO_{4}^{2 -} + 4 Br^{-} + 10 H^{+}$ …
Chemistry · Redox Reactions · MCQ
Q3.Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: The stability order of +1 oxidation state of $Ga$ , In and $Tl$ is Ga Reason R: The inert pair effect…
Chemistry · P Block Elements · MCQ
Q4.Iron (III) catalyses the reaction between iodide and persulphate ions, in which A. $Fe^{3 +}$ oxidises the iodide ion B. $Fe^{3 +}$ oxidises the persulphate ion C. $Fe^{2 +}$ reduces the iodide ion D. $Fe^{2 +}$ …
Chemistry · D and F Block Elements · MCQ
Q5.Which of the following are aromatic? Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Among the following halogens $F_{2}, Cl_{2}, Br_{2} and I_{2}$ Which can undergo disproportionation reactions?
Chemistry · P Block Elements · MCQ
Q7.Which among the following compounds will undergo fastest $S N_{2}$ reaction.
Chemistry · Haloalkanes and Haloarenes · MCQ
Q8.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q9.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Periodic Table and Periodicity · MCQ
Q10.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Salt Analysis · MCQ
Q11.Number of Complexes with even number of electrons in $t_{2g}$ orbitals is - $[Fe (H_{2} O)_{6}]^{2 +}, [Co (H_{2} O)_{6}]^{2 +}, [Co (H_{2} O)_{6}]^{3 +}, [Cu (H_{2} O)_{6}]^{2 +}, [Cr (H_{2} O)_{6}]^{2 +}$ …
Chemistry · Coordination Compounds · MCQ
Q12.For the given hypothetical reactions, the equilibrium constants are as follows : $X ⇌ Y; K_{1} = 1.0 Y ⇌ Z; K_{2} = 2.0 Z ⇌ W; K_{3} = 4.0$ …
Chemistry · Chemical Equilibrium · MCQ
Q13.An octahedral complex with the formula $CoCl_{3} \cdot nNH_{3}$ upon reaction with excess of $AgNO_{3}$ solution gives 2 moles of $AgCl$ . Consider the oxidation state of $Co$ in the complex is ' $x$ '.…
Chemistry · Coordination Compounds · MCQ
Q14.In the given compound, the number of 2 $^{\circ}$ carbon atom/s is . Includes diagram
Chemistry · Hydrocarbons · MCQ
Q15.Identify the major products A and B respectively in the following set of reactions. Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q16.Identify the product (P) in the following reaction: Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q17.Given below are two statements : In the light of the above statements, choose the most appropriate answer from the options given below: Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q18.Given below are two statements: Statement I: $N (CH_{3})_{3}$ and $P (CH_{3})_{3}$ can act as ligands to form transition metal complexes. Statement II: As N and P are from same group, the…
Chemistry · Coordination Compounds · MCQ
Q19.The incorrect statement regarding the given structure is Includes diagram
Chemistry · Biomolecules · MCQ
Q20.Match List I with List II Choose the correct answer from the options given below: Includes table
Chemistry · Coordination Compounds · MCQ
Q21.If $279 g$ of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be g. (nearest integer) (consider complete conversion).
Chemistry · Compounds Containing Nitrogen · Numerical
Q22.Consider the following reaction $A + B \to C$ The time taken for A to become $1/ 4^{th}$ of its initial concentration is twice the time taken to become $1/2$ of the same. Also, when the change…
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q23.Major product B of the following reaction has $π$ -bond. Includes diagram
Chemistry · Hydrocarbons · Numerical
Q24.A hypothetical electromagnetic wave is show below. The frequency of the wave is $x \times 1 0^{19} Hz$ . $x =$ (nearest integer) Includes diagram
Chemistry · Structure of Atom · Numerical
Q25.Consider the figure provided. $1 mol$ of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at $1 8^{\circ} C$ . If the piston is moved to position $B$ , keeping the temperature unchanged,… Includes diagram
Chemistry · Thermodynamics · Numerical
Q26.A solution containing $10 g$ of an electrolyte $AB_{2}$ in $100 g$ of water boils at $100.5 2^{\circ} C$ . The degree of ionization of the electrolyte $(α)$ is $\times 1 0^{- 1}$ …
Chemistry · Solutions · Numerical
Q27.Number of molecules from the following which are exceptions to octet rule is . $CO_{2}, NO_{2}, H_{2} SO_{4}, BF_{3}, CH_{4}, SiF_{4}, ClO_{2}, PCl_{5}, BeF_{2}, C_{2} H_{6}, CHCl_{3}, CBr_{4}$ …
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q28.The number of optical isomers in following compound is : . Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q29.The 'spin only' magnetic moment value of $MO_{4}^{2 -}$ is BM. (Where M is a metal having least metallic radii. among $Sc, Ti, V, Cr, Mn$ and $Zn$ …
Chemistry · Coordination Compounds · Numerical
Q30.Number of amine compounds from the following giving solids which are soluble in $NaOH$ upon reaction with Hinsberg's reagent is . Includes diagram
Chemistry · Compounds Containing Nitrogen · Numerical
Q31.Let $A = 210 a 35 01 b$ . If $A^{3} = 4 A^{2} - A - 21 I$ , where $I$ is the identity matrix of order $3 \times 3$ , then $2 a + 3 b$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q32.The value of $k \in N$ for which the integral $I_{n} = \int_{0}^{1} (1 - x^{k})^{n} d x, n \in N$ , satisfies $147 I_{20} = 148 I_{21}$ is
Mathematics · Definite Integration · MCQ
Q33.Let $f (x) = 4 cos^{3} x + 33 cos^{2} x - 10$ . The number of points of local maxima of $f$ in interval $(0, 2 π)$ is
Mathematics · Application of Derivatives · MCQ
Q34.The set of all $α$ , for which the vectors $a = α t \hat{i} + 6 \hat{j} - 3 \hat{k}$ and $b = t \hat{i} - 2 \hat{j} - 2 α t \hat{k}$ are inclined at an obtuse angle for all $t \in R$ , is
Mathematics · Vector Algebra · MCQ
Q35.Let the circles $C_{1} : (x - α)^{2} + (y - β)^{2} = r_{1}^{2}$ and $C_{2} : (x - 8)^{2} + (y - \frac{15}{2})^{2} = r_{2}^{2}$ touch each other externally at the point $(6, 6)$ . If the point $(6, 6)$ divides the line segment joining the centres of the circles…
Mathematics · Circle · MCQ
Q36.Let $f (x)$ be a positive function such that the area bounded by $y = f (x), y = 0$ from $x = 0$ to $x = a > 0$ is $e^{- a} + 4 a^{2} + a - 1$ . Then the differential equation, whose general solution is $y = c_{1} f (x) + c_{2}$ , where $c_{1}$ and $c_{2}$ are arbitrary…
Mathematics · Differential Equations · MCQ
Q37.Let $H : \frac{- x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ be the hyperbola, whose eccentricity is $3$ and the length of the latus rectum is $43$ . Suppose the point $(α, 6), α > 0$ lies on $H$ . If $β$ is the product of the…
Mathematics · Hyperbola · MCQ
Q38.The number of critical points of the function $f (x) = (x - 2)^{2/3} (2 x + 1)$ is
Mathematics · Application of Derivatives · MCQ
Q39.Let $y = y (x)$ be the solution of the differential equation $(1 + y^{2}) e^{t a n x} d x + cos^{2} x (1 + e^{2 t a n x}) d y = 0, y (0) = 1$ . Then $y (\frac{π}{4})$ is equal to
Mathematics · Differential Equations · MCQ
Q40.Let the sum of two positive integers be 24 . If the probability, that their product is not less than $\frac{3}{4}$ times their greatest possible product, is $\frac{m}{n}$ , where $gcd (m, n) = 1$ , then $n$ - $m$ equals
Mathematics · Probability · MCQ
Q41.For the function $f (x) = (cos x) - x + 1, x \in R$ , between the following two statements (S1) $f (x) = 0$ for only one value of $x$ in $[0, π]$ . (S2) $f (x)$ is decreasing in $[0, \frac{π}{2}]$ and increasing in $[\frac{π}{2}, π]$ …
Mathematics · Application of Derivatives · MCQ
Q42.Let $P (x, y, z)$ be a point in the first octant, whose projection in the $x y$ -plane is the point $Q$ . Let $O P = γ$ ; the angle between $O Q$ and the positive $x$ -axis be $θ$ ; and the angle between $O P$ and the positive $z$ -axis…
Mathematics · 3D Geometry · MCQ
Q43.Let $z$ be a complex number such that $∣ z + 2∣ = 1$ and $lm (\frac{z + 1}{z + 2}) = \frac{1}{5}$ . Then the value of $∣ Re (\overline{z + 2}) ∣$ is
Mathematics · Complex Numbers · MCQ
Q44.The sum of all the solutions of the equation $(8)^{2 x} - 16 \cdot (8)^{x} + 48 = 0$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q45.The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4 x + y = 14$ and $3 x - 2 y = 5$ , respectively. The point $(2, - \frac{4}{3})$ divides the third side $BC$ internally in the ratio $2 : 1$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q46.If $sin x = - \frac{3}{5}$ , where $π < x < \frac{3 π}{2}$ , then $80 (tan^{2} x - cos x)$ is equal to
Mathematics · Trigonometric Ratio and Identites · MCQ
Q47.Let $[t]$ be the greatest integer less than or equal to $t$ . Let $A$ be the set of all prime factors of 2310 and $f : A \to Z$ be the function $f (x) = [lo g_{2} (x^{2} + [\frac{x ^{3}}{5}])]$ . The…
Mathematics · Permutations and Combinations · MCQ
Q48.If the set $R = {(a, b) : a + 5 b = 42, a, b \in N}$ has $m$ elements and $\sum_{n = 1}^{m} (1 - i^{n!}) = x + i y$ , where $i = - 1$ , then the value of $m + x + y$ is
Mathematics · Complex Numbers · MCQ
Q49.If the shortest distance between the lines $L_{1} : r = (2 + λ) \hat{i} + (1 - 3 λ) \hat{j} + (3 + 4 λ) \hat{k}, L_{2} : r = 2 (1 + μ) \hat{i} + 3 (1 + μ) \hat{j} + (5 + μ) \hat{k}, λ \in R μ \in R$ …
Mathematics · 3D Geometry · MCQ
Q50.Let $I (x) = \int \frac{6}{s i n ^{2} x ( 1 - c o t x ) ^{2}} d x$ . If $I (0) = 3$ , then $I (\frac{π}{12})$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q51.If the orthocentre of the triangle formed by the lines $2 x + 3 y - 1 = 0, x + 2 y - 1 = 0$ and $a x + b y - 1 = 0$ , is the centroid of another triangle, whose circumcentre and orthocentre respectively are $(3, 4)$ and $(- 6, - 8)$ , then the value of $∣ a - b ∣$ is…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q52.If the range of $f (θ) = \frac{s i n ^{4} θ + 3 c o s ^{2} θ}{s i n ^{4} θ + c o s ^{2} θ}, θ \in R$ is $[α, β]$ , then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{α}{β}$ …
Mathematics · Functions · Numerical
Q53.Let $a = 9 \hat{i} - 13 \hat{j} + 25 \hat{k}, b = 3 \hat{i} + 7 \hat{j} - 13 \hat{k}$ and $c = 17 \hat{i} - 2 \hat{j} + \hat{k}$ be three given vectors. If $r$ is a vector such that $r \times a = (b + c) \times a$ …
Mathematics · Vector Algebra · Numerical
Q54.Let the positive integers be written in the form : If the $k^{th}$ row contains exactly $k$ numbers for every natural number $k$ , then the row in which the number 5310 will be, is . Includes diagram
Mathematics · Sequences and Series · Numerical
Q55.The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to .
Mathematics · Permutations and Combinations · Numerical
Q56.Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\overset{ˉ}{X}$ and $\overset{ˉ}{Y}$ are the means of $X$ and $Y$ …
Mathematics · Probability · Numerical
Q57.Let $α = \sum_{r = 0}^{n} (4 r^{2} + 2 r + 1)^{n} C_{r}$ and $β = (\sum_{r = 0}^{n} \frac{^{n} C _{r}}{r + 1}) + \frac{1}{n + 1}$ . If $140 < \frac{2 α}{β} < 281$ , then the value of $n$ is .
Mathematics · Sequences and Series · Numerical
Q58.Let $A = [21 - 1 1]$ . If the sum of the diagonal elements of $A^{13}$ is $3^{n}$ , then $n$ is equal to .
Mathematics · Matrices and Determinants · Numerical
Q59.Let the area of the region enclosed by the curve $y = min {sin x, cos x}$ and the $x$ axis between $x = - π$ to $x = π$ be $A$ . Then $A^{2}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q60.The value of $lim_{x \to 0} 2 (\frac{1 - c o s x c o s 2 x 3 c o s 3 x \dots\dots . 10 c o s 10 x}{x ^{2}})$ is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q61.A stationary particle breaks into two parts of masses $m_{A}$ and $m_{B}$ which move with velocities $v_{A}$ and $v_{B}$ respectively. The ratio of their kinetic energies $(K_{B} : K_{A})$ is :
Physics · Center of Mass · MCQ
Q62.Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
Physics · Electrostatics · MCQ
Q63.Two planets $A$ and $B$ having masses $m_{1}$ and $m_{2}$ move around the sun in circular orbits of $r_{1}$ and $r_{2}$ radii respectively. If angular momentum of $A$ is $L$ and that of $B$ is $3 L$ , the ratio of time period $(\frac{T _{A}}{T _{B}})$ …
Physics · Gravitation · MCQ
Q64.Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 1 0^{- 4} N$ . If $360 W / cm^{2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:
Physics · Electromagnetic Waves · MCQ
Q65.In an expression $a \times 1 0^{b}$ :
Physics · Units and Measurements · MCQ
Q66.A clock has $75 cm, 60 cm$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly…
Physics · Circular Motion · MCQ
Q67.The output $Y$ of following circuit for given inputs is : Includes diagram
Physics · Electronic Devices · MCQ
Q68.A player caught a cricket ball of mass $150 g$ moving at a speed of $20 m / s$ . If the catching process is completed in $0.1 s$ , the magnitude of force exerted by the ball on the hand of the player is:
Physics · Laws of Motion · MCQ
Q69.Three bodies A, B and C have equal kinetic energies and their masses are $400 g, 1.2 kg$ and $1.6 kg$ respectively. The ratio of their linear momenta is :
Physics · Work Power and Energy · MCQ
Q70.Young's modulus is determined by the equation given by $Y = 49000 \frac{m}{l} \frac{dyne}{cm ^{2}}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young…
Physics · Properties of Matter · MCQ
Q71.Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field…
Physics · Magnetic Properties of Matter · MCQ
Q72.A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $(2 7^{\circ} C)$ . The ratio of specific heat of gases at constant volume respectively is:
Physics · Heat and Thermodynamics · MCQ
Q73.A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:
Physics · Alternating Current · MCQ
Q74.The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1 mm$ . The main scale reading is $2 cm$ …
Physics · Units and Measurements · MCQ
Q75.Critical angle of incidence for a pair of optical media is $4 5^{\circ}$ . The refractive indices of first and second media are in the ratio:
Physics · Geometrical Optics · MCQ
Q76.A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h = 6.63 $\times 1 0^{- 34} J s, m_{e} = 9.0 \times 1 0^{- 31} kg$ and $m_{p} = 1836$ …
Physics · Dual Nature of Radiation · MCQ
Q77.Correct Bernoulli's equation is (symbols have their usual meaning) :
Physics · Properties of Matter · MCQ
Q78.Binding energy of a certain nucleus is $18 \times 1 0^{8} J$ . How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:
Physics · Atoms and Nuclei · MCQ
Q79.In the given circuit, the terminal potential difference of the cell is : Includes diagram
Physics · Current Electricity · MCQ
Q80.Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V _{a}}{V _{d}}$ and the ratio $\frac{V _{b}}{V _{c}}$ is: Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q81.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $(\frac{a - 1}{a})$ then the value of $a$ is .
Physics · Waves · Numerical
Q82.An electric field, $E = \frac{2 i ^ + 6 j ^ + 8 k ^}{6}$ passes through the surface of $4 m^{2}$ area having unit vector $\overset{n}{^} = (\frac{2 i ^ + j ^ + k ^}{6})$ .…
Physics · Electrostatics · Numerical
Q83.Three vectors $OP, OQ$ and $OR$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A x$ . The… Includes diagram
Physics · Vector Algebra · Numerical
Q84.A square loop PQRS having 10 turns, area $3.6 \times 1 0^{- 3} m^{2}$ and resistance $100Ω$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B = 0.5 T$ as shown. Work done in… Includes diagram
Physics · Magnetics · Numerical
Q85.A liquid column of height $0.04 cm$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 1 0^{3} kg m^{- 3}$ and surface tension of soap solution is $0.28 Nm^{- 1}$ …
Physics · Properties of Matter · Numerical
Q86.A uniform thin metal plate of mass $10 kg$ with dimensions is shown. The ratio of $x$ and y coordinates of center of mass of plate in $\frac{n}{9}$ . The value of $n$ is . Includes diagram
Physics · Center of Mass · Numerical
Q87.Resistance of a wire at $0^{\circ} C, 10 0^{\circ} C$ and $t^{\circ} C$ is found to be $10Ω, 10.2Ω$ and $10.95Ω$ respectively. The temperature $t$ in Kelvin scale is .
Physics · Current Electricity · Numerical
Q88.A parallel beam of monochromatic light of wavelength $600 nm$ passes through single slit of $0.4 mm$ width. Angular divergence corresponding to second order minima would be $\times 1 0^{- 3} rad$ …
Physics · Wave Optics · Numerical
Q89.An electron with kinetic energy $5 eV$ enters a region of uniform magnetic field of 3 $μ T$ perpendicular to its direction. An electric field $E$ is applied perpendicular to the direction of velocity and…
Physics · Magnetics · Numerical
Q90.In an alpha particle scattering experiment distance of closest approach for the $α$ particle is $4.5 \times 1 0^{- 14} m$ . If target nucleus has atomic number 80 , then maximum velocity of $α$ -particle is $\times 1 0^{5} m / s$ …
Physics · Atoms and Nuclei · Numerical