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2010 · Shift 1

84 questions · JEE Advanced

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2010 · Shift 1

2010 · Shift 1

84 questions · JEE Advanced

Chemistry28 questions Mathematics28 questions Physics28 questions

Chemical Bonding and Molecular StructureChemistry · 1 questions ThermodynamicsChemistry · 3 questions Ionic EquilibriumChemistry · 2 questions HydrogenChemistry · 1 questions Basics of Organic ChemistryChemistry · 2 questions HydrocarbonsChemistry · 1 questions ElectrochemistryChemistry · 2 questions Chemical Kinetics and Nuclear ChemistryChemistry · 3 questions Some Basic Concepts of ChemistryChemistry · 1 questions BiomoleculesChemistry · 2 questions Alcohols Phenols and EthersChemistry · 2 questions Coordination CompoundsChemistry · 2 questions Isolation of ElementsChemistry · 3 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 2 questions P Block ElementsChemistry · 1 questions Trigonometric Functions and EquationsMathematics · 3 questions Complex NumbersMathematics · 2 questions Quadratic Equation and InequalitiesMathematics · 1 questions Sequences and SeriesMathematics · 1 questions ParabolaMathematics · 1 questions HyperbolaMathematics · 3 questions Properties of TriangleMathematics · 2 questions Application of DerivativesMathematics · 1 questions 3D GeometryMathematics · 2 questions Vector AlgebraMathematics · 2 questions ProbabilityMathematics · 1 questions Definite IntegrationMathematics · 3 questions Application of IntegrationMathematics · 1 questions Matrices and DeterminantsMathematics · 4 questions FunctionsMathematics · 1 questions Simple Harmonic MotionPhysics · 4 questions Laws of MotionPhysics · 1 questions Impulse and MomentumPhysics · 1 questions GravitationPhysics · 3 questions Heat and ThermodynamicsPhysics · 4 questions ElectrostaticsPhysics · 1 questions Units and MeasurementsPhysics · 1 questions Current ElectricityPhysics · 4 questions Alternating CurrentPhysics · 1 questions MagnetismPhysics · 3 questions Geometrical OpticsPhysics · 2 questions WavesPhysics · 2 questions Dual Nature of RadiationPhysics · 1 questions

Q1.Based on VSEPR theory, the number of 90 degree F-Br-F angles in $B r F_{5}$ is
Chemistry · Chemical Bonding and Molecular Structure · Numerical
Q2.The species which by definition has ZERO standard molar enthalpy of formation at 298 K is
Chemistry · Thermodynamics · MCQ
Q3.Among the following, the intensive property is (properties are)
Chemistry · Thermodynamics · Multiple correct
Q4.Aqueous solution of $H N O_{3}$ , $K O H$ and $C H_{3} C O O H$ and $C H_{3} C O O N a$ of identical concentrations are provided. The pairs of solutions which form a buffer upon mixing is(are)
Chemistry · Ionic Equilibrium · Multiple correct
Q5.Amongst the following the total number of compounds whose aqueous solution turns red litmus paper blue is $K C N$ , $K_{2} S O_{4}$ , $(N H_{4})_{2} C_{2} O_{4}$ , $N a C l$ , $Z n (N O_{3})_{2}$ , $F e C l_{3}$ , $K_{2} C O_{3}$ , $N H_{4} N O_{3}$ and $L i C N$
Chemistry · Ionic Equilibrium · Numerical
Q6.The reagent(s) used for softening the temporary hardness of water is (are)
Chemistry · Hydrogen · Multiple correct
Q7.The total number of cyclic isomers possible for a hydrocarbon with the molecular formula $C_{4} H_{6}$ is
Chemistry · Basics of Organic Chemistry · Numerical
Q8.The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and and alkyne
Chemistry · Hydrocarbons · MCQ
Q9.The bond energy (in kcal mol-1) of a $C - C$ single bond is approximately
Chemistry · Thermodynamics · MCQ
Q10.The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and…
Chemistry · Electrochemistry · MCQ
Q11.The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and…
Chemistry · Electrochemistry · MCQ
Q12.The concentration of R in the reaction R $\to$ P was measured as a function of time and the following data is obtained The order of reaction is Includes table
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q13.The number of neutrons emitted when $_{92}^{235} U$ undergoes controlled nuclear fission to $_{54}^{142} X e$ and $_{38}^{90} S r$ is
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q14.A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q15.The correct statement about the following disaccharide is : Includes diagram
Chemistry · Biomolecules · MCQ
Q16.In the reaction the products are : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.Plots showing the variation of the rate constant ( $k$ ) with temperature ( $T$ ) are given below. The point that follows Arrhenius equation is
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q18.The correct structure of ethylenediaminetetraacetic acid (EDTA) is
Chemistry · Coordination Compounds · MCQ
Q19.The ionisation isomer of $[Cr (H_{2} O)_{4} Cl (N O_{2})] Cl$ is
Chemistry · Coordination Compounds · MCQ
Q20.In the Newman projection for 2,2-dimethylbutane, X and Y can, respectively, be Includes diagram
Chemistry · Basics of Organic Chemistry · Multiple correct
Q21.In the reaction The intermediate(s) is(are) Includes diagram
Chemistry · Alcohols Phenols and Ethers · Multiple correct
Q22.Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper inculcated chalcanthite (CuSO $_{4}$ . 5H $_{2}$ O), atacamite (Cu $_{2}$ Cl(OH) $_{3}$ ), cuprite (Cu $_{2}$ O),…
Chemistry · Isolation of Elements · MCQ
Q23.Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper inculcated chalcanthite (CuSO $_{4}$ . 5H $_{2}$ O), atacamite (Cu $_{2}$ Cl(OH) $_{3}$ ), cuprite (Cu $_{2}$ O),…
Chemistry · Isolation of Elements · MCQ
Q24.Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper inculcated chalcanthite (CuSO $_{4}$ . 5H $_{2}$ O), atacamite (Cu $_{2}$ Cl(OH) $_{3}$ ), cuprite (Cu $_{2}$ O),…
Chemistry · Isolation of Elements · MCQ
Q25.The total number of basic groups in the following form of lysine is Includes diagram
Chemistry · Biomolecules · Numerical
Q26.In the scheme given below, the total number of intra molecular aldol condensation products formed from Y is . Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q27.Amongst the following, the total number of compounds soluble in aqueous $N a O H$ is . Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Numerical
Q28.The value of $n$ in the molecular formula $B e_{n} A l_{2} S i_{6} O_{18}$ is .
Chemistry · P Block Elements · Numerical
Q29.The number of values of $θ$ in the interval, $(- \frac{π}{2}, \frac{π}{2})$ such that $θ e \frac{nπ}{5}$ for $n = 0, \pm 1, \pm 2$ and $tan θ = cot 5 θ$ as well as $sin 2 θ = cos 4 θ$ …
Mathematics · Trigonometric Functions and Equations · Numerical
Q30.The number of all possible values of $θ$ where $0 < θ < π,$ for which the system of equations $(y + z) cos 3 θ = (x y z) sin 3 θ x sin 3 θ = \frac{2 c o s 3 θ}{y} + \frac{2 s i n 3 θ}{z} (x y z) sin 3 θ = (y + 2 z) cos 3 θ + y s in 3 θ$ …
Mathematics · Trigonometric Functions and Equations · Numerical
Q31.The maximum value of the expression $\frac{1}{s i n ^{2} θ + 3 s i n θ c o s θ + 5 c o s ^{2} θ}$ is
Mathematics · Trigonometric Functions and Equations · Numerical
Q32.Let $z_{1}$ and $z_{2}$ be two distinct complex number and let z =( 1 - t) $z_{1}$ + t $z_{2}$ for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then
Mathematics · Complex Numbers · Multiple correct
Q33.Let $p$ and $q$ be real numbers such that $p e 0, p^{3} e q$ and $p^{3} e - q .$ If $p^{3} e - q .$ and $β$ are nonzero complex numbers satisfying $α + β = - p$ and $α^{3} + β^{3} = q,$ then a quadratic…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let $S_{k}$ = 1, 2,....., 100, denote the sum of the infinite geometric series whose first term is $\frac{k - 1}{k !}$ and the common ratio is $\frac{1}{k}$ . Then the value of $\frac{100 ^{2}}{100 !} + k = 1 \sum 100 (k^{2} - 3 k + 1) S_{k}$ …
Mathematics · Sequences and Series · Numerical
Q35.Let $A$ and $B$ be two distinct points on the parabola $y^{2} = 4 x$ . If the axis of the parabola touches a circle of radius $r$ having $A B$ as its diameter, then the slope of the line joining $A$ and $B$ can be
Mathematics · Parabola · Multiple correct
Q36.The circle $x^{2} + y^{2} - 8 x = 0$ and hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ intersect at the points $A$ and $B$ . Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
Mathematics · Hyperbola · MCQ
Q37.The circle $x^{2} + y^{2} - 8 x = 0$ and hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ intersect at the points $A$ and $B$ . Equation of the circle with $A B$ as its diameter is
Mathematics · Hyperbola · MCQ
Q38.The line $2 x + y = 1$ is tangent to the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ . If this line passes through the point of intersection of the nearest directrix and the $x$ -axis, then the eccentricity of the…
Mathematics · Hyperbola · Numerical
Q39.If the angles $C$ and $C$ of a triangle are in an arithmetic progression and if $c$ and $c$ denote the lengths of the sides opposite to $C$ and $C$ respectively, then the value of the expression $\frac{a}{c} sin 2 C + \frac{c}{a} sin 2 A$ …
Mathematics · Properties of Triangle · MCQ
Q40.Let $f$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f (1) = 1$ . If the $y$ -intercept of the tangent at any point $P (x, y)$ on the curve $y = f (x)$ is equal to the cube of the abscissa of $P$ , then find…
Mathematics · Application of Derivatives · Numerical
Q41.If the distance between the plane $A x - 2 y + z = d$ and the plane containing the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is $6,$ then $∣ d ∣$ …
Mathematics · 3D Geometry · Numerical
Q42.If $a$ and $b$ are vectors in space given by $a = \frac{i - 2 j}{5}$ and $b = \frac{2 i + j + 3 k}{14},$ …
Mathematics · Vector Algebra · Numerical
Q43.Equation of the plane containing the straight line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2}$ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3}$ …
Mathematics · 3D Geometry · MCQ
Q44.Let $P, Q, R$ and $S$ be the points on the plane with position vectors $- 2 i - j, 4 i, 3 i + 3 j$ and $- 3 i + 2 j$ respectively. The quadrilateral $P QR S$ must be a
Mathematics · Vector Algebra · MCQ
Q45.Let $ω$ be a complex cube root of unity with $ω e 1.$ A fair die is thrown three times. If $r_{1}, r_{2}$ and $r_{3}$ are the numbers obtained on the die, then the probability that $ω^{r_{1}} + ω^{r_{2}} + ω^{r_{3}} = 0$ …
Mathematics · Probability · MCQ
Q46.For any real number $x,$ let $x .$ denote the largest integer less than or equal to $x .$ Let $f$ be a real valued function defined on the interval $[- 10, 10]$ by $f (x) = {x - [x] 1 + [x] - x i f [x] i s o dd, i f [x] i s e v e n$ …
Mathematics · Definite Integration · Numerical
Q47.Let $f$ be a real-valued function defined on the interval $(0, \infty)$ by $f (x) = ln x + 0 \int x 1 + sin t d t .$ then which of the following statement(s) is (are) true?
Mathematics · Application of Integration · Multiple correct
Q48.The value of $0 \int 1 \frac{x ^{4} ( 1 - x ) ^{4}}{1 + x ^{2}} d x$ is (are)
Mathematics · Definite Integration · MCQ
Q49.The value of $x \to 0 lim \frac{1}{x ^{3}} 0 \int x \frac{t l n ( 1 + t )}{t ^{4} + 4} d t$ is
Mathematics · Definite Integration · MCQ
Q50.Let $A B C$ be a triangle such that $∠ A C B = \frac{π}{6}$ and let $c$ and $c$ denote the lengths of the sides opposite to $A$ , $B$ and $C$ respectively. The value(s) of $x$ for which $a = x^{2} + x + 1, b = x^{2} - 1$ …
Mathematics · Properties of Triangle · MCQ
Q51.The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system $A x y z = 100$ has exactly two distinct…
Mathematics · Matrices and Determinants · MCQ
Q52.Let $h$ and $h$ be real valued functions defined on the interval $[0, 1]$ by $f (x) = e^{x^{2}} + e^{- x^{2}}$ , $g (x) = x e^{x^{2}} + e^{- x^{2}}$ and $h (x) = x^{2} e^{x^{2}} + e^{- x^{2}}$ . If $c$ and $c$ denote, respectively, the absolute maximum of $h$ and $h$ …
Mathematics · Functions · MCQ
Q53.Let $z_{1}$ and $z_{2}$ be two distinct complex numbers let $z = (1 - t) z_{1} + t z_{2}$ for some real number t with $0 I f$ \operatorname{Arg}(w) $d e n o t es t h e p r in c i p a l a r g u m e n t o f an o n z er oco m pl e x n u mb er$ w$, then :
Mathematics · Complex Numbers · Multiple correct
Q54.Let $p$ be an odd prime number and $T_{p}$ be the following set of $2 \times 2$ matrices : $T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots, p - 1}}$ …
Mathematics · Matrices and Determinants · MCQ
Q55.Let $p$ be an odd prime number and $T_{p}$ be the following set of $2 \times 2$ matrices : $T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots, p - 1}}$ …
Mathematics · Matrices and Determinants · MCQ
Q56.Let $p$ be an odd prime number and $T_{p}$ be the following set of $2 \times 2$ matrices : $T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots, p - 1}}$ …
Mathematics · Matrices and Determinants · MCQ
Q57.A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its crosssectional area is 4.9 $\times$ 10-7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs…
Physics · Simple Harmonic Motion · Numerical
Q58.A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force… Includes diagram
Physics · Laws of Motion · MCQ
Q59.A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms−1. Which of the following statement(s) is (are) correct for the…
Physics · Impulse and Momentum · Multiple correct
Q60.A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular…
Physics · Gravitation · Numerical
Q61.Gravitational acceleration on the surface of a planet is $\frac{6}{11} g$ , where $g$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $\frac{2}{3}$ times that of the earth.…
Physics · Gravitation · Numerical
Q62.A real gas behaves like an ideal gas if its
Physics · Heat and Thermodynamics · MCQ
Q63.Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperature T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies,…
Physics · Heat and Thermodynamics · Numerical
Q64.A piece of ice (heat capacity = 2100 J kg-1 oC-1 and latent heat = 3.36 $\times$ 105 J kg-1 ) of mass m grams is at - 5 oC at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water…
Physics · Heat and Thermodynamics · Numerical
Q65.A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the $x$ -axis are shown in the figure. These lines suggest that Includes diagram
Physics · Electrostatics · Multiple correct
Q66.A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of…
Physics · Units and Measurements · Multiple correct
Q67.Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100, 60 and 40 W bulbs have filament resistances R100, R60 and R40 respectively,…
Physics · Current Electricity · MCQ
Q68.To verify Ohm's law, a student is provided with a test resitor RT, a high resistance R1, a small resistance R2, two identical galvanometers G1 and G2, and a variable voltage source V. The correct circuit to carry out the experiment is
Physics · Current Electricity · MCQ
Q69.An AC voltage source of variable angular frequency $ω$ and fixed amplitude V0 is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $ω$ is increased
Physics · Alternating Current · MCQ
Q70.A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of… Includes diagram
Physics · Magnetism · MCQ
Q71.A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is Includes diagram
Physics · Gravitation · MCQ
Q72.Consider a thin square sheet of side L and thickness, made of a material of resistivity $ρ$ . The resistance between two opposite faces, shown by the shaded areas in the figure is Includes diagram
Physics · Current Electricity · MCQ
Q73.One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choose the correct option(s) from the following: Includes diagram
Physics · Heat and Thermodynamics · Multiple correct
Q74.A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60 $^{\circ}$ (see figure). If the refractive index of the material of the prism is $3$ , which of the following is(are)… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q75.Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that… Includes diagram
Physics · Magnetism · MCQ
Q76.Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that… Includes diagram
Physics · Magnetism · MCQ
Q77.When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple harmonic motion. The corresponding time period is proportional to $\frac{m}{k}$ , as can be seen easily using dimensional… Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q78.When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple harmonic motion. The corresponding time period is proportional to $\frac{m}{k}$ , as can be seen easily using dimensional… Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q79.When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple harmonic motion. The corresponding time period is proportional to $\frac{m}{k}$ , as can be seen easily using dimensional… Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q80.A stationary source is emitting sound at a fixed frequency f0, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f0. What is the difference in the…
Physics · Waves · Numerical
Q81.The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m25 to m50. The ratio $\frac{m _{25}}{m _{50}}$ is …
Physics · Geometrical Optics · Numerical
Q82.An $α$ -particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ α$ and $λ$ p, respectively. The ratio $\frac{λ _{p}}{λ _{α}}$ …
Physics · Dual Nature of Radiation · Numerical
Q83.When two identical batteries of internal resistance 1 $Ω$ each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25…
Physics · Current Electricity · Numerical
Q84.When two progressive waves $y_{1} = 4 sin (2 x - 6 t)$ and $y_{2} = 3 sin (2 x - 6 t - \frac{π}{2})$ are superimposed, the amplitude of the resultant wave is .
Physics · Waves · Numerical