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2016 · Shift 1

54 questions · JEE Advanced

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2016 · Shift 1

2016 · Shift 1

54 questions · JEE Advanced

Chemistry18 questions Mathematics18 questions Physics18 questions

Chemical Kinetics and Nuclear ChemistryChemistry · 2 questions SolutionsChemistry · 1 questions ThermodynamicsChemistry · 1 questions Gaseous StateChemistry · 1 questions Chemical Bonding and Molecular StructureChemistry · 1 questions Structure of AtomChemistry · 1 questions Compounds Containing NitrogenChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 2 questions Basics of Organic ChemistryChemistry · 1 questions Redox ReactionsChemistry · 1 questions Coordination CompoundsChemistry · 2 questions D and F Block ElementsChemistry · 1 questions P Block ElementsChemistry · 2 questions PolymersChemistry · 1 questions Trigonometric Functions and EquationsMathematics · 1 questions 3D GeometryMathematics · 1 questions ProbabilityMathematics · 1 questions Definite IntegrationMathematics · 1 questions Differential EquationsMathematics · 2 questions Application of DerivativesMathematics · 1 questions Properties of TriangleMathematics · 1 questions DifferentiationMathematics · 1 questions ParabolaMathematics · 1 questions CircleMathematics · 1 questions Mathematical Induction and Binomial TheoremMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions Quadratic Equation and InequalitiesMathematics · 1 questions Matrices and DeterminantsMathematics · 3 questions Limits Continuity and DifferentiabilityMathematics · 1 questions Units and MeasurementsPhysics · 1 questions Heat and ThermodynamicsPhysics · 2 questions Properties of MatterPhysics · 1 questions Rotational MotionPhysics · 2 questions Geometrical OpticsPhysics · 3 questions Dual Nature of RadiationPhysics · 1 questions Electromagnetic InductionPhysics · 2 questions WavesPhysics · 1 questions Atoms and NucleiPhysics · 3 questions Current ElectricityPhysics · 2 questions

Q1.A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of…
Chemistry · Chemical Kinetics and Nuclear Chemistry · Multiple correct
Q2.According to the Arrhenius equation,
Chemistry · Chemical Kinetics and Nuclear Chemistry · Multiple correct
Q3.The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm–3 . The ratio of the molecular weights of the solute and solvent, $(\frac{M W _{so l u t e}}{M W _{so l v e n t}})$ …
Chemistry · Solutions · Numerical
Q4.One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surrounding ( $Δ$ Ssurr)in JK–1 is (1L…
Chemistry · Thermodynamics · MCQ
Q5.The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of…
Chemistry · Gaseous State · Numerical
Q6.The compound(s) with TWO lone pairs of electrons on the central atom is(are)
Chemistry · Chemical Bonding and Molecular Structure · Multiple correct
Q7.P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is $4 π r^{2} d r$ . The quantitative ketch of the dependence of P…
Chemistry · Structure of Atom · MCQ
Q8.The product(s) of the following reaction sequence is (are) Includes diagram
Chemistry · Compounds Containing Nitrogen · Multiple correct
Q9.Positive Tollen’s test is observed for
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q10.In the following mono-bromination reaction, the number of possible chiral product(s) is (are)... Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q11.In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitative oxidise thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is....
Chemistry · Redox Reactions · Numerical
Q12.The possible number of geometrical isomers for the complex $[C o L_{2} C l_{2}]^{-}$ (L= $H_{2} N C H_{2} C H_{2} O^{-}$ ) is (are)...
Chemistry · Coordination Compounds · Numerical
Q13.The reagent(s) that can selectively precipitate $S^{2 -}$ from a mixture of $S^{2 -}$ and SO $_{4}^{2 -}$ in aqueous solution is (are) :
Chemistry · D and F Block Elements · Multiple correct
Q14.The crystalline form of borax has.
Chemistry · P Block Elements · Multiple correct
Q15.The increasing order of atomic radii of the following group 13 elements is
Chemistry · P Block Elements · MCQ
Q16.On complete hydrogenation, natural rubber produces
Chemistry · Polymers · MCQ
Q17.Among $[N i (C O)_{4}]$ , $[N i C l_{4}]^{2 -}$ , [Co(NH3)4)Cl2]Cl, $N a_{3} [C o F_{6}]$ , $N a_{2} O_{2}$ and $C s O_{2}$ , the total number of paramagnetic compound is
Chemistry · Coordination Compounds · MCQ
Q18.The correct statements about of the following reaction sequence is (are) Cumene ( $C_{9} H$ {}_{12} $)$ $(ii) H_{3} O^{+} ⟶ (i) O_{2}$ $P$ $⟶ C H C l_{3} / N a O H$ …
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q19.Let $S = {x \in (- π, π) : x e 0, \pm \frac{π}{2}} .$ The sum of all distinct solutions of the equation $3 sec x + csc x + 2 (tan x - cot x) = 0$ in the set S is equal to
Mathematics · Trigonometric Functions and Equations · MCQ
Q20.Consider a pyramid $O P QR S$ located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$ as origin, and $O P$ and $O R$ along the $x$ -axis and the $y$ -axis, respectively. The base $O P QR$ of the pyramid is a square with $O P = 3.$ …
Mathematics · 3D Geometry · Multiple correct
Q21.A computer producing factory has only two plants $T_{1}$ and $T_{2} .$ Plant $T_{1}$ produces $20$ % and plant $T_{2}$ produces $80$ % of the total computers produced. $7$ % of computers produced in the factory turn out to be defective. It is…
Mathematics · Probability · MCQ
Q22.The total number of distinct $x \in [0, 1]$ for which $0 \int x \frac{t ^{2}}{1 + t ^{4}} d t = 2 x - 1$
Mathematics · Definite Integration · Numerical
Q23.A solution curve of the differential equation $(x^{2} + x y + 4 x + 2 y + 4) \frac{d y}{d x} - y^{2} = 0,$ $x > 0,$ passes through the point $(1, 3)$ . Then the solution curve
Mathematics · Differential Equations · Multiple correct
Q24.The least value of a $4 a x^{2} + \frac{1}{x} \geq 1,$ for which $4 a x^{2} + \frac{1}{x} \geq 1,$ , for all $x > 0$ . is
Mathematics · Application of Derivatives · MCQ
Q25.In a triangle $Δ X Y Z$ , let $x, y, z$ be the lengths of sides opposite to the angles $X, Y, Z$ respectively, and $2 s = x + y + z$ . If $\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}$ and area of incircle of the triangle $X Y Z$ …
Mathematics · Properties of Triangle · Multiple correct
Q26.Let $f : R \to R, g : R \to R$ and $h : R \to R$ be differentiable functions such that $f (x) = x^{3} + 3 x + 2, g (f (x)) = x$ and $h (g (g (x))) = x$ …
Mathematics · Differentiation · Multiple correct
Q27.The circle $C_{1} : x^{2} + y^{2} = 3,$ with centre at $O$ , intersects the parabola $x^{2} = 2 y$ at the point $P$ in the first quadrant, Let the tangent to the circle $C_{1}$ , at $P$ touches other two circles $C_{2}$ and $C_{3}$ at $R_{2}$ …
Mathematics · Parabola · Multiple correct
Q28.Let RS be the diameter of the circle $x^{2} + y^{2} = 1$ , where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at…
Mathematics · Circle · Multiple correct
Q29.Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1 + x)^{2} + (1 + x)^{3} + ........ + (1 + x)^{49} + (1 + m x)^{50}$ …
Mathematics · Mathematical Induction and Binomial Theorem · Numerical
Q30.A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number…
Mathematics · Permutations and Combinations · MCQ
Q31.Let $- \frac{π}{6} < θ < - \frac{π}{12} .$ Suppose $α_{1}$ and $β_{1}$ are the roots of the equation $x^{2} - 2 x sec θ + 1 = 0$ and $α_{2}$ and $β_{2}$ are the roots of the equation $x^{2} + 2 x tan θ - 1 = 0. I f α_{1} > β_{1}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.Let $f : (0, \infty) \to R$ be a differentiable function such that $f^{'} (x) = 2 - \frac{f ( x )}{x}$ for all $x \in (0, \infty)$ and $f (1) e 1$ . Then
Mathematics · Differential Equations · Multiple correct
Q33.Let $P = 323 - 1 0 - 5 - 2 α 0$ , where $α \in$ R. Suppose $Q = [q_{ij}]$ is a matrix such that PQ = kl, where k $\in$ R, k $e$ …
Mathematics · Matrices and Determinants · Multiple correct
Q34.The total number of distinct x $\in$ R for which $x 2 x 3 x x^{2} 4 x^{2} 9 x^{2} 1 + x^{3} 1 + 8 x^{3} 1 + 27 x^{3} = 10$ is …
Mathematics · Matrices and Determinants · Numerical
Q35.Let $z = \frac{- 1 + 3 i}{2}$ , where $i = - 1$ , and r, s $\in$ {1, 2, 3}. Let $P = [(- z)^{r} z^{2 s} z^{2 s} z^{r}]$ and I be the identity…
Mathematics · Matrices and Determinants · Numerical
Q36.Let $α$ , $β \in$ R be such that $x \to 0 lim \frac{x ^{2} s i n ( β x )}{α x - s i n x} = 1$ . Then 6( $α$ + $β$ ) equals .
Mathematics · Limits Continuity and Differentiability · Numerical
Q37.A length-scale (l) depends on the permittivity ( $ε$ ) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each…
Physics · Units and Measurements · Multiple correct
Q38.A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays $lo g_{2} (\frac{P}{P _{0}})$ , where P0 is a constant. When…
Physics · Heat and Thermodynamics · Numerical
Q39.Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm–3 and viscosity $η$ = 3 poiseulles. Sphere Q is dropped into a liquid of…
Physics · Properties of Matter · Numerical
Q40.The position vector $r$ of a particle of mass m is given by the following equation $r (t) = α t^{3} i + β t^{2} j,$ where $α = \frac{10}{3} m s^{- 3}$ , $β = 5 m s^{- 2}$ …
Physics · Rotational Motion · Multiple correct
Q41.A uniform wooden stick of mass 1.6 kg and length $l$ rests in an inclined manner on a smooth, vertical wall of height h ( < $l$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick…
Physics · Rotational Motion · MCQ
Q42.A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refractive index n = $2$ . Light undergoes total internal reflection in the prism at the face PR when a has a minimum… Includes diagram
Physics · Geometrical Optics · MCQ
Q43.In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the… Includes table
Physics · Dual Nature of Radiation · MCQ
Q44.A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates… Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q45.A plano-convex lens is made of material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex…
Physics · Geometrical Optics · Multiple correct
Q46.A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90 $^{\circ}$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the… Includes diagram
Physics · Electromagnetic Induction · Multiple correct
Q47.Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car in initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/h along…
Physics · Waves · Multiple correct
Q48.A transparent slab of thickness d has a refractive index n (z) that increases with z. Here, z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2… Includes diagram
Physics · Geometrical Optics · Multiple correct
Q49.Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?
Physics · Atoms and Nuclei · Multiple correct
Q50.An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a…
Physics · Current Electricity · Multiple correct
Q51.A hydrogen atom in its ground state is irradiated by light of wavelength 970 $A o$ . Taking hc = 1.237 $\times$ 10 $-$ 6 eVm and the ground state energy of hydrogen atom as $-$ 13.6 eV, the number of lines present in the…
Physics · Atoms and Nuclei · Numerical
Q52.The isotope $_{5}^{12} B$ having a mass 12.014 u undergoes $β$ -decay to $_{6}^{12} C$ . $_{6}^{12} C$ has an excited state of the nucleus ( $_{6}^{12} C$ *) at 4.041 MeV above its ground state. If $_{5}^{12} B$ decays to $_{6}^{12} C$ *, the maximum kinetic…
Physics · Atoms and Nuclei · Numerical
Q53.An infinite line charge of uniform electric charge density l lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity e…
Physics · Current Electricity · MCQ
Q54.Two inductors L1 (inductance 1mH, internal resistance 3 $Ω$ ) and L2 (inductance 2 mH, internal resistance 4 $Ω$ ), and a resistor R (resistance 12 $Ω$ ) are all connected in parallel across a 5V battery. The circuit is…
Physics · Electromagnetic Induction · Numerical