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2010 · Shift 2

57 questions · JEE Advanced

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2010 · Shift 2

2010 · Shift 2

57 questions · JEE Advanced

Chemistry19 questions Mathematics19 questions Physics19 questions

Chemical Bonding and Molecular StructureChemistry · 2 questions Some Basic Concepts of ChemistryChemistry · 1 questions Structure of AtomChemistry · 3 questions Periodic Table and PeriodicityChemistry · 1 questions P Block ElementsChemistry · 2 questions Alcohols Phenols and EthersChemistry · 1 questions Solid StateChemistry · 1 questions Coordination CompoundsChemistry · 2 questions Compounds Containing NitrogenChemistry · 2 questions ThermodynamicsChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 3 questions 3D GeometryMathematics · 2 questions Complex NumbersMathematics · 1 questions Application of DerivativesMathematics · 1 questions Trigonometric Functions and EquationsMathematics · 1 questions Mathematical Induction and Binomial TheoremMathematics · 1 questions Sequences and SeriesMathematics · 1 questions EllipseMathematics · 3 questions Properties of TriangleMathematics · 1 questions Definite IntegrationMathematics · 1 questions Matrices and DeterminantsMathematics · 1 questions FunctionsMathematics · 3 questions Application of IntegrationMathematics · 1 questions ProbabilityMathematics · 1 questions Vector AlgebraMathematics · 1 questions Units and MeasurementsPhysics · 1 questions Properties of MatterPhysics · 3 questions Heat and ThermodynamicsPhysics · 1 questions WavesPhysics · 1 questions ElectrostaticsPhysics · 2 questions Work Power and EnergyPhysics · 1 questions Geometrical OpticsPhysics · 4 questions Atoms and NucleiPhysics · 4 questions CapacitorPhysics · 1 questions Alternating CurrentPhysics · 1 questions

Q1.The species having pyramidal shape is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q2.Silver (atomic weight = 108 g mol-1) has a density of 10.5 g.cm-3. The number of silver atoms on a surface of area 10-12 m2 can be expressed in scientific notation as y $\times$ 10x. The value of x is?
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q3.The hydrogen like species $L i^{2 +}$ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state…
Chemistry · Structure of Atom · MCQ
Q4.The hydrogen like species $L i^{2 +}$ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state…
Chemistry · Structure of Atom · MCQ
Q5.The hydrogen like species $L i^{2 +}$ is in a spherically symmetric state S1 with one radial node. Upon absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its energy is equal to the ground state…
Chemistry · Structure of Atom · MCQ
Q6.Among the following, the number of elements showing only one non-zero oxidation state is : O, Cl, F, N, P, Sn, Tl, Na, Ti
Chemistry · Periodic Table and Periodicity · Numerical
Q7.Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule $B_{2}$ is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q8.The total number of diprotic acids among the following is: $H_{3} P O_{4}$ , $H_{2} S O_{4}$ , $H_{3} P O_{3}$ , $H_{2} C O_{3}$ , $H_{2} S_{2} O_{7}$ , $H_{3} B O_{3}$ , $H_{3} P O_{2}$ , $H_{2} C r O_{4}$ and $H_{2} S O_{3}$
Chemistry · P Block Elements · Numerical
Q9.The compounds $S$ and $S$ were separately subjected to nitration using $HNO_{3} / H_{2} SO_{4}$ mixture. The major product formed in each case respectively, is :
Chemistry · Alcohols Phenols and Ethers · MCQ
Q10.The packing efficiency of the twodimensional square unit cell shown below is Includes diagram
Chemistry · Solid State · MCQ
Q11.The complex showing a spin-only magnetic moment of 2.82 B.M. is :
Chemistry · Coordination Compounds · MCQ
Q12.In the reaction, The structure of the product T is : Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q13.One mole of an ideal gas is taken from $a$ to $b$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $W_{s}$ and that dotted line… Includes diagram
Chemistry · Thermodynamics · Numerical
Q14.Total number of geometrical isomers for the complex $[RhCl (CO) (PPh_{3}) (NH_{3})]$ is .
Chemistry · Coordination Compounds · Numerical
Q15.Two aliphatic aldehydes $P$ and $Q$ react in the presence of aqueous $K_{2} CO_{3}$ to give compound $R$ , which upon treatment with $H C N$ provides compound $S$ . On acidification and… Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q16.Two aliphatic aldehydes $P$ and $Q$ react in the presence of aqueous $K_{2} CO_{3}$ to give compound $R$ , which upon treatment with $H C N$ provides compound $S$ . On acidification and… Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q17.Two aliphatic aldehydes $P$ and $Q$ react in the presence of aqueous $K_{2} CO_{3}$ to give compound $R$ , which upon treatment with $H C N$ provides compound $S$ . On acidification and… Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q18.Match the reactions in Column I with appropriate options in Column II. Includes table Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q19.All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II. Includes table
Chemistry · P Block Elements · MCQ
Q20.Match the statement in Column- $I$ with the values in Column- $I I$ Column- $I$ (A) A line from the origin meets the lines $\frac{x - 2}{1} = \frac{y - 1}{- 2} = \frac{z + 1}{1}$ and $\frac{x - \frac{8}{3}}{2} = \frac{y + 3}{- 1} = \frac{z - 1}{1}$ …
Mathematics · 3D Geometry · MCQ
Q21.Match the statements in Column I with those in Column II. [Note : Here z takes value in the complex plane and Im z and Re z denotes, respectively, the imaginary part and the real part of z.] Column I (A) The set of points z satisfying $∣ z - i ∣ z ∥ = ∣ z + i ∣ z ∥$ …
Mathematics · Complex Numbers · MCQ
Q22.Let $f$ be a function defined on $R$ (the set of all real numbers) such that $f^{'} (x) = 2010 (x - 2009) (x - 2010)^{2} (x - 2011)^{3} (x - 2012)^{4}$ for all $x \in R$ If $g$ …
Mathematics · Application of Derivatives · Numerical
Q23.If the distance of the point $P (1, - 2, 1)$ from the plane $x + 2 y - 2 z = α,$ where $α > 0,$ is $5,$ then the foot of the perpendicular from $P$ to the planes is
Mathematics · 3D Geometry · MCQ
Q24.Two parallel chords of a circle of radius 2 are at a distance $3 + 1$ apart. If the chords subtend at the center , angles of $\frac{π}{k}$ and $\frac{2 π}{k},$ where $k > 0,$ then the value of $[k]$ is [Note…
Mathematics · Trigonometric Functions and Equations · Numerical
Q25.For $r = 0, 1, ....,$ let $A_{r}, B_{r}$ and $C_{r}$ denote, respectively, the coefficient of $X^{r}$ in the expansions of $(1 + x)^{10}, (1 + x)^{20}$ and $(1 + x)^{30} .$ Then $r = 1 \sum 10 A_{r} (B_{10} B_{r} - C_{10} A_{r})$ …
Mathematics · Mathematical Induction and Binomial Theorem · MCQ
Q26.Let $a_{1}, a_{2}, a_{3}$ ......, $a_{11}$ be real numbers satisfying $a_{1} = 15, 27 - 2 a_{2} > 0 an d a_{k} = 2 a_{k - 1} - a_{k - 2} f or k = 3, 4, ........11$ . if $\frac{a _{1}^{2} + a _{2}^{2} + .... + a _{11}^{2}}{11} = 90$ …
Mathematics · Sequences and Series · Numerical
Q27.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The coordinates of $A$ and $B$ are
Mathematics · Ellipse · MCQ
Q28.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The orthocentre of the triangle $P A B$ is
Mathematics · Ellipse · MCQ
Q29.Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The equation of the locus of the point whose distances from the point $P$ and the line $A B$ …
Mathematics · Ellipse · MCQ
Q30.Consider a triangle $A B C$ and let $c$ and $c$ denote the lengths of the sides opposit to vertices $C$ and $C$ respectively. Suppose $a = 6, b = 10$ and the area of the triangle is $153$ , if $∠ A C B$ is obtuse and if $r$ …
Mathematics · Properties of Triangle · Numerical
Q31.Let $f$ be a real-valued function defined on the interval $(- 1, 1)$ such that $e^{- x} f (x) = 2 + 0 \int x t^{4} + 1 d t,$ for all $x \in (- 1, 1)$ , and let $f^{- 1}$ be the inverse…
Mathematics · Definite Integration · MCQ
Q32.Let $k$ be a positive real number and let $A B = 2 k - 1 2 k - 2 k 2 k 1 2 k 2 k - 2 k - 1 and = 0 1 - 2 k - k 2 k - 1 0 - 2 k k 2 k 0 .$ …
Mathematics · Matrices and Determinants · Numerical
Q33.Let $S = {1, 2, 3, 4}$ . The total number of unordered pairs of disjoint subsets of $S$ is equal to :
Mathematics · Functions · MCQ
Q34.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The area bounded by the curve $y = f (x)$ and the lines $x = 0, y = 0$ and $x = t,$ …
Mathematics · Application of Integration · MCQ
Q35.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The real numbers lies in the interval
Mathematics · Functions · MCQ
Q36.Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The function $f^{'} (x)$ is
Mathematics · Functions · MCQ
Q37.A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station $B$ . The probability of each station receving the signal correctly is $\frac{3}{4}$ .…
Mathematics · Probability · MCQ
Q38.Two adjacent sides of a parallelogram $A B C D$ are given by $A B = 2 i + 10 j + 11 k$ and $A D = - i + 2 j + 2 k$ The side $A D$ is rotated by an acute…
Mathematics · Vector Algebra · MCQ
Q39.A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
Physics · Units and Measurements · MCQ
Q40.When liquid medicine of density $ρ$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.…
Physics · Properties of Matter · MCQ
Q41.When liquid medicine of density $ρ$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.…
Physics · Properties of Matter · MCQ
Q42.When liquid medicine of density $ρ$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.…
Physics · Properties of Matter · MCQ
Q43.A diatomic ideal gas is compressed adiabatically $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is a Ti, the value of $a$ is
Physics · Heat and Thermodynamics · Numerical
Q44.A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the…
Physics · Waves · MCQ
Q45.A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 π}{7} \times 1 0^{5} V m^{- 1} .$ When the field is switched off, the drop is observed to fall…
Physics · Electrostatics · MCQ
Q46.A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $σ$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional… Includes diagram
Physics · Electrostatics · MCQ
Q47.A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the… Includes diagram
Physics · Work Power and Energy · MCQ
Q48.A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is
Physics · Geometrical Optics · MCQ
Q49.A large glass slab ( $μ$ = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?
Physics · Geometrical Optics · Numerical
Q50.Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3}$ m to $\frac{50}{7}$ m in 30 s. What is the speed of the object in km per hour?
Physics · Geometrical Optics · Numerical
Q51.To determine the half-life of a radioactive element, a student plots a graph of $ln \frac{d N ( t )}{d t}$ versus t. Here, $\frac{d N ( t )}{d t}$ is the rate of radioactive decay at time t. If the number of radioactive… Includes diagram
Physics · Atoms and Nuclei · Numerical
Q52.At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1) Includes diagram
Physics · Capacitor · Numerical
Q53.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of…
Physics · Atoms and Nuclei · MCQ
Q54.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of…
Physics · Atoms and Nuclei · MCQ
Q55.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of…
Physics · Atoms and Nuclei · MCQ
Q56.Two transparent media of refractive indices $μ_{1}$ and $μ_{3}$ have a solid lens shaped transparent material of refractive index $μ_{2}$ between them as shown in figures in Column II. A ray traversing these media is also shown in the… Includes diagram
Physics · Geometrical Optics · MCQ
Q57.You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in… Includes diagram
Physics · Alternating Current · MCQ