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2012 · Shift 1

60 questions · JEE Advanced

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2012 · Shift 1

2012 · Shift 1

60 questions · JEE Advanced

Chemistry20 questions Mathematics20 questions Physics20 questions

Chemical Kinetics and Nuclear ChemistryChemistry · 2 questions Some Basic Concepts of ChemistryChemistry · 1 questions Surface ChemistryChemistry · 1 questions HydrocarbonsChemistry · 1 questions Structure of AtomChemistry · 1 questions Solid StateChemistry · 1 questions Aldehydes Ketones and Carboxylic AcidsChemistry · 4 questions Coordination CompoundsChemistry · 1 questions P Block ElementsChemistry · 2 questions Gaseous StateChemistry · 1 questions D and F Block ElementsChemistry · 1 questions ThermodynamicsChemistry · 1 questions Basics of Organic ChemistryChemistry · 2 questions BiomoleculesChemistry · 1 questions Trigonometric Functions and EquationsMathematics · 1 questions Complex NumbersMathematics · 1 questions Vector AlgebraMathematics · 1 questions ProbabilityMathematics · 1 questions Permutations and CombinationsMathematics · 1 questions CircleMathematics · 1 questions EllipseMathematics · 1 questions HyperbolaMathematics · 1 questions ParabolaMathematics · 1 questions Application of DerivativesMathematics · 2 questions Indefinite IntegralsMathematics · 1 questions Application of IntegrationMathematics · 1 questions Differential EquationsMathematics · 1 questions 3D GeometryMathematics · 1 questions Limits Continuity and DifferentiabilityMathematics · 2 questions Matrices and DeterminantsMathematics · 1 questions FunctionsMathematics · 1 questions Quadratic Equation and InequalitiesMathematics · 1 questions ElectrostaticsPhysics · 4 questions Heat and ThermodynamicsPhysics · 2 questions Units and MeasurementsPhysics · 1 questions Rotational MotionPhysics · 2 questions Geometrical OpticsPhysics · 1 questions Simple Harmonic MotionPhysics · 1 questions Wave OpticsPhysics · 1 questions MagnetismPhysics · 2 questions Properties of MatterPhysics · 1 questions Laws of MotionPhysics · 1 questions Current ElectricityPhysics · 1 questions Electromagnetic InductionPhysics · 1 questions Dual Nature of RadiationPhysics · 1 questions Impulse and MomentumPhysics · 1 questions

Q1.An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of $[\frac{t _{1/8}}{t _{1/10}}] \times 10$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q2.The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table? $_{29}^{63} C u$ + $_{1}^{1} H \to 6_{0}^{1} n$ …
Chemistry · Chemical Kinetics and Nuclear Chemistry · Numerical
Q3.29.2 % (w/w) $H C l$ stock solution has density of 1.25 g mL-1 . The molecular weight of $H C l$ is 36.5 g mol-1 . The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M $H C l$ is
Chemistry · Some Basic Concepts of Chemistry · Numerical
Q4.Choose the correct reason for the stability of the Iyophobic colloidal particles
Chemistry · Surface Chemistry · Multiple correct
Q5.In allene ( $C_{3} H_{4}$ ), the type(s) of hybridisation of the carbon atoms is (are):
Chemistry · Hydrocarbons · MCQ
Q6.The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [ $α_{0}$ is Bohr radius]
Chemistry · Structure of Atom · MCQ
Q7.A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is Includes diagram
Chemistry · Solid State · MCQ
Q8.The carboxyl functional group ( $-$ COOH) is present in
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q9.As per IUPAC nomenclature, the name of the complex $[C o (H_{2} O)_{4} (N H_{3})_{2}] C l_{3}$ is
Chemistry · Coordination Compounds · MCQ
Q10.Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?
Chemistry · P Block Elements · MCQ
Q11.For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm L2 mol $-$ 2) is Includes diagram
Chemistry · Gaseous State · MCQ
Q12.The number of aldol reactions that occur in the given transformation are Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q13.The colour of light absorbed by an aqueous solution of $C u S O_{4}$ is
Chemistry · D and F Block Elements · MCQ
Q14.The number of optically active products obtained from the complete ozonolysis of the given compound is . Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q15.Which of the following hydrogen halides reacts with $A g N O_{3}$ (aq.) to give a precipitate that dissolves in $N a_{2} S_{2} O_{3}$ (aq.) ?
Chemistry · P Block Elements · Multiple correct
Q16.Identify the binary mixtures that can be separated into individual compounds, by differential extraction, as shown in the given scheme. Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q17.For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is(are) correct? (Take $Δ$ … Includes diagram
Chemistry · Thermodynamics · Multiple correct
Q18.Which of the following molecules, in pure form, is(are) unstable at room temperature?
Chemistry · Basics of Organic Chemistry · Multiple correct
Q19.The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positively charged at pH = 7.0 ? Includes table Includes diagram
Chemistry · Biomolecules · Numerical
Q20.When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is . Includes diagram
Chemistry · Basics of Organic Chemistry · Numerical
Q21.Let $θ, φ \in [0, 2 π]$ be such that $2 cos θ (1 - sin φ) = sin^{2} θ (tan \frac{θ}{2} + cot \frac{θ}{2}) cos φ - 1, tan (2 π - θ) > 0$ …
Mathematics · Trigonometric Functions and Equations · Multiple correct
Q22.Let z be a complex number such that the imaginary part of z is non-zero and $a = z^{2} + z + 1$ is real. Then a cannot take the value
Mathematics · Complex Numbers · MCQ
Q23.If $a, b$ and $c$ are unit vectors satisfying $a - b^{2} + b - c^{2} + c - a^{2} = 9,$ …
Mathematics · Vector Algebra · Numerical
Q24.A ship is fitted with three engines $E_{1}, E_{2}$ and $E_{3}$ . The engines function independently of each other with respective probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ . For the ship to be operational at least two of its…
Mathematics · Probability · Multiple correct
Q25.The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is
Mathematics · Permutations and Combinations · MCQ
Q26.The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle $x^{2} + y^{2} = 9$ is
Mathematics · Circle · MCQ
Q27.The ellipse $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0, 4)$ circumscribes the rectangle $R$ . The…
Mathematics · Ellipse · MCQ
Q28.Tangents are drawn to the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1,$ parallel to the straight line $2 x - y = 1,$ The points of contact of the tangents on the hyperbola are
Mathematics · Hyperbola · Multiple correct
Q29.Let $S$ be the focus of the parabola $y^{2} = 8 x$ and let $P Q$ be the common chord of the circle $x^{2} + y^{2} - 2 x - 4 y = 0$ and the given parabola. The area of the triangle $P QS$ is
Mathematics · Parabola · Numerical
Q30.Let $f : I R \to I R$ be defined as $f (x) = ∣ x ∣ + x^{2} - 1 .$ The total number of points at which $f$ attains either a local maximum or a local minimum is
Mathematics · Application of Derivatives · Numerical
Q31.Let $p (x)$ be a real polynomial of least degree which has a local maximum at $x = 1$ and a local minimum at $x = 3$ . If $p (1) = 6$ and $p (3) = 2$ , then $p^{'} (0)$ is
Mathematics · Application of Derivatives · Numerical
Q32.The integral $\int \frac{s e c ^{2} x}{( s e c x + t a n x ) ^{9/2}} d x$ equals (for some arbitrary constant $K$ )
Mathematics · Indefinite Integrals · MCQ
Q33.Let $S$ be the area of the region enclosed by $y = e^{- x^{2}}$ , $y = 0$ , $x = 0$ , and $x = 1$ ; then
Mathematics · Application of Integration · Multiple correct
Q34.If $y (x)$ satisfies the differential equation $y^{'} - y t an x = 2 x sec x$ and $y (0) = 0,$ then
Mathematics · Differential Equations · Multiple correct
Q35.The point $P$ is the intersection of the straight line joining the points $Q (2, 3, 5)$ and $R (1, - 1, 4)$ with the plane $5 x - 4 y - z = 1.$ If $S$ is the foot of the perpendicular drawn from the point $T (2, 1, 4)$ to $QR,$ then the length of the…
Mathematics · 3D Geometry · MCQ
Q36.If $x \to \infty lim (\frac{x ^{2} + x + 1}{x + 1} - a x - b) = 4$ , then
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let $P = [a_{ij}]$ be a 3 $\times$ 3 matrix and let $Q = [b_{ij}]$ , where $b_{ij} = 2^{i + j} a_{ij}$ for $1 \leq i, j \leq 3$ . If the determinant of P is 2, then the determinant of the matrix Q is
Mathematics · Matrices and Determinants · MCQ
Q38.Let $f (x) = {x^{2} cos \frac{π}{x}, 0, x e 0 x = 0$ x $\in$ R, then f is
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.The function $f : [0, 3] \to [1, 29]$ , defined by $f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1$ , is
Mathematics · Functions · MCQ
Q40.The value of $6 + lo g_{3/2} (\frac{1}{3 2} 4 - \frac{1}{3 2} 4 - \frac{1}{3 2} 4 - \frac{1}{3 2} ...)$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q41.A cubical region of side $a$ has its center at the origin. It encloses three fixed point charges, $- q$ at $(0, - a /4, 0), + 3 q$ at $(0, 0, 0)$ and $- q$ at $(0, + a /4, 0) .$ Choose the correct… Includes diagram
Physics · Electrostatics · Multiple correct
Q42.Consider a thin spherical shell of radius $R$ with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $E (r)$ and the…
Physics · Electrostatics · MCQ
Q43.Two large vertical and parallel metal plates having a separation of $1 c m$ are connected to a $D C$ voltage source of potential difference $X$ . A proton is released at rest midway between the two plates. It is found to move at $4 5^{\circ}$ …
Physics · Electrostatics · MCQ
Q44.A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $(\frac{v _{r m s} ( h e l i u m )}{v _{r m s} ( a r g o n )})$ …
Physics · Heat and Thermodynamics · MCQ
Q45.In the determination of Young's modulus $(Y = \frac{4 M Lg}{π l d ^{2}})$ by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length…
Physics · Units and Measurements · MCQ
Q46.A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the xy-plane with centre at O and constant angular speed $ω$ . If the angular momentum of… Includes diagram
Physics · Rotational Motion · MCQ
Q47.A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both curved surface are of the same radius of curvature R = 14 cm. For this… Includes diagram
Physics · Geometrical Optics · MCQ
Q48.A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $ω$ , as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the rod… Includes diagram
Physics · Rotational Motion · MCQ
Q49.Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T,…
Physics · Heat and Thermodynamics · MCQ
Q50.A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and… Includes diagram
Physics · Simple Harmonic Motion · MCQ
Q51.Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are $β$ G, $β$ R and $β$ B, respectively. Then,
Physics · Wave Optics · MCQ
Q52.Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields $E = E_{0} j$ and $B = B_{0} j$ . At time t = 0, this charge has…
Physics · Magnetism · Multiple correct
Q53.A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,
Physics · Properties of Matter · Multiple correct
Q54.A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $θ$ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary… Includes diagram
Physics · Laws of Motion · Multiple correct
Q55.For the resistance network shown in the figure, choose the correct option(s). Includes diagram
Physics · Current Electricity · Multiple correct
Q56.A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R) having two turns is placed with its centre at z = $3$ R along the axis of the circular wire loop, as shown in… Includes diagram
Physics · Electromagnetic Induction · Numerical
Q57.An infinitely long solid cylinder of radius R has a uniform volume charge density $ρ$ . It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at… Includes diagram
Physics · Electrostatics · Numerical
Q58.A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is …
Physics · Dual Nature of Radiation · Numerical
Q59.A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is IO and IP respectively.… Includes diagram
Physics · Impulse and Momentum · Numerical
Q60.A cylinder cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic… Includes diagram
Physics · Magnetism · Numerical