2010 · Shift 0

78 questions · JEE Main

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JEE Main
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2010 · Shift 0

2010 · Shift 0

78 questions · JEE Main

Chemistry26 questions Mathematics24 questions Physics28 questions

Q1.One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q2.The correct order of increasing basicity of the given conjugate bases (R = $C H_{3}$ ) is
Chemistry · Basics of Organic Chemistry · MCQ
Q3.Out of the following, the alkene that exhibits optical isomerism is
Chemistry · Basics of Organic Chemistry · MCQ
Q4.Solubility product of silver bromide is 5.0 $\times$ 10–13. The quantity of potassium bromide (molar mass taken as 120g of mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is :
Chemistry · Ionic Equilibrium · MCQ
Q5.In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11 Select the correct statement for a saturated 0.034 M solution of the carbonic acid.
Chemistry · Chemical Equilibrium · MCQ
Q6.At 25°C, the solubility product of $M g (O H)_{2}$ is 1.0 $\times$ 10–11. At which pH, will $M g^{2 +}$ ions start precipitating in the form of $M g (O H)_{2}$ from a solution of 0.001 M $M g^{2 +}$ ions?
Chemistry · Ionic Equilibrium · MCQ
Q7.Three reactions involving $H_{2} P O_{4}^{-}$ are given below : (i) $H_{3} P O_{4}$ + $H_{2} O$ $\to$ $H_{3} O^{+}$ + $H_{2} P O_{4}^{-}$ (ii) $H_{2} P O_{4}^{-}$ + $H_{2} O$ $\to H P O_{4}^{2 -}$ + $H_{3} O^{+}$ (iii) $H_{2} P O_{4}^{-}$ + $O H^{-}$ $\to$ $H_{3} P O_{4}$ + $O^{2 -}$ In which of the above does $H_{2} P O_{4}^{-}$ …
Chemistry · Ionic Equilibrium · MCQ
Q8.For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is the temperature at equilibrium, the reaction would be spontaneous when :
Chemistry · Thermodynamics · MCQ
Q9.The standard enthalpy of formation of $N H_{3}$ is –46.0 kJ mol–1. If the enthalpy of formation of $H_{2}$ from its atoms is –436 kJ mol–1 and that of $N_{2}$ is –712 kJ mol–1, the average bond enthalpy of N–H bond in $N H_{3}$ is :
Chemistry · Thermodynamics · MCQ
Q10.Biuret test is not given by
Chemistry · Biomolecules · MCQ
Q11.In the chemical reactions, the compounds $^{'} A^{'}$ and $^{'} B^{'}$ respectively are Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q12.The main product of the following reaction is $C_{6} H_{5} C H_{2} C H (O H) C H (C H_{3})_{2} co n c . H_{2} S O_{4} ?$
Chemistry · Hydrocarbons · MCQ
Q13.Consider the following bromides : The correct order of $S_{N} 1$ reactive is Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q14.From amongst the following alcohols the one that would react fastest with conc. $H C l$ and anhydrous $Z n C l_{2}$ , is
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.A solution containing 2.675g of $C o C l_{3}$ . 6 $N H_{3}$ (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of $A g N O_{3}$ to give 4.78 g of $A g C l$ (molar mass = 143.5 g…
Chemistry · Coordination Compounds · MCQ
Q16.Which one of the following has an optical isomer ? (en = ethylenediamine)
Chemistry · Coordination Compounds · MCQ
Q17.29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete…
Chemistry · Practical Organic Chemistry · MCQ
Q18.The time for half life period of a certain reaction A $\to$ products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1 if it is…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q19.Consider the reaction : $C l_{2}$ (aq) + $H_{2} S$ (aq) → $S$ (s) + 2 $H^{+}$ (aq) + 2 $C l^{-}$ (aq) The rate equation for this reaction is rate = k [ $C l_{2}$ ] [ $H_{2} S$ ] Which of these mechanisms is/are consistent with this rate equation? (A) $C l_{2}$ +…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q20.The Gibbs energy for the decomposition of $A l_{2} O_{3}$ at 500oC is as follows : $\frac{2}{3} A l_{2} O_{3} \to \frac{4}{3} A l + O_{2}$ , $Δ_{r} G$ = + 966 kJ mol–1 The potential difference needed for electrolytic reduction of $A l_{2} O_{3}$ at 500oC…
Chemistry · Electrochemistry · MCQ
Q21.The correct order of $E_{M^{2 +} / M}^{o}$ values with negative sign for the four successive elements Cr, Mn, Fe and Co is :
Chemistry · Electrochemistry · MCQ
Q22.On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane…
Chemistry · Solutions · MCQ
Q23.If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (∆Tf), when 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is (Kf = 1.86 K kg…
Chemistry · Solutions · MCQ
Q24.The correct sequence which shows decreasing order of the ionic radii of the elements is
Chemistry · Periodic Table and Periodicity · MCQ
Q25.Ionisation energy of $H e^{+}$ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of $L i^{2 +}$ is
Chemistry · Structure of Atom · MCQ
Q26.The energy required to break one mole of Cl–Cl bonds in $C l_{2}$ is 242 kJ mol–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is (c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)
Chemistry · Structure of Atom · MCQ
Q27.For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
Mathematics · Statistics · MCQ
Q28.Let $f : R \to R$ be a positive increasing function with $x \to \infty lim \frac{f ( 3 x )}{f ( x )} = 1$ . Then $x \to \infty lim \frac{f ( 2 x )}{f ( x )} =$
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.The number of complex numbers z such that $∣ z - 1 ∣ = ∣ z + 1 ∣ = ∣ z - i ∣$ equals :
Mathematics · Complex Numbers · MCQ
Q30.Let $f : R \to R$ be defined by $f (x) = {k - 2 x, i f 2 x + 3, i f x \leq - 1 x > - 1$ If $f$ has a local minimum at $x = - 1$ , then a possible value of $k$ …
Mathematics · Application of Derivatives · MCQ
Q31.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :
Mathematics · Probability · MCQ
Q32.Four numbers are chosen at random (without replacement) from the set ${1, 2, 3, ....20} .$ Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85} .$ Statement -…
Mathematics · Probability · MCQ
Q33.Solution of the differential equation $cos x d y = y (sin x - y) d x, 0 < x < \frac{π}{2}$ is :
Mathematics · Differential Equations · MCQ
Q34.Let $p (x)$ be a function defined on $R$ such that $p^{'} (x) = p^{'} (1 - x),$ for all $x \in [0, 1], p (0) = 1$ and $p (1) = 41.$ Then $0 \int 1 p (x) d x$ equals :
Mathematics · Definite Integration · MCQ
Q35.The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is
Mathematics · Area Under the Curves · MCQ
Q36.The number of $3 \times 3$ non-singular matrices, with four entries as $1$ and all other entries as $0$ , is :
Mathematics · Matrices and Determinants · MCQ
Q37.Consider the system of linear equations; $x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1$ The system has :
Mathematics · Matrices and Determinants · MCQ
Q38.Let $A$ be a $2 \times 2$ matrix with non-zero entries and let $A^{2} = I,$ where $I$ is $2 \times 2$ identity matrix. Define $T r (A) =$ sum of diagonal elements of $A$ and $∣ A ∣ =$ determinant of matrix $A$ . Statement- 1: $T r (A) = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q39.Let $f : R \to R$ be a continuous function defined by $f (x) = \frac{1}{e ^{x} + 2 e ^{- x}}$ Statement - 1 : $f (c) = \frac{1}{3},$ for some $c \in R$ . Statement - 2 : $0 < f (x) \leq \frac{1}{2 2},$ …
Mathematics · Application of Derivatives · MCQ
Q40.Let $f : (- 1, 1) \to R$ be a differentiable function with $f (0) = - 1$ and $f^{'} (0) = 1$ . Let $g (x) = [f (2 f (x) + 2)]^{2}$ . Then $g^{'} (0) =$ …
Mathematics · Differentiation · MCQ
Q41.If two tangents drawn from a point $P$ to the parabola $y^{2} = 4 x$ are at right angles, then the locus of $P$ is
Mathematics · Parabola · MCQ
Q42.The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :
Mathematics · Circle · MCQ
Q43.The line $L$ given by $\frac{x}{5} + \frac{y}{b} = 1$ passes through the point $(13, 32)$ . The line K is parrallel to $L$ and has the equation $\frac{x}{c} + \frac{y}{3} = 1.$ Then the distance between $L$ and $K$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{t h}$ minute. If $a_{1}$ = $a_{2}$ = ....= $a_{10}$ = 150 and $a_{10}$ , $a_{11}$ ,.... are in an AP with common difference - 2, then the…
Mathematics · Sequences and Series · MCQ
Q45.There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
Mathematics · Permutations and Combinations · MCQ
Q46.If $α$ and $β$ are the roots of the equation $x^{2} - x + 1 = 0,$ then $α^{2009} + β^{2009} =$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let $cos (α + β) = \frac{4}{5}$ and $sin (α - β) = \frac{5}{13},$ where $0 \leq α, β \leq \frac{π}{4} .$ Then $t an 2 α$ =
Mathematics · Trigonometric Ratio and Identites · MCQ
Q48.A line $A B$ in three-dimensional space makes angles $4 5^{\circ}$ and $12 0^{\circ}$ with the positive $x$ -axis and the positive $y$ -axis respectively. If $A B$ makes an acute angle $θ$ with the positive $z$ -axis, then $θ$ …
Mathematics · 3D Geometry · MCQ
Q49.If the vectors $a = i - j + 2 k, b = 2 i + 4 j + k$ and $c = λ i + j + μ k$ are…
Mathematics · Vector Algebra · MCQ
Q50.Consider the following relations $R = {(x, y) ∣ x, y$ are real numbers and $x = w y$ for some rational number $w}$ ; $S = {(\frac{m}{n}, \frac{p}{q}) ∣ m, n, p$ and $q$ are integers such that $n, q e q 0$ and $q m = p m}$ …
Mathematics · Sets and Relations · MCQ
Q51.The combination of gates shown below yields Includes diagram
Physics · Electronic Devices · MCQ
Q52.If a source of power $4 k W$ produces $1 0^{20}$ photons/second, the radiation belongs to a part of the spectrum called
Physics · Dual Nature of Radiation · MCQ
Q53.A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c .$ The speed of daughter nuclei is
Physics · Atoms and Nuclei · MCQ
Q54.A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c .$ The binding energy per nucleon for the parent nucleus is $E_{1}$ and that for the daughter nuclei is $E_{2} .$ …
Physics · Atoms and Nuclei · MCQ
Q55.Statement - $1$ : When ultraviolet light is incident on a photocell, its stopping potential is $V_{0}$ and the maximum kinetic energy of the photoelectrons is $K_{m a x}$ . When the ultraviolet light is replaced by $X$ -rays, both $V_{0}$ …
Physics · Dual Nature of Radiation · MCQ
Q56.In the circuit shown below, the key $K$ is closed at $t = 0.$ The current through the battery is Includes diagram
Physics · Alternating Current · MCQ
Q57.A rectangular loop has a sliding connector $P Q$ of length $l$ and resistance $R Ω$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_{1}, I_{2}$ … Includes diagram
Physics · Electromagnetic Induction · MCQ
Q58.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Geometrical Optics · MCQ
Q59.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Wave Optics · MCQ
Q60.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Geometrical Optics · MCQ
Q61.A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^{3} + 5,$ where $s$ is in metres and $t$ is in seconds. The radius of the path is $20 m .$ … Includes diagram
Physics · Circular Motion · MCQ
Q62.A small particle of mass $m$ is projected at an angle $θ$ with the $x$ -axis with an initial velocity $v_{0}$ in the $x$ - $y$ plane as shown in the figure. At a time $t < \frac{v _{0} s i n θ}{g},$ the angular momentum of the… Includes diagram
Physics · Rotational Motion · MCQ
Q63.The figure shows the position $-$ time $(x - t)$ graph of one-dimensional motion of body of mass $0.4 k g .$ The magnitude of each impulse is Includes diagram
Physics · Center of Mass · MCQ
Q64.Two long parallel wires are at a distance $2 d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $X X^{'}$ is given by
Physics · Magnetics · MCQ
Q65.In a series $L C R$ circuit $R = 200Ω$ and the voltage and the frequency of the main supply is $220 V$ and $50 H z$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $3 0^{\circ} .$ On…
Physics · Alternating Current · MCQ
Q66.Two conductors have the same resistance at $0^{\circ} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2} .$ The respective temperature coefficients of their series and parallel combinations are nearly
Physics · Current Electricity · MCQ
Q67.Let $C$ be the capacitance of a capacitor discharging through a resistor $R .$ Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to…
Physics · Capacitor · MCQ
Q68.A thin semi-circular ring of radius $r$ has a positive charges $q$ distributed uniformly over it. The net field $E$ at the center $O$ is Includes diagram
Physics · Electrostatics · MCQ
Q69.Let there be a spherically symmetric charge distribution with charge density varying as $ρ (r) = ρ_{0} (\frac{5}{4} - \frac{r}{R})$ upto $r = R,$ and $ρ (r) = 0$ for $r > R,$ where $r$ …
Physics · Electrostatics · MCQ
Q70.The equation of a wave on a string of linear mass density $0.04 k g m^{- 1}$ is given by $y = 0.02 (m) sin [2 π (\frac{t}{0.04 ( s )} - \frac{x}{0.50 ( m )})] .$ The…
Physics · Waves · MCQ
Q71.A ball is made of a material of density $ρ$ where $ρ_{o i l} < ρ < ρ_{w a t er}$ with $ρ_{o i l}$ and $ρ_{w a t er}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If…
Physics · Properties of Matter · MCQ
Q72.Two fixed frictionless inclined planes making an angle $3 0^{\circ}$ and $6 0^{\circ}$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with… Includes diagram
Physics · Laws of Motion · MCQ
Q73.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $3 0^{\circ}$ with each other. When suspended in a liquid of density $0.8 g c m^{- 3},$ the angle remains the same. If density of the…
Physics · Electrostatics · MCQ
Q74.Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.
Physics · Center of Mass · MCQ
Q75.The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}},$ where $a$ and $b$ are constants and $x$ is the distance…
Physics · Work Power and Energy · MCQ
Q76.For a particle in uniform circular motion the acceleration $a$ at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)
Physics · Circular Motion · MCQ
Q77.A particle is moving with velocity $v = k (y i + x j)$ , where K is a constant. The general equation for its path is
Physics · Motion in A Plane · MCQ
Q78.The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $\times$ 10–3 are
Physics · Units and Measurements · MCQ

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2010 · Shift 0

78 questions · JEE Main

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2010 · Shift 0

2010 · Shift 0

78 questions · JEE Main

Chemistry26 questions Mathematics24 questions Physics28 questions

Q1.One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q2.The correct order of increasing basicity of the given conjugate bases (R = $C H_{3}$ ) is
Chemistry · Basics of Organic Chemistry · MCQ
Q3.Out of the following, the alkene that exhibits optical isomerism is
Chemistry · Basics of Organic Chemistry · MCQ
Q4.Solubility product of silver bromide is 5.0 $\times$ 10–13. The quantity of potassium bromide (molar mass taken as 120g of mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is :
Chemistry · Ionic Equilibrium · MCQ
Q5.In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11 Select the correct statement for a saturated 0.034 M solution of the carbonic acid.
Chemistry · Chemical Equilibrium · MCQ
Q6.At 25°C, the solubility product of $M g (O H)_{2}$ is 1.0 $\times$ 10–11. At which pH, will $M g^{2 +}$ ions start precipitating in the form of $M g (O H)_{2}$ from a solution of 0.001 M $M g^{2 +}$ ions?
Chemistry · Ionic Equilibrium · MCQ
Q7.Three reactions involving $H_{2} P O_{4}^{-}$ are given below : (i) $H_{3} P O_{4}$ + $H_{2} O$ $\to$ $H_{3} O^{+}$ + $H_{2} P O_{4}^{-}$ (ii) $H_{2} P O_{4}^{-}$ + $H_{2} O$ $\to H P O_{4}^{2 -}$ + $H_{3} O^{+}$ (iii) $H_{2} P O_{4}^{-}$ + $O H^{-}$ $\to$ $H_{3} P O_{4}$ + $O^{2 -}$ In which of the above does $H_{2} P O_{4}^{-}$ …
Chemistry · Ionic Equilibrium · MCQ
Q8.For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is the temperature at equilibrium, the reaction would be spontaneous when :
Chemistry · Thermodynamics · MCQ
Q9.The standard enthalpy of formation of $N H_{3}$ is –46.0 kJ mol–1. If the enthalpy of formation of $H_{2}$ from its atoms is –436 kJ mol–1 and that of $N_{2}$ is –712 kJ mol–1, the average bond enthalpy of N–H bond in $N H_{3}$ is :
Chemistry · Thermodynamics · MCQ
Q10.Biuret test is not given by
Chemistry · Biomolecules · MCQ
Q11.In the chemical reactions, the compounds $^{'} A^{'}$ and $^{'} B^{'}$ respectively are Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q12.The main product of the following reaction is $C_{6} H_{5} C H_{2} C H (O H) C H (C H_{3})_{2} co n c . H_{2} S O_{4} ?$
Chemistry · Hydrocarbons · MCQ
Q13.Consider the following bromides : The correct order of $S_{N} 1$ reactive is Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q14.From amongst the following alcohols the one that would react fastest with conc. $H C l$ and anhydrous $Z n C l_{2}$ , is
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.A solution containing 2.675g of $C o C l_{3}$ . 6 $N H_{3}$ (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of $A g N O_{3}$ to give 4.78 g of $A g C l$ (molar mass = 143.5 g…
Chemistry · Coordination Compounds · MCQ
Q16.Which one of the following has an optical isomer ? (en = ethylenediamine)
Chemistry · Coordination Compounds · MCQ
Q17.29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete…
Chemistry · Practical Organic Chemistry · MCQ
Q18.The time for half life period of a certain reaction A $\to$ products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1 if it is…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q19.Consider the reaction : $C l_{2}$ (aq) + $H_{2} S$ (aq) → $S$ (s) + 2 $H^{+}$ (aq) + 2 $C l^{-}$ (aq) The rate equation for this reaction is rate = k [ $C l_{2}$ ] [ $H_{2} S$ ] Which of these mechanisms is/are consistent with this rate equation? (A) $C l_{2}$ +…
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q20.The Gibbs energy for the decomposition of $A l_{2} O_{3}$ at 500oC is as follows : $\frac{2}{3} A l_{2} O_{3} \to \frac{4}{3} A l + O_{2}$ , $Δ_{r} G$ = + 966 kJ mol–1 The potential difference needed for electrolytic reduction of $A l_{2} O_{3}$ at 500oC…
Chemistry · Electrochemistry · MCQ
Q21.The correct order of $E_{M^{2 +} / M}^{o}$ values with negative sign for the four successive elements Cr, Mn, Fe and Co is :
Chemistry · Electrochemistry · MCQ
Q22.On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane…
Chemistry · Solutions · MCQ
Q23.If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (∆Tf), when 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is (Kf = 1.86 K kg…
Chemistry · Solutions · MCQ
Q24.The correct sequence which shows decreasing order of the ionic radii of the elements is
Chemistry · Periodic Table and Periodicity · MCQ
Q25.Ionisation energy of $H e^{+}$ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of $L i^{2 +}$ is
Chemistry · Structure of Atom · MCQ
Q26.The energy required to break one mole of Cl–Cl bonds in $C l_{2}$ is 242 kJ mol–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is (c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)
Chemistry · Structure of Atom · MCQ
Q27.For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
Mathematics · Statistics · MCQ
Q28.Let $f : R \to R$ be a positive increasing function with $x \to \infty lim \frac{f ( 3 x )}{f ( x )} = 1$ . Then $x \to \infty lim \frac{f ( 2 x )}{f ( x )} =$
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.The number of complex numbers z such that $∣ z - 1 ∣ = ∣ z + 1 ∣ = ∣ z - i ∣$ equals :
Mathematics · Complex Numbers · MCQ
Q30.Let $f : R \to R$ be defined by $f (x) = {k - 2 x, i f 2 x + 3, i f x \leq - 1 x > - 1$ If $f$ has a local minimum at $x = - 1$ , then a possible value of $k$ …
Mathematics · Application of Derivatives · MCQ
Q31.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :
Mathematics · Probability · MCQ
Q32.Four numbers are chosen at random (without replacement) from the set ${1, 2, 3, ....20} .$ Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85} .$ Statement -…
Mathematics · Probability · MCQ
Q33.Solution of the differential equation $cos x d y = y (sin x - y) d x, 0 < x < \frac{π}{2}$ is :
Mathematics · Differential Equations · MCQ
Q34.Let $p (x)$ be a function defined on $R$ such that $p^{'} (x) = p^{'} (1 - x),$ for all $x \in [0, 1], p (0) = 1$ and $p (1) = 41.$ Then $0 \int 1 p (x) d x$ equals :
Mathematics · Definite Integration · MCQ
Q35.The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is
Mathematics · Area Under the Curves · MCQ
Q36.The number of $3 \times 3$ non-singular matrices, with four entries as $1$ and all other entries as $0$ , is :
Mathematics · Matrices and Determinants · MCQ
Q37.Consider the system of linear equations; $x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1$ The system has :
Mathematics · Matrices and Determinants · MCQ
Q38.Let $A$ be a $2 \times 2$ matrix with non-zero entries and let $A^{2} = I,$ where $I$ is $2 \times 2$ identity matrix. Define $T r (A) =$ sum of diagonal elements of $A$ and $∣ A ∣ =$ determinant of matrix $A$ . Statement- 1: $T r (A) = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q39.Let $f : R \to R$ be a continuous function defined by $f (x) = \frac{1}{e ^{x} + 2 e ^{- x}}$ Statement - 1 : $f (c) = \frac{1}{3},$ for some $c \in R$ . Statement - 2 : $0 < f (x) \leq \frac{1}{2 2},$ …
Mathematics · Application of Derivatives · MCQ
Q40.Let $f : (- 1, 1) \to R$ be a differentiable function with $f (0) = - 1$ and $f^{'} (0) = 1$ . Let $g (x) = [f (2 f (x) + 2)]^{2}$ . Then $g^{'} (0) =$ …
Mathematics · Differentiation · MCQ
Q41.If two tangents drawn from a point $P$ to the parabola $y^{2} = 4 x$ are at right angles, then the locus of $P$ is
Mathematics · Parabola · MCQ
Q42.The circle $x^{2} + y^{2} = 4 x + 8 y + 5$ intersects the line $3 x - 4 y = m$ at two distinct points if :
Mathematics · Circle · MCQ
Q43.The line $L$ given by $\frac{x}{5} + \frac{y}{b} = 1$ passes through the point $(13, 32)$ . The line K is parrallel to $L$ and has the equation $\frac{x}{c} + \frac{y}{3} = 1.$ Then the distance between $L$ and $K$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{t h}$ minute. If $a_{1}$ = $a_{2}$ = ....= $a_{10}$ = 150 and $a_{10}$ , $a_{11}$ ,.... are in an AP with common difference - 2, then the…
Mathematics · Sequences and Series · MCQ
Q45.There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
Mathematics · Permutations and Combinations · MCQ
Q46.If $α$ and $β$ are the roots of the equation $x^{2} - x + 1 = 0,$ then $α^{2009} + β^{2009} =$
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let $cos (α + β) = \frac{4}{5}$ and $sin (α - β) = \frac{5}{13},$ where $0 \leq α, β \leq \frac{π}{4} .$ Then $t an 2 α$ =
Mathematics · Trigonometric Ratio and Identites · MCQ
Q48.A line $A B$ in three-dimensional space makes angles $4 5^{\circ}$ and $12 0^{\circ}$ with the positive $x$ -axis and the positive $y$ -axis respectively. If $A B$ makes an acute angle $θ$ with the positive $z$ -axis, then $θ$ …
Mathematics · 3D Geometry · MCQ
Q49.If the vectors $a = i - j + 2 k, b = 2 i + 4 j + k$ and $c = λ i + j + μ k$ are…
Mathematics · Vector Algebra · MCQ
Q50.Consider the following relations $R = {(x, y) ∣ x, y$ are real numbers and $x = w y$ for some rational number $w}$ ; $S = {(\frac{m}{n}, \frac{p}{q}) ∣ m, n, p$ and $q$ are integers such that $n, q e q 0$ and $q m = p m}$ …
Mathematics · Sets and Relations · MCQ
Q51.The combination of gates shown below yields Includes diagram
Physics · Electronic Devices · MCQ
Q52.If a source of power $4 k W$ produces $1 0^{20}$ photons/second, the radiation belongs to a part of the spectrum called
Physics · Dual Nature of Radiation · MCQ
Q53.A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c .$ The speed of daughter nuclei is
Physics · Atoms and Nuclei · MCQ
Q54.A nucleus of mass $M + Δ m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c .$ The binding energy per nucleon for the parent nucleus is $E_{1}$ and that for the daughter nuclei is $E_{2} .$ …
Physics · Atoms and Nuclei · MCQ
Q55.Statement - $1$ : When ultraviolet light is incident on a photocell, its stopping potential is $V_{0}$ and the maximum kinetic energy of the photoelectrons is $K_{m a x}$ . When the ultraviolet light is replaced by $X$ -rays, both $V_{0}$ …
Physics · Dual Nature of Radiation · MCQ
Q56.In the circuit shown below, the key $K$ is closed at $t = 0.$ The current through the battery is Includes diagram
Physics · Alternating Current · MCQ
Q57.A rectangular loop has a sliding connector $P Q$ of length $l$ and resistance $R Ω$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_{1}, I_{2}$ … Includes diagram
Physics · Electromagnetic Induction · MCQ
Q58.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Geometrical Optics · MCQ
Q59.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Wave Optics · MCQ
Q60.An initially parallel cylindrical beam travels in a medium of refractive index $μ (I) = μ_{0} + μ_{2} I,$ where $μ_{0}$ and $μ_{2}$ are positive constants and $I$ is the intensity of the light beam. The…
Physics · Geometrical Optics · MCQ
Q61.A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^{3} + 5,$ where $s$ is in metres and $t$ is in seconds. The radius of the path is $20 m .$ … Includes diagram
Physics · Circular Motion · MCQ
Q62.A small particle of mass $m$ is projected at an angle $θ$ with the $x$ -axis with an initial velocity $v_{0}$ in the $x$ - $y$ plane as shown in the figure. At a time $t < \frac{v _{0} s i n θ}{g},$ the angular momentum of the… Includes diagram
Physics · Rotational Motion · MCQ
Q63.The figure shows the position $-$ time $(x - t)$ graph of one-dimensional motion of body of mass $0.4 k g .$ The magnitude of each impulse is Includes diagram
Physics · Center of Mass · MCQ
Q64.Two long parallel wires are at a distance $2 d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $X X^{'}$ is given by
Physics · Magnetics · MCQ
Q65.In a series $L C R$ circuit $R = 200Ω$ and the voltage and the frequency of the main supply is $220 V$ and $50 H z$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $3 0^{\circ} .$ On…
Physics · Alternating Current · MCQ
Q66.Two conductors have the same resistance at $0^{\circ} C$ but their temperature coefficients of resistance are $α_{1}$ and $α_{2} .$ The respective temperature coefficients of their series and parallel combinations are nearly
Physics · Current Electricity · MCQ
Q67.Let $C$ be the capacitance of a capacitor discharging through a resistor $R .$ Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to…
Physics · Capacitor · MCQ
Q68.A thin semi-circular ring of radius $r$ has a positive charges $q$ distributed uniformly over it. The net field $E$ at the center $O$ is Includes diagram
Physics · Electrostatics · MCQ
Q69.Let there be a spherically symmetric charge distribution with charge density varying as $ρ (r) = ρ_{0} (\frac{5}{4} - \frac{r}{R})$ upto $r = R,$ and $ρ (r) = 0$ for $r > R,$ where $r$ …
Physics · Electrostatics · MCQ
Q70.The equation of a wave on a string of linear mass density $0.04 k g m^{- 1}$ is given by $y = 0.02 (m) sin [2 π (\frac{t}{0.04 ( s )} - \frac{x}{0.50 ( m )})] .$ The…
Physics · Waves · MCQ
Q71.A ball is made of a material of density $ρ$ where $ρ_{o i l} < ρ < ρ_{w a t er}$ with $ρ_{o i l}$ and $ρ_{w a t er}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If…
Physics · Properties of Matter · MCQ
Q72.Two fixed frictionless inclined planes making an angle $3 0^{\circ}$ and $6 0^{\circ}$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with… Includes diagram
Physics · Laws of Motion · MCQ
Q73.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $3 0^{\circ}$ with each other. When suspended in a liquid of density $0.8 g c m^{- 3},$ the angle remains the same. If density of the…
Physics · Electrostatics · MCQ
Q74.Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.
Physics · Center of Mass · MCQ
Q75.The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}},$ where $a$ and $b$ are constants and $x$ is the distance…
Physics · Work Power and Energy · MCQ
Q76.For a particle in uniform circular motion the acceleration $a$ at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)
Physics · Circular Motion · MCQ
Q77.A particle is moving with velocity $v = k (y i + x j)$ , where K is a constant. The general equation for its path is
Physics · Motion in A Plane · MCQ
Q78.The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $\times$ 10–3 are
Physics · Units and Measurements · MCQ