2009 · Shift 0

76 questions · JEE Main

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JEE Main
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2009 · Shift 0

2009 · Shift 0

76 questions · JEE Main

Chemistry25 questions Mathematics22 questions Physics29 questions

Q1.A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?
Chemistry · Solutions · MCQ
Q2.The number of stereoisomers possible for a compound of the molecular formula $C H_{3}$ - $C H$ = $C H$ - $C H (O H)$ - Me is :
Chemistry · Basics of Organic Chemistry · MCQ
Q3.The alkene that exhibits geometrical isomerism is :
Chemistry · Basics of Organic Chemistry · MCQ
Q4.The IUPAC name of neopentane is
Chemistry · Basics of Organic Chemistry · MCQ
Q5.Arrange the carbanions, $(C H_{3})_{3} \overline{C}$ , $\overline{C} C l_{3}$ , $(C H_{3})_{2} \overline{C} H$ , $C_{6} H_{5} \overline{C} H_{2}$ in order of their decreasing stability :
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Solid $B a (N O_{3})_{2}$ is gradually dissolved in a 1.0 $\times$ 10-4 M $N a_{2} C O_{3}$ solution. At what concentration of $B a^{2 +}$ will a precipitate begin to form ? (Ksp for $B a C O_{3}$ = 5.1 $\times$ 10−9 )
Chemistry · Ionic Equilibrium · MCQ
Q7.On the basis of the following thermochemical data : ( $Δ_{f} G^{o} H_{(a q)}^{+}$ = 0) $H_{2} O$ (l) $\to$ $H^{+}$ (aq) + $O H^{-}$ (aq); $Δ H$ = 57.32 kJ $H_{2}$ (g) + $\frac{1}{2} O_{2} (g) \to$ $H_{2} O$ (l); $Δ H$ = -286.20 kJ The value of enthalpy of…
Chemistry · Thermodynamics · MCQ
Q8.Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the…
Chemistry · Solutions · MCQ
Q9.In Cannizzaro reaction given below $2 PhCHO^{(-)} OH PhCH_{2} OH + PhCOO^{-}$ the slowest step is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q10.The set representing the correct order of ionic radius is :
Chemistry · Periodic Table and Periodicity · MCQ
Q11.The two functional groups present in a typical carbohydrate are
Chemistry · Biomolecules · MCQ
Q12.Which of the following on heating with aqueous KOH, produces acetaldehyde ?
Chemistry · Haloalkanes and Haloarenes · MCQ
Q13.A liquid was mixed with ethanol and a drop of concentrated $H_{2} S O_{4}$ was added. A compound with a fruity smell was formed. The liquid was :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is :
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.Which of the following has an optical isomer ?
Chemistry · Coordination Compounds · MCQ
Q16.Which of the following pairs represents linkage isomers ?
Chemistry · Coordination Compounds · MCQ
Q17.Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect?
Chemistry · D and F Block Elements · MCQ
Q18.In context with the transition elements, which of the following statements is incorrect ?
Chemistry · D and F Block Elements · MCQ
Q19.The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2=0.301) :
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q20.In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $C H_{3} O H$ (l) + 3/2 $O_{2}$ $\to$ $C O_{2}$ (g) + 2 $H_{2} O$ (l) At 298K standard Gibb’s energies of formation for $C H_{3} O H$ (l), $H_{2} O$ (l) and $C O_{2}$ (g)…
Chemistry · Electrochemistry · MCQ
Q21.Given : $E_{F e^{3 +} / F e}^{o}$ = -0.036V; $E_{F e^{2 +} / F e}^{o}$ = -0.439 V The value of standard electrode potential for the change, $F e^{3 +}$ (aq) + e- $\to$ $F e^{2 +}$ (aq) will be
Chemistry · Electrochemistry · MCQ
Q22.Using MO theory, predict which of the following species has the shortest bond length?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q23.In which of the following arrangements, the sequence is not strictly according to the property written against it
Chemistry · Periodic Table and Periodicity · MCQ
Q24.In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 $\times$ 10-34 kg m2s-1, mass of electron, em = 9.1 $\times$ 10-31 kg)
Chemistry · Structure of Atom · MCQ
Q25.Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 103 ms−1 (Mass of proton = 1.67 $\times$ 10-27 kg and h = 6.63 $\times$ 10-34 Js) :
Chemistry · Structure of Atom · MCQ
Q26.Statement - 1 : The variance of first n even natural numbers is $\frac{n ^{2} - 1}{4}$ Statement - 2 : The sum of first n natural numbers is $\frac{n ( n + 1 )}{2}$ and the sum of squares of first n natural numbers is $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ …
Mathematics · Statistics · MCQ
Q27.If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
Mathematics · Statistics · MCQ
Q28.For real x, let f(x) = x3 + 5x + 1, then
Mathematics · Functions · MCQ
Q29.Let $f (x) = (x + 1)^{2} - 1, x \geq - 1$ Statement - 1 : The set ${x : f (x) = f^{- 1} (x)} = {0, - 1}$ . Statement - 2 : $f$ is a bijection.
Mathematics · Functions · MCQ
Q30.If $z - \frac{4}{z} = 2,$ then the maximum value of $∣ z ∣$ is equal to :
Mathematics · Complex Numbers · MCQ
Q31.Let $y$ be an implicit function of $x$ defined by $x^{2 x} - 2 x^{x} cot y - 1 = 0$ . Then $y^{'} (1)$ equals
Mathematics · Differentiation · MCQ
Q32.One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ...., 49.$ Then the probability that the sum of the digits on the selected ticket is $8$ , given that the product of these digits is zer, equals :
Mathematics · Probability · MCQ
Q33. $0 \int π [cot x] d x,$ where $[.]$ denotes the greatest integer function, is equal to:
Mathematics · Definite Integration · MCQ
Q34.The area of the region bounded by the parabola $(y - 2)^{2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q35.Let $a, b, c$ be such that $b (a + c) e 0$ if $a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 + a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q36.Given $P (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $x = 0$ is the only real root of $P^{'} (x) = 0.$ If $P (- 1) < P (1),$ then in the interval $[- 1, 1] :$
Mathematics · Application of Derivatives · MCQ
Q37.Let $f (x) = x ∣ x ∣$ and $g (x) = sin x .$ Statement-1: gof is differentiable at $x = 0$ and its derivative is continuous at that point. Statement-2: gof is twice differentiable at $x = 0$ .
Mathematics · Limits Continuity and Differentiability · MCQ
Q38.The ellipse $x^{2} + 4 y^{2} = 4$ is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point $(4, 0)$ . Then the equation of the ellipse is :
Mathematics · Ellipse · MCQ
Q39.Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the…
Mathematics · Circle · MCQ
Q40.The lines $p (p^{2} + 1) x - y + q = 0$ and $(p^{2} + 1)^{2} x + (p^{2} + 1) y + 2 q$ $= 0$ are perpendicular to a common line for :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.The shortest distance between the line $y - x = 1$ and the curve $x = y^{2}$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.The remainder left out when $8^{2 n} - (62)^{2 n + 1}$ is divided by 9 is :
Mathematics · Binomial Theorem · MCQ
Q43.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q44.If the roots of the equation $b x^{2} + c x + a = 0$ imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q45.Let A and B denote the statements A: $cos α + cos β + cos γ = 0$ B: $sin α + sin β + sin γ = 0$ If $cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2},$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are :
Mathematics · 3D Geometry · MCQ
Q47.If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then :
Mathematics · Sets and Relations · MCQ
Q48.The logic circuit shown below has the input waveforms $^{'} A^{'}$ and $^{'} B^{'}$ as shown. Pick out the correct output waveform. Output is Includes diagram
Physics · Electronic Devices · MCQ
Q49.A $p$ - $n$ junction $(D)$ shown in the figure can act as a rectifier. An alternating current source $(V)$ is connected in the circuit. The current $(I)$ in the resistor $(R)$ can be shown by : Includes diagram
Physics · Electronic Devices · MCQ
Q50.The above is a plot of binding energy per nucleon $E_{b},$ against the nuclear mass $M; A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions : $(i) A + B \to C + ε (ii) C \to A + B + ε (iii) D + E \to F + ε (i v) F \to D + E + ε,$ … Includes diagram
Physics · Atoms and Nuclei · MCQ
Q51.The surface of a metal is illuminated with the light of $400 nm .$ The kinetic energy of the ejected photoelectrons was found to be $1.68 e V .$ The work function of the metal is : $(h c = 1240 e V . nm)$
Physics · Dual Nature of Radiation · MCQ
Q52.The transition from the state $n = 4$ to $n = 3$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :
Physics · Atoms and Nuclei · MCQ
Q53.A transparent solid cylindrical rod has a refractive index of $\frac{2}{3} .$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $θ$ for which the… Includes diagram
Physics · Geometrical Optics · MCQ
Q54.An inductor of inductance $L = 400 m H$ and resistors of resistance $R_{1} = 2Ω$ and $R_{2} = 2Ω$ are connected to a battery of $e m f 12 V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is… Includes diagram
Physics · Alternating Current · MCQ
Q55.In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and…
Physics · Geometrical Optics · MCQ
Q56.A mixture of light, consisting of wavelength $590 nm$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it…
Physics · Wave Optics · MCQ
Q57.A current loop $A B C D$ is held fixed on the plane of the paper as shown in the figure. The arcs $B C$ (radius $= b$ ) and $D A$ (radius $= a$ ) of the loop are joined by two straight wires $A B$ and $C D$ . A steady current $I$ is flowing in the… Includes diagram
Physics · Magnetics · MCQ
Q58.A current loop $A B C D$ is held fixed on the plane of the paper as shown in the figure. The arcs $B C$ (radius $= b$ ) and $D A$ (radius $= a$ ) of the loop are joined by two straight wires $A B$ and $C D$ . A steady current $I$ is flowing in the… Includes diagram
Physics · Magnetics · MCQ
Q59.Two points $P$ and $Q$ are maintained at the potentials of $10 V$ and $- 4 V$ , respectively. The work done in moving $100$ electrons from $P$ to $Q$ is :
Physics · Electrostatics · MCQ
Q60.Consider a rubber ball freely falling from a height $h = 4.9 m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time…
Physics · Motion in A Straight Line · MCQ
Q61.(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.) Statement-1 : For a charged particle moving from point $P$ to point $Q$ , the net…
Physics · Electrostatics · MCQ
Q62.A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q / q$ equals:
Physics · Electrostatics · MCQ
Q63.Let $P (r) = \frac{Q}{π R ^{4}} r$ be the change density distribution for a solid sphere of radius $R$ and total charge $Q$ . For a point $^{'} p^{'}$ inside the sphere at distance $r_{1}$ from the center of the sphere, the…
Physics · Electrostatics · MCQ
Q64.Three sound waves of equal amplitudes have frequencies $(v - 1), v, (v + 1) .$ They superpose to give beats. The number of beats produced per second will be :
Physics · Waves · MCQ
Q65.If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?
Physics · Simple Harmonic Motion · MCQ
Q66.Two moles of helium gas are taken over the cycle $A B C D$ , as shown in the $P$ - $T$ diagram. The net work done on the gas in the cycle $A B C D A$ is: Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q67.Two moles of helium gas are taken over the cycle $A B C D,$ as shown in the $P$ - $T$ diagram. The work done on the gas in taking it from $D$ to $A$ is : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q68.Two moles of helium gas are taken over the cycle $A B C D,$ as shown in the $P$ - $T$ diagram. Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q69.A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $θ$ along the length $x$ of the bar from its hot end is best described by which of the following figures?
Physics · Heat and Thermodynamics · MCQ
Q70.One $k g$ of a diatomic gas is at a pressure of $8 \times 1 0^{4} N / m^{2} .$ The density of the gas is $4 k g / m^{3}$ . What is the energy of the gas due to its thermal motion ?
Physics · Heat and Thermodynamics · MCQ
Q71.Statement - 1: The temperature dependence of resistance is usually given as $R = R_{0} (1 + α Δ t) .$ The resistance of wire changes from $100Ω$ to $150Ω$ when its temperature is increased from $2 7^{\circ} C$ …
Physics · Heat and Thermodynamics · MCQ
Q72.Two wires are made of the same material and have the same volume. However wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3 A .$ If the length of wire $1$ increases by $Δ x$ on applying force $F,$ how much…
Physics · Properties of Matter · MCQ
Q73.The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g =$ the acceleration due to gravity on the surface of the earth) in terms of $R,$ the radius of the earth, is:
Physics · Gravitation · MCQ
Q74.A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $ω$ . Its center of mass rises to a maximum height of:
Physics · Rotational Motion · MCQ
Q75.A particle has an initial velocity $3 i + 4 j$ and an acceleration of $0.4 i + 0.3 j$ . Its speed after 10 s is:
Physics · Motion in A Plane · MCQ
Q76.In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(= $0. 5^{\circ}$ …
Physics · Units and Measurements · MCQ

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2009 · Shift 0

76 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
2009 · Shift 0

2009 · Shift 0

76 questions · JEE Main

Chemistry25 questions Mathematics22 questions Physics29 questions

Q1.A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?
Chemistry · Solutions · MCQ
Q2.The number of stereoisomers possible for a compound of the molecular formula $C H_{3}$ - $C H$ = $C H$ - $C H (O H)$ - Me is :
Chemistry · Basics of Organic Chemistry · MCQ
Q3.The alkene that exhibits geometrical isomerism is :
Chemistry · Basics of Organic Chemistry · MCQ
Q4.The IUPAC name of neopentane is
Chemistry · Basics of Organic Chemistry · MCQ
Q5.Arrange the carbanions, $(C H_{3})_{3} \overline{C}$ , $\overline{C} C l_{3}$ , $(C H_{3})_{2} \overline{C} H$ , $C_{6} H_{5} \overline{C} H_{2}$ in order of their decreasing stability :
Chemistry · Basics of Organic Chemistry · MCQ
Q6.Solid $B a (N O_{3})_{2}$ is gradually dissolved in a 1.0 $\times$ 10-4 M $N a_{2} C O_{3}$ solution. At what concentration of $B a^{2 +}$ will a precipitate begin to form ? (Ksp for $B a C O_{3}$ = 5.1 $\times$ 10−9 )
Chemistry · Ionic Equilibrium · MCQ
Q7.On the basis of the following thermochemical data : ( $Δ_{f} G^{o} H_{(a q)}^{+}$ = 0) $H_{2} O$ (l) $\to$ $H^{+}$ (aq) + $O H^{-}$ (aq); $Δ H$ = 57.32 kJ $H_{2}$ (g) + $\frac{1}{2} O_{2} (g) \to$ $H_{2} O$ (l); $Δ H$ = -286.20 kJ The value of enthalpy of…
Chemistry · Thermodynamics · MCQ
Q8.Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the…
Chemistry · Solutions · MCQ
Q9.In Cannizzaro reaction given below $2 PhCHO^{(-)} OH PhCH_{2} OH + PhCOO^{-}$ the slowest step is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q10.The set representing the correct order of ionic radius is :
Chemistry · Periodic Table and Periodicity · MCQ
Q11.The two functional groups present in a typical carbohydrate are
Chemistry · Biomolecules · MCQ
Q12.Which of the following on heating with aqueous KOH, produces acetaldehyde ?
Chemistry · Haloalkanes and Haloarenes · MCQ
Q13.A liquid was mixed with ethanol and a drop of concentrated $H_{2} S O_{4}$ was added. A compound with a fruity smell was formed. The liquid was :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is :
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.Which of the following has an optical isomer ?
Chemistry · Coordination Compounds · MCQ
Q16.Which of the following pairs represents linkage isomers ?
Chemistry · Coordination Compounds · MCQ
Q17.Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect?
Chemistry · D and F Block Elements · MCQ
Q18.In context with the transition elements, which of the following statements is incorrect ?
Chemistry · D and F Block Elements · MCQ
Q19.The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2=0.301) :
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q20.In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $C H_{3} O H$ (l) + 3/2 $O_{2}$ $\to$ $C O_{2}$ (g) + 2 $H_{2} O$ (l) At 298K standard Gibb’s energies of formation for $C H_{3} O H$ (l), $H_{2} O$ (l) and $C O_{2}$ (g)…
Chemistry · Electrochemistry · MCQ
Q21.Given : $E_{F e^{3 +} / F e}^{o}$ = -0.036V; $E_{F e^{2 +} / F e}^{o}$ = -0.439 V The value of standard electrode potential for the change, $F e^{3 +}$ (aq) + e- $\to$ $F e^{2 +}$ (aq) will be
Chemistry · Electrochemistry · MCQ
Q22.Using MO theory, predict which of the following species has the shortest bond length?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q23.In which of the following arrangements, the sequence is not strictly according to the property written against it
Chemistry · Periodic Table and Periodicity · MCQ
Q24.In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 $\times$ 10-34 kg m2s-1, mass of electron, em = 9.1 $\times$ 10-31 kg)
Chemistry · Structure of Atom · MCQ
Q25.Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 103 ms−1 (Mass of proton = 1.67 $\times$ 10-27 kg and h = 6.63 $\times$ 10-34 Js) :
Chemistry · Structure of Atom · MCQ
Q26.Statement - 1 : The variance of first n even natural numbers is $\frac{n ^{2} - 1}{4}$ Statement - 2 : The sum of first n natural numbers is $\frac{n ( n + 1 )}{2}$ and the sum of squares of first n natural numbers is $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ …
Mathematics · Statistics · MCQ
Q27.If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
Mathematics · Statistics · MCQ
Q28.For real x, let f(x) = x3 + 5x + 1, then
Mathematics · Functions · MCQ
Q29.Let $f (x) = (x + 1)^{2} - 1, x \geq - 1$ Statement - 1 : The set ${x : f (x) = f^{- 1} (x)} = {0, - 1}$ . Statement - 2 : $f$ is a bijection.
Mathematics · Functions · MCQ
Q30.If $z - \frac{4}{z} = 2,$ then the maximum value of $∣ z ∣$ is equal to :
Mathematics · Complex Numbers · MCQ
Q31.Let $y$ be an implicit function of $x$ defined by $x^{2 x} - 2 x^{x} cot y - 1 = 0$ . Then $y^{'} (1)$ equals
Mathematics · Differentiation · MCQ
Q32.One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ...., 49.$ Then the probability that the sum of the digits on the selected ticket is $8$ , given that the product of these digits is zer, equals :
Mathematics · Probability · MCQ
Q33. $0 \int π [cot x] d x,$ where $[.]$ denotes the greatest integer function, is equal to:
Mathematics · Definite Integration · MCQ
Q34.The area of the region bounded by the parabola $(y - 2)^{2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q35.Let $a, b, c$ be such that $b (a + c) e 0$ if $a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 + a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q36.Given $P (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ such that $x = 0$ is the only real root of $P^{'} (x) = 0.$ If $P (- 1) < P (1),$ then in the interval $[- 1, 1] :$
Mathematics · Application of Derivatives · MCQ
Q37.Let $f (x) = x ∣ x ∣$ and $g (x) = sin x .$ Statement-1: gof is differentiable at $x = 0$ and its derivative is continuous at that point. Statement-2: gof is twice differentiable at $x = 0$ .
Mathematics · Limits Continuity and Differentiability · MCQ
Q38.The ellipse $x^{2} + 4 y^{2} = 4$ is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point $(4, 0)$ . Then the equation of the ellipse is :
Mathematics · Ellipse · MCQ
Q39.Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(- 1, 0)$ is equal to $\frac{1}{3}$ . Then the…
Mathematics · Circle · MCQ
Q40.The lines $p (p^{2} + 1) x - y + q = 0$ and $(p^{2} + 1)^{2} x + (p^{2} + 1) y + 2 q$ $= 0$ are perpendicular to a common line for :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.The shortest distance between the line $y - x = 1$ and the curve $x = y^{2}$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.The remainder left out when $8^{2 n} - (62)^{2 n + 1}$ is divided by 9 is :
Mathematics · Binomial Theorem · MCQ
Q43.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q44.If the roots of the equation $b x^{2} + c x + a = 0$ imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q45.Let A and B denote the statements A: $cos α + cos β + cos γ = 0$ B: $sin α + sin β + sin γ = 0$ If $cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2},$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are :
Mathematics · 3D Geometry · MCQ
Q47.If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then :
Mathematics · Sets and Relations · MCQ
Q48.The logic circuit shown below has the input waveforms $^{'} A^{'}$ and $^{'} B^{'}$ as shown. Pick out the correct output waveform. Output is Includes diagram
Physics · Electronic Devices · MCQ
Q49.A $p$ - $n$ junction $(D)$ shown in the figure can act as a rectifier. An alternating current source $(V)$ is connected in the circuit. The current $(I)$ in the resistor $(R)$ can be shown by : Includes diagram
Physics · Electronic Devices · MCQ
Q50.The above is a plot of binding energy per nucleon $E_{b},$ against the nuclear mass $M; A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions : $(i) A + B \to C + ε (ii) C \to A + B + ε (iii) D + E \to F + ε (i v) F \to D + E + ε,$ … Includes diagram
Physics · Atoms and Nuclei · MCQ
Q51.The surface of a metal is illuminated with the light of $400 nm .$ The kinetic energy of the ejected photoelectrons was found to be $1.68 e V .$ The work function of the metal is : $(h c = 1240 e V . nm)$
Physics · Dual Nature of Radiation · MCQ
Q52.The transition from the state $n = 4$ to $n = 3$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :
Physics · Atoms and Nuclei · MCQ
Q53.A transparent solid cylindrical rod has a refractive index of $\frac{2}{3} .$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $θ$ for which the… Includes diagram
Physics · Geometrical Optics · MCQ
Q54.An inductor of inductance $L = 400 m H$ and resistors of resistance $R_{1} = 2Ω$ and $R_{2} = 2Ω$ are connected to a battery of $e m f 12 V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is… Includes diagram
Physics · Alternating Current · MCQ
Q55.In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and…
Physics · Geometrical Optics · MCQ
Q56.A mixture of light, consisting of wavelength $590 nm$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it…
Physics · Wave Optics · MCQ
Q57.A current loop $A B C D$ is held fixed on the plane of the paper as shown in the figure. The arcs $B C$ (radius $= b$ ) and $D A$ (radius $= a$ ) of the loop are joined by two straight wires $A B$ and $C D$ . A steady current $I$ is flowing in the… Includes diagram
Physics · Magnetics · MCQ
Q58.A current loop $A B C D$ is held fixed on the plane of the paper as shown in the figure. The arcs $B C$ (radius $= b$ ) and $D A$ (radius $= a$ ) of the loop are joined by two straight wires $A B$ and $C D$ . A steady current $I$ is flowing in the… Includes diagram
Physics · Magnetics · MCQ
Q59.Two points $P$ and $Q$ are maintained at the potentials of $10 V$ and $- 4 V$ , respectively. The work done in moving $100$ electrons from $P$ to $Q$ is :
Physics · Electrostatics · MCQ
Q60.Consider a rubber ball freely falling from a height $h = 4.9 m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time…
Physics · Motion in A Straight Line · MCQ
Q61.(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.) Statement-1 : For a charged particle moving from point $P$ to point $Q$ , the net…
Physics · Electrostatics · MCQ
Q62.A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q / q$ equals:
Physics · Electrostatics · MCQ
Q63.Let $P (r) = \frac{Q}{π R ^{4}} r$ be the change density distribution for a solid sphere of radius $R$ and total charge $Q$ . For a point $^{'} p^{'}$ inside the sphere at distance $r_{1}$ from the center of the sphere, the…
Physics · Electrostatics · MCQ
Q64.Three sound waves of equal amplitudes have frequencies $(v - 1), v, (v + 1) .$ They superpose to give beats. The number of beats produced per second will be :
Physics · Waves · MCQ
Q65.If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?
Physics · Simple Harmonic Motion · MCQ
Q66.Two moles of helium gas are taken over the cycle $A B C D$ , as shown in the $P$ - $T$ diagram. The net work done on the gas in the cycle $A B C D A$ is: Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q67.Two moles of helium gas are taken over the cycle $A B C D,$ as shown in the $P$ - $T$ diagram. The work done on the gas in taking it from $D$ to $A$ is : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q68.Two moles of helium gas are taken over the cycle $A B C D,$ as shown in the $P$ - $T$ diagram. Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q69.A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $θ$ along the length $x$ of the bar from its hot end is best described by which of the following figures?
Physics · Heat and Thermodynamics · MCQ
Q70.One $k g$ of a diatomic gas is at a pressure of $8 \times 1 0^{4} N / m^{2} .$ The density of the gas is $4 k g / m^{3}$ . What is the energy of the gas due to its thermal motion ?
Physics · Heat and Thermodynamics · MCQ
Q71.Statement - 1: The temperature dependence of resistance is usually given as $R = R_{0} (1 + α Δ t) .$ The resistance of wire changes from $100Ω$ to $150Ω$ when its temperature is increased from $2 7^{\circ} C$ …
Physics · Heat and Thermodynamics · MCQ
Q72.Two wires are made of the same material and have the same volume. However wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3 A .$ If the length of wire $1$ increases by $Δ x$ on applying force $F,$ how much…
Physics · Properties of Matter · MCQ
Q73.The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g =$ the acceleration due to gravity on the surface of the earth) in terms of $R,$ the radius of the earth, is:
Physics · Gravitation · MCQ
Q74.A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $ω$ . Its center of mass rises to a maximum height of:
Physics · Rotational Motion · MCQ
Q75.A particle has an initial velocity $3 i + 4 j$ and an acceleration of $0.4 i + 0.3 j$ . Its speed after 10 s is:
Physics · Motion in A Plane · MCQ
Q76.In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(= $0. 5^{\circ}$ …
Physics · Units and Measurements · MCQ