2018 · Shift 0

71 questions · JEE Main

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JEE Main
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2018 · Shift 0

2018 · Shift 0

71 questions · JEE Main

Chemistry26 questions Mathematics18 questions Physics27 questions

Q1.The increasing order of basicity of the following compounds is : Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q2.An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?
Chemistry · Ionic Equilibrium · MCQ
Q3.The predominant form of histamine present in human blood is (pKa, Histidine = 6.0)
Chemistry · Biomolecules · MCQ
Q4.Glucose on prolonged heating with HI gives
Chemistry · Biomolecules · MCQ
Q5.The major product formed in the following reaction is : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q6.Phenol reacts with methyl chloroformate in the presence of $N a O H$ to form product A. A reacts with $B r_{2}$ to form product B. A and B are respectively :
Chemistry · Alcohols Phenols and Ethers · MCQ
Q7.Phenol on treatment with $C O_{2}$ in the presence of $N a O H$ followed by acidification produces compound X as the major product. X on treatment with $(C H_{3} C O)_{2} O$ in the presence of catalytic amount of $H_{2} S O_{4}$ produces:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q8.The trans-alkenes are formed by the reduction of alkynes with
Chemistry · Hydrocarbons · MCQ
Q9.The major product of the following reaction is: Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q10.Which of the following compounds will be suitable for Kjeldahl’s method for nitrogen estimation?
Chemistry · Practical Organic Chemistry · MCQ
Q11.The compound that does not produce nitrogen gas by the thermal decomposition is :
Chemistry · P Block Elements · MCQ
Q12.The oxidation states of Cr in $[C r (H_{2} O)_{6}] C l_{3}$ , $[C r (C_{6} H_{6})_{2}]$ and $K_{2} [C r (C N)_{2} (O)_{2} (O_{2}) (N H_{3})]$ respectively are :
Chemistry · Coordination Compounds · MCQ
Q13.Consider the following reaction and statements: $[C o (N H_{3})_{4} B r_{2}]^{+}$ + $B r^{-}$ $\to$ $[C o (N H_{3})_{3} B r_{3}]$ + $N H_{3}$ (I) Two isomers are produced if the reactant complex ion is a cis-isomer (II) Two isomers are produced if the reactant complex…
Chemistry · Coordination Compounds · MCQ
Q14.Which of the following compounds contain(s) no covalent bond(s)? $K C l$ , $P H_{3}$ , $O_{2}$ , $B_{2} H_{6}$ , $H_{2} S O_{4}$
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q15.How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B = 10.8 u)
Chemistry · Electrochemistry · MCQ
Q16.At 518oC the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr, was 1.00 Torr s–1 when 5% had reacted and 0.5 Torr s–1 when 33% had reacted. The order of the reaction is
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q17.Which of the following salts is the most basic in aqueous solution?
Chemistry · Ionic Equilibrium · MCQ
Q18.Which of the following are Lewis acids?
Chemistry · Ionic Equilibrium · MCQ
Q19.An aqueous solution contains 0.10 M $H_{2} S$ and 0.20 M $H C l$ . If the equilibrium constants for the formation of $H S^{-}$ from $H_{2} S$ is 1.0 $\times$ 10–7 and that of $S^{2 -}$ from $H S^{-}$ ions is 1.2 $\times$ 10–13 then the concentration of $S^{2 -}$ …
Chemistry · Ionic Equilibrium · MCQ
Q20.An aqueous solution contains an unknown concentration of $B a^{2 +}$ . When 50 mL of a 1 M solution of $N a_{2} S O_{4}$ is added, $B a S O_{4}$ just begins to precipitate. The final volume is 500 mL. The solubility product of $B a S O_{4}$ is 1 $\times$ …
Chemistry · Ionic Equilibrium · MCQ
Q21.For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?
Chemistry · Solutions · MCQ
Q22.Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction? Includes diagram
Chemistry · Thermodynamics · MCQ
Q23.The combustion of benzene(l) gives $C O_{2}$ (g) and $H_{2} O$ (l). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol–1 at 25oC; heat of combustion (in kJ mol–1) of benzene at constant pressure will be : (R = 8.314 JK–1…
Chemistry · Thermodynamics · MCQ
Q24.Total number of lone pair of electrons in $I_{3}^{-}$ ion is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q25.According to molecular orbital theory, which of the following will not be a viable molecule?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q26.The ratio of mass percent of C and H of an organic compound ( $C_{X} H_{Y} O_{Z}$ ) is 6 : 1. If one molecule of the above compound ( $C_{X} H_{Y} O_{Z}$ ) contains half as much oxygen as required to burn one molecule of compound $C_{X} H_{Y}$ completely to $C O_{2}$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q27.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. The number of such arrangements is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let S = { $x \in$ R : $x \geq$ 0 and $2 ∣ x - 3 ∣ + x (x - 6) + 6 = 0$ }. Then S
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.If $α, β \in C$ are the distinct roots of the equation x2 - x + 1 = 0, then $α^{101} + β^{107}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q30.If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then $\frac{x z}{y ^{2}}$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q31.If $x - 4 2 x 2 x 2 x x - 4 2 x 2 x 2 x x - 4 = (A + B x) (x - A)^{2}$ then the ordered pair (A, B) is…
Mathematics · Matrices and Determinants · MCQ
Q32.Two sets A and B are as under : A = {( $a$ , b) $\in$ R $\times$ R : | $a$ - 5| < 1 and |b - 5| < 1}; B = {( $a$ , b) $\in$ R $\times$ R : 4( $a$ - 6)2 + 9(b - 5)2 $\leq$ 36 }; Then
Mathematics · Sets and Relations · MCQ
Q33.Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ......... , $a_{49}$ be in A.P. such that $k = 0 \sum 12 a_{4 k + 1} = 416$ and $a_{9} + a_{43} = 66$ . $a_{1}^{2} + a_{2}^{2} + ....... + a_{17}^{2} = 140 m$ , then m is equal to
Mathematics · Sequences and Series · MCQ
Q34.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,…
Mathematics · Probability · MCQ
Q35.If $i = 1 \sum 9 (x_{i} - 5) = 9$ and $i = 1 \sum 9 (x_{i} - 5)^{2} = 45$ , then the standard deviation of the 9 items $x_{1}, x_{2}, ......., x_{9}$ is
Mathematics · Statistics · MCQ
Q36.Let $u$ be a vector coplanar with the vectors $a = 2 i + 3 j - k$ and $b = j + k$ . If $u$ is perpendicular to $a$ …
Mathematics · Vector Algebra · MCQ
Q37.A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let y = y(x) be the solution of the differential equation $sin x \frac{d y}{d x} + y cos x = 4 x$ , $x \in (0, π)$ . If $y (\frac{π}{2}) = 0$ , then $y (\frac{π}{6})$ is equal to :
Mathematics · Differential Equations · MCQ
Q39.The integral $\int \frac{s i n ^{2} x c o s ^{2} x}{( s i n ^{5} x + c o s ^{3} x s i n ^{2} x + s i n ^{3} x c o s ^{2} x + c o s ^{5} x ) ^{2}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q40.The value of $- π /2 \int π /2 \frac{s i n ^{2} x}{1 + 2 ^{x}} d x$ is
Mathematics · Definite Integration · MCQ
Q41.Let g(x) = cosx2, f(x) = $x$ and $α, β (α < β)$ be the roots of the quadratic equation 18x2 - 9 $π$ x + $π^{2}$ = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the…
Mathematics · Area Under the Curves · MCQ
Q42.Let S = { t $\in R : f (x) = ∣ x - π ∣ . (e^{∣ x ∣} - 1) sin ∣ x ∣$ is not differentiable at t}, then the set S is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let $f (x) = x^{2} + \frac{1}{x ^{2}}$ and $g (x) = x - \frac{1}{x}$ , $x \in R - {- 1, 0, 1}$ . If $h (x) = \frac{f ( x )}{g ( x )}$ , then the local…
Mathematics · Application of Derivatives · MCQ
Q44.For each t $\in R$ , let [t] be the greatest integer less than or equal to t. Then $x \to 0^{+} lim x ([\frac{1}{x}] + [\frac{2}{x}] + ..... + [\frac{15}{x}])$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $\times$ 103 kg/m3 and its Young’s modulus is 9.27 $\times$ 1010 Pa. What will be the fundamental frequency…
Physics · Waves · MCQ
Q46.The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $μ$ m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes…
Physics · Wave Optics · MCQ
Q47.An EM wave from air enters a medium. The electric fields are $E_{1}$ = $E_{01} x cos [2 π v (\frac{z}{c} - t)]$ in air and $E_{2}$ = $E_{02} x cos [k (2 z - c t)]$ …
Physics · Electromagnetic Waves · MCQ
Q48.In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20 sin $(30 t - \frac{π}{4})$ In one cycle of a.c., the average power consumed by the circuit and the wattless current are,…
Physics · Alternating Current · MCQ
Q49.The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$ …
Physics · Magnetics · MCQ
Q50.An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r $_{α}$ respectively in a uniform magnetic field B. The relation between re, rp, r $_{α}$ is:
Physics · Magnetics · MCQ
Q51.On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k $Ω$ . How much was the resistance on the left slot before interchanging the…
Physics · Current Electricity · MCQ
Q52.Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $Ω$ . The internal resistances of the two batteries are 1 $Ω$ and 2 $Ω$ respectively. The voltage across the load lies between :
Physics · Current Electricity · MCQ
Q53.Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $+ σ$ , $- σ$ and $+ σ$ respectively. The potential of shell B is :
Physics · Electrostatics · MCQ
Q54.A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :
Physics · Capacitor · MCQ
Q55.A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02…
Physics · Simple Harmonic Motion · MCQ
Q56.Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The…
Physics · Wave Optics · MCQ
Q57.The mass of a hydrogen molecule is 3.32 $\times$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on…
Physics · Center of Mass · MCQ
Q58.Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.
Physics · Heat and Thermodynamics · MCQ
Q59.A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then :
Physics · Gravitation · MCQ
Q60.From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre… Includes diagram
Physics · Rotational Motion · MCQ
Q61.A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - \frac{k}{2 r ^{2}}$ Its total energy is:
Physics · Work Power and Energy · MCQ
Q62.A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical…
Physics · Properties of Matter · MCQ
Q63.Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is : Includes diagram
Physics · Rotational Motion · MCQ
Q64.In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between…
Physics · Center of Mass · MCQ
Q65.Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on… Includes diagram
Physics · Laws of Motion · MCQ
Q66.All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Physics · Motion in A Straight Line · MCQ
Q67.The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the…
Physics · Units and Measurements · MCQ
Q68.The reading of the ammeter for a silicon diode in the given circuit is : Includes diagram
Physics · Electronic Devices · MCQ
Q69.If the series limit frequency of the Lyman series is $u_{L}$ , then the series limit frequency of the Pfund series is:
Physics · Atoms and Nuclei · MCQ
Q70.It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of…
Physics · Atoms and Nuclei · MCQ
Q71.An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $λ_{n}$ , $λ_{g}$ be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let $Λ_{n}$ …
Physics · Atoms and Nuclei · MCQ

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2018 · Shift 0

71 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
2018 · Shift 0

2018 · Shift 0

71 questions · JEE Main

Chemistry26 questions Mathematics18 questions Physics27 questions

Q1.The increasing order of basicity of the following compounds is : Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q2.An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination?
Chemistry · Ionic Equilibrium · MCQ
Q3.The predominant form of histamine present in human blood is (pKa, Histidine = 6.0)
Chemistry · Biomolecules · MCQ
Q4.Glucose on prolonged heating with HI gives
Chemistry · Biomolecules · MCQ
Q5.The major product formed in the following reaction is : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q6.Phenol reacts with methyl chloroformate in the presence of $N a O H$ to form product A. A reacts with $B r_{2}$ to form product B. A and B are respectively :
Chemistry · Alcohols Phenols and Ethers · MCQ
Q7.Phenol on treatment with $C O_{2}$ in the presence of $N a O H$ followed by acidification produces compound X as the major product. X on treatment with $(C H_{3} C O)_{2} O$ in the presence of catalytic amount of $H_{2} S O_{4}$ produces:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q8.The trans-alkenes are formed by the reduction of alkynes with
Chemistry · Hydrocarbons · MCQ
Q9.The major product of the following reaction is: Includes diagram
Chemistry · Haloalkanes and Haloarenes · MCQ
Q10.Which of the following compounds will be suitable for Kjeldahl’s method for nitrogen estimation?
Chemistry · Practical Organic Chemistry · MCQ
Q11.The compound that does not produce nitrogen gas by the thermal decomposition is :
Chemistry · P Block Elements · MCQ
Q12.The oxidation states of Cr in $[C r (H_{2} O)_{6}] C l_{3}$ , $[C r (C_{6} H_{6})_{2}]$ and $K_{2} [C r (C N)_{2} (O)_{2} (O_{2}) (N H_{3})]$ respectively are :
Chemistry · Coordination Compounds · MCQ
Q13.Consider the following reaction and statements: $[C o (N H_{3})_{4} B r_{2}]^{+}$ + $B r^{-}$ $\to$ $[C o (N H_{3})_{3} B r_{3}]$ + $N H_{3}$ (I) Two isomers are produced if the reactant complex ion is a cis-isomer (II) Two isomers are produced if the reactant complex…
Chemistry · Coordination Compounds · MCQ
Q14.Which of the following compounds contain(s) no covalent bond(s)? $K C l$ , $P H_{3}$ , $O_{2}$ , $B_{2} H_{6}$ , $H_{2} S O_{4}$
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q15.How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B = 10.8 u)
Chemistry · Electrochemistry · MCQ
Q16.At 518oC the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr, was 1.00 Torr s–1 when 5% had reacted and 0.5 Torr s–1 when 33% had reacted. The order of the reaction is
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q17.Which of the following salts is the most basic in aqueous solution?
Chemistry · Ionic Equilibrium · MCQ
Q18.Which of the following are Lewis acids?
Chemistry · Ionic Equilibrium · MCQ
Q19.An aqueous solution contains 0.10 M $H_{2} S$ and 0.20 M $H C l$ . If the equilibrium constants for the formation of $H S^{-}$ from $H_{2} S$ is 1.0 $\times$ 10–7 and that of $S^{2 -}$ from $H S^{-}$ ions is 1.2 $\times$ 10–13 then the concentration of $S^{2 -}$ …
Chemistry · Ionic Equilibrium · MCQ
Q20.An aqueous solution contains an unknown concentration of $B a^{2 +}$ . When 50 mL of a 1 M solution of $N a_{2} S O_{4}$ is added, $B a S O_{4}$ just begins to precipitate. The final volume is 500 mL. The solubility product of $B a S O_{4}$ is 1 $\times$ …
Chemistry · Ionic Equilibrium · MCQ
Q21.For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?
Chemistry · Solutions · MCQ
Q22.Which of the following lines correctly show the temperature dependence of equilibrium constant K, for an exothermic reaction? Includes diagram
Chemistry · Thermodynamics · MCQ
Q23.The combustion of benzene(l) gives $C O_{2}$ (g) and $H_{2} O$ (l). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol–1 at 25oC; heat of combustion (in kJ mol–1) of benzene at constant pressure will be : (R = 8.314 JK–1…
Chemistry · Thermodynamics · MCQ
Q24.Total number of lone pair of electrons in $I_{3}^{-}$ ion is
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q25.According to molecular orbital theory, which of the following will not be a viable molecule?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q26.The ratio of mass percent of C and H of an organic compound ( $C_{X} H_{Y} O_{Z}$ ) is 6 : 1. If one molecule of the above compound ( $C_{X} H_{Y} O_{Z}$ ) contains half as much oxygen as required to burn one molecule of compound $C_{X} H_{Y}$ completely to $C O_{2}$ …
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q27.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. The number of such arrangements is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let S = { $x \in$ R : $x \geq$ 0 and $2 ∣ x - 3 ∣ + x (x - 6) + 6 = 0$ }. Then S
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.If $α, β \in C$ are the distinct roots of the equation x2 - x + 1 = 0, then $α^{101} + β^{107}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q30.If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then $\frac{x z}{y ^{2}}$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q31.If $x - 4 2 x 2 x 2 x x - 4 2 x 2 x 2 x x - 4 = (A + B x) (x - A)^{2}$ then the ordered pair (A, B) is…
Mathematics · Matrices and Determinants · MCQ
Q32.Two sets A and B are as under : A = {( $a$ , b) $\in$ R $\times$ R : | $a$ - 5| < 1 and |b - 5| < 1}; B = {( $a$ , b) $\in$ R $\times$ R : 4( $a$ - 6)2 + 9(b - 5)2 $\leq$ 36 }; Then
Mathematics · Sets and Relations · MCQ
Q33.Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ......... , $a_{49}$ be in A.P. such that $k = 0 \sum 12 a_{4 k + 1} = 416$ and $a_{9} + a_{43} = 66$ . $a_{1}^{2} + a_{2}^{2} + ....... + a_{17}^{2} = 140 m$ , then m is equal to
Mathematics · Sequences and Series · MCQ
Q34.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,…
Mathematics · Probability · MCQ
Q35.If $i = 1 \sum 9 (x_{i} - 5) = 9$ and $i = 1 \sum 9 (x_{i} - 5)^{2} = 45$ , then the standard deviation of the 9 items $x_{1}, x_{2}, ......., x_{9}$ is
Mathematics · Statistics · MCQ
Q36.Let $u$ be a vector coplanar with the vectors $a = 2 i + 3 j - k$ and $b = j + k$ . If $u$ is perpendicular to $a$ …
Mathematics · Vector Algebra · MCQ
Q37.A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let y = y(x) be the solution of the differential equation $sin x \frac{d y}{d x} + y cos x = 4 x$ , $x \in (0, π)$ . If $y (\frac{π}{2}) = 0$ , then $y (\frac{π}{6})$ is equal to :
Mathematics · Differential Equations · MCQ
Q39.The integral $\int \frac{s i n ^{2} x c o s ^{2} x}{( s i n ^{5} x + c o s ^{3} x s i n ^{2} x + s i n ^{3} x c o s ^{2} x + c o s ^{5} x ) ^{2}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q40.The value of $- π /2 \int π /2 \frac{s i n ^{2} x}{1 + 2 ^{x}} d x$ is
Mathematics · Definite Integration · MCQ
Q41.Let g(x) = cosx2, f(x) = $x$ and $α, β (α < β)$ be the roots of the quadratic equation 18x2 - 9 $π$ x + $π^{2}$ = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the…
Mathematics · Area Under the Curves · MCQ
Q42.Let S = { t $\in R : f (x) = ∣ x - π ∣ . (e^{∣ x ∣} - 1) sin ∣ x ∣$ is not differentiable at t}, then the set S is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let $f (x) = x^{2} + \frac{1}{x ^{2}}$ and $g (x) = x - \frac{1}{x}$ , $x \in R - {- 1, 0, 1}$ . If $h (x) = \frac{f ( x )}{g ( x )}$ , then the local…
Mathematics · Application of Derivatives · MCQ
Q44.For each t $\in R$ , let [t] be the greatest integer less than or equal to t. Then $x \to 0^{+} lim x ([\frac{1}{x}] + [\frac{2}{x}] + ..... + [\frac{15}{x}])$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $\times$ 103 kg/m3 and its Young’s modulus is 9.27 $\times$ 1010 Pa. What will be the fundamental frequency…
Physics · Waves · MCQ
Q46.The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 $μ$ m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young’s fringes…
Physics · Wave Optics · MCQ
Q47.An EM wave from air enters a medium. The electric fields are $E_{1}$ = $E_{01} x cos [2 π v (\frac{z}{c} - t)]$ in air and $E_{2}$ = $E_{02} x cos [k (2 z - c t)]$ …
Physics · Electromagnetic Waves · MCQ
Q48.In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20 sin $(30 t - \frac{π}{4})$ In one cycle of a.c., the average power consumed by the circuit and the wattless current are,…
Physics · Alternating Current · MCQ
Q49.The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$ …
Physics · Magnetics · MCQ
Q50.An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r $_{α}$ respectively in a uniform magnetic field B. The relation between re, rp, r $_{α}$ is:
Physics · Magnetics · MCQ
Q51.On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k $Ω$ . How much was the resistance on the left slot before interchanging the…
Physics · Current Electricity · MCQ
Q52.Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $Ω$ . The internal resistances of the two batteries are 1 $Ω$ and 2 $Ω$ respectively. The voltage across the load lies between :
Physics · Current Electricity · MCQ
Q53.Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $+ σ$ , $- σ$ and $+ σ$ respectively. The potential of shell B is :
Physics · Electrostatics · MCQ
Q54.A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :
Physics · Capacitor · MCQ
Q55.A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02…
Physics · Simple Harmonic Motion · MCQ
Q56.Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The…
Physics · Wave Optics · MCQ
Q57.The mass of a hydrogen molecule is 3.32 $\times$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on…
Physics · Center of Mass · MCQ
Q58.Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.
Physics · Heat and Thermodynamics · MCQ
Q59.A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then :
Physics · Gravitation · MCQ
Q60.From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre… Includes diagram
Physics · Rotational Motion · MCQ
Q61.A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - \frac{k}{2 r ^{2}}$ Its total energy is:
Physics · Work Power and Energy · MCQ
Q62.A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical…
Physics · Properties of Matter · MCQ
Q63.Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is : Includes diagram
Physics · Rotational Motion · MCQ
Q64.In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between…
Physics · Center of Mass · MCQ
Q65.Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on… Includes diagram
Physics · Laws of Motion · MCQ
Q66.All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
Physics · Motion in A Straight Line · MCQ
Q67.The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the…
Physics · Units and Measurements · MCQ
Q68.The reading of the ammeter for a silicon diode in the given circuit is : Includes diagram
Physics · Electronic Devices · MCQ
Q69.If the series limit frequency of the Lyman series is $u_{L}$ , then the series limit frequency of the Pfund series is:
Physics · Atoms and Nuclei · MCQ
Q70.It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of…
Physics · Atoms and Nuclei · MCQ
Q71.An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $λ_{n}$ , $λ_{g}$ be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let $Λ_{n}$ …
Physics · Atoms and Nuclei · MCQ