2013 · Shift 0

75 questions · JEE Main

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JEE Main
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2013 · Shift 0

2013 · Shift 0

75 questions · JEE Main

Chemistry26 questions Mathematics21 questions Physics28 questions

Q1.A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0oC. As it does so, it absorbs 208J of heat. The values of q and w for the process will be : (R = 8.314 J/mol K) ( l n…
Chemistry · Thermodynamics · MCQ
Q2.How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?
Chemistry · Ionic Equilibrium · MCQ
Q3.A compound with molecular mass 180 is acylated with $C H_{3} C O C l$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:
Chemistry · Compounds Containing Nitrogen · MCQ
Q4.An organic compound A upon reacting with $N H_{3}$ gives $B .$ On heating $B$ gives $C . C$ in presence of $K O H$ reacts with $B r_{2}$ to given $C H_{3} C H_{2} N H_{2} 2. A$ is :
Chemistry · Compounds Containing Nitrogen · MCQ
Q5.Arrange the following compounds in order of decreasing acidity : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q6.Compound $(A), C_{8} H_{9} B r,$ gives a white precipitate when warmed with alcoholic $A g N O_{3} .$ Oxidation of $(A)$ gives an acid $(B), C_{8} H_{6} O_{4} . (B)$ easily forms anhydride on…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.The order of stability of the following carbocations : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q8.Synthesis of each molecule of glucose in photosynthesis involves:
Chemistry · Biomolecules · MCQ
Q9.The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:
Chemistry · Compounds Containing Nitrogen · MCQ
Q10.An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q11.Which of the following complex species is not expected to exhibit optical isomerism?
Chemistry · Coordination Compounds · MCQ
Q12.Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest $E_{M^{3 +} / M^{2 +}}^{0}$ value?
Chemistry · D and F Block Elements · MCQ
Q13.Which of the following arrangements does not represent the correct order of the property stated against it?
Chemistry · D and F Block Elements · MCQ
Q14.The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be:(R = 8.314 JK–1 mol–1 and log 2 = 0.301)
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q15.Given $E_{C r^{2 +} / C r}^{o}$ = -0.74 V; $E_{M n O_{4}^{-} / M n^{2 +}}^{o}$ = 1.51 V $E_{C r_{2} O_{7}^{2 -} / C r^{3 +}}^{o}$ = 1.33 V; $E_{C l / C l^{-}}^{o}$ = 1.36 V Based on the data given above, strongest oxidising agent will be :
Chemistry · Electrochemistry · MCQ
Q16.The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q17.A solution of (– $l$ ) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small amount of $S b C l_{5}$ , due to the formation of :
Chemistry · Haloalkanes and Haloarenes · MCQ
Q18.In which of the following pairs of molecules/ions, both the species are not likely to exist?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q19.Stability of the species $L i_{2}$ , $L i_{2}^{-}$ and $L i_{2}^{+}$ increases in the order of:
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q20.Which one of the following molecules is expected to exhibit diamagnetic behaviour?
Chemistry · Chemical Bonding and Molecular Structure · Multiple correct
Q21.The first ionization potential of $N a$ is 5.1 eV. The value of electron gain enthalpy of $N a^{+}$ will be:
Chemistry · Periodic Table and Periodicity · MCQ
Q22.Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?
Chemistry · Periodic Table and Periodicity · MCQ
Q23.Energy of an electron is given by $E = - 2.178 \times 1 0^{- 18} J (\frac{Z ^{2}}{n ^{2}})$ . Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be (h = 6.62 × 10−34 Js…
Chemistry · Structure of Atom · MCQ
Q24.Experimentally it was found that a metal oxide has formula $M 0.98 O$ . Metal $M$ , present as $M^{2 +}$ and $M^{3 +}$ in its oxide. Fraction of the metal which exists as $M^{3 +}$ would be
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q25.A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of $C O_{2}$ . The empirical formula of the hydrocarbon is
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q26.Consider the following reaction: $x M n O_{4}^{-} + y C_{2} O_{4}^{2 -}$ + z $H^{+}$ $\to$ x $M n^{2 +}$ + 2y $C O_{2}$ + $\frac{z}{2} H_{2} O$ The value's of x, y and z in the reaction are, respectively :
Chemistry · Redox Reactions · MCQ
Q27.Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $\times$ B having 3 or more elements is :
Mathematics · Permutations and Combinations · MCQ
Q28.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
Mathematics · Statistics · MCQ
Q29. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $x$ is given by $\frac{d p}{d x} = 100 - 12 x .$ If the firm employs $25$ more workers,…
Mathematics · Differential Equations · MCQ
Q31.The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0, x$ -axis, and lying in the first quadrant is :
Mathematics · Area Under the Curves · MCQ
Q32.Statement-1 : The value of the integral $π /6 \int π /3 \frac{d x}{1 + t a n x}$ is equal to $π /6$ Statement-2 : $a \int b f (x) d x = a \int b f (a + b - x) d x .$ …
Mathematics · Definite Integration · MCQ
Q33.If $\int f (x) d x = ψ (x),$ then $\int x^{5} f (x^{3}) d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q34.If $x, y, z$ are in A.P. and $tan^{- 1} x, tan^{- 1} y$ and $tan^{- 1} z$ are also in A.P., then :
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.If $y = sec (tan^{- 1} x),$ then $\frac{d y}{d x}$ at $x = 1$ is equal to :
Mathematics · Differentiation · MCQ
Q36.The equation of the circle passing through the foci of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ , and having centre at $(0, 3)$ is :
Mathematics · Ellipse · MCQ
Q37.The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.A ray of light along $x + 3 y = 3$ gets reflected upon reaching $X$ -axis, the equation of the reflected ray is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.The term independent of $x$ in expansion of $(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}$ is
Mathematics · Binomial Theorem · MCQ
Q40.Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n + 1} - T_{n}$ = 10, then the value of n is :
Mathematics · Permutations and Combinations · MCQ
Q41.If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.The number of values of $k$ , for which the system of equations : $(k + 1) x + 8 y = 4 k k x + (k + 3) y = 3 k - 1$ has no solution, is
Mathematics · Matrices and Determinants · MCQ
Q43.The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$
Mathematics · Application of Derivatives · MCQ
Q44.If z is a complex number of unit modulus and argument $θ$ , then arg $(\frac{1 + z}{1 + z})$ equals :
Mathematics · Complex Numbers · MCQ
Q45.The expression $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A}$ can be written as:
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.If the vectors $A B = 3 i + 4 k$ and $A C = 5 i - 2 j + 4 k$ are the sides of a triangle $A B C,$ then the length of the median through $A$ is :
Mathematics · Vector Algebra · MCQ
Q47.If the lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}$ and $\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar, then $k$ can have :
Mathematics · 3D Geometry · MCQ
Q48.Diameter of a plano-convex lens is $6 c m$ and thickness at the center is $3 mm$ . If speed of light in material of lens is $2 \times 1 0^{8} m / s,$ the focal length of the lens is
Physics · Geometrical Optics · MCQ
Q49.The $I$ - $V$ characteristic of an $L E D$ is
Physics · Electronic Devices · MCQ
Q50.The anode voltage of a photocell is kept fixed. The wavelength $λ$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows :
Physics · Dual Nature of Radiation · MCQ
Q51.In a hydrogen like atom electron make transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1,$ the frequency of radiation emitted is proportional to :
Physics · Atoms and Nuclei · MCQ
Q52.The magnetic field in a travelling electromagnetic wave has a peak value of $20 n T$ . The peak value of electric field strength is :
Physics · Electromagnetic Waves · MCQ
Q53.A diode detector is used to detect an amplitude modulated wave of $60%$ modulation by using a condenser of capacity $250$ picofarad in parallel with a load resistance $100$ kilo $o hm .$ Find the maximum modulated frequency which could be… Includes diagram
Physics · Electronic Devices · MCQ
Q54.The graph between angle of deviation $(δ)$ and angle of incidence $(i)$ for a triangular prism is represented by
Physics · Geometrical Optics · MCQ
Q55.Two coherent point sources $S_{1}$ and $S_{2}$ are separated by a small distance $^{'} d^{'}$ as shown. The fringes obtained on the screen will be Includes diagram
Physics · Wave Optics · MCQ
Q56.In an $L C R$ circuit as shown below both switches are open initially. Now switch $S_{1}$ is closed, $S_{2}$ kept open. ( $q$ is charge on the capacitor and $τ = R C$ is Capacitance time constant). Which of the following statement is correct… Includes diagram
Physics · Alternating Current · MCQ
Q57.A metallic rod of length $^{'} ℓ^{'}$ is tied to a string of length $2 ℓ$ and made to rotate with angular speed $w$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $^{'} B^{'}$ in the region, the $e . m . f$ … Includes diagram
Physics · Electromagnetic Induction · MCQ
Q58.A beam of unpolarised light of intensity $I_{0}$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $4 5^{\circ}$ relative to that of $A$ . The…
Physics · Wave Optics · MCQ
Q59.A circular loop of radius $0.3 c m$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $15 c m .$ If a current of $2.0 A$ flows through the smaller loop, than the flux linked with bigger loop is
Physics · Electromagnetic Induction · MCQ
Q60.Two short bar magnets of length $1 c m$ each have magnetic moments $1.20 A m^{2}$ and $1.00 A m^{2}$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common…
Physics · Magnetic Properties of Matter · MCQ
Q61.This questions has Statement - $I$ and Statement - $I I$ . Of the four choices given after the Statements, choose the one that best describes into two Statements. Statement - $I$ : Higher the range, greater is the…
Physics · Current Electricity · MCQ
Q62.The supply voltage to room is $120 V .$ The resistance of the lead wires is $6Ω$ . A $60 W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240 W$ heater is switched on in parallel to the bulb?
Physics · Current Electricity · MCQ
Q63.Two capacitors $C_{1}$ and $C_{2}$ are charged to $120 V$ and $200 V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then
Physics · Capacitor · MCQ
Q64.A charge $Q$ is uniformly distributed over a long rod $A B$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is Includes diagram
Physics · Electrostatics · MCQ
Q65.Two charges, each equals to $q,$ are kept at $x = - a$ and $x = a$ on the $x$ -axis. A particle of mass $m$ and charge $q_{0} = \frac{q}{2}$ is placed at the origin. If charge $q_{0}$ is given a small displacement $$\left( {y \lt \lt a}…
Physics · Electrostatics · MCQ
Q66.A sonometer wire of length $1.5 m$ is made of steel. The tension in it produces an elastic strain of $1%$ . What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 1 0^{3} k g / m^{3}$ and $2.2 \times 1 0^{11} N / m^{2}$ …
Physics · Waves · MCQ
Q67.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M .$ The piston and the cylinder have equal cross sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and…
Physics · Simple Harmonic Motion · MCQ
Q68.The above $p$ - $v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q69.Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $T,$ density of liquid is…
Physics · Heat and Thermodynamics · MCQ
Q70.A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $σ$ at equilibrium…
Physics · Properties of Matter · MCQ
Q71.What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ?
Physics · Gravitation · MCQ
Q72.A hoop of radius $r$ and mass $m$ rotating with an angular velocity $ω_{0}$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it…
Physics · Rotational Motion · MCQ
Q73.This question has statement $I$ and statement $I I$ . Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $I$ : A point particle of mass $m$ moving with…
Physics · Center of Mass · MCQ
Q74.A projectile is given an initial velocity of $(i + 2 j)$ m/s, where $i$ is along the ground and $j$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:
Physics · Motion in A Plane · MCQ
Q75.Let [ $ε_{0}$ ] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
Physics · Units and Measurements · MCQ

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2013 · Shift 0

75 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
2013 · Shift 0

2013 · Shift 0

75 questions · JEE Main

Chemistry26 questions Mathematics21 questions Physics28 questions

Q1.A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0oC. As it does so, it absorbs 208J of heat. The values of q and w for the process will be : (R = 8.314 J/mol K) ( l n…
Chemistry · Thermodynamics · MCQ
Q2.How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?
Chemistry · Ionic Equilibrium · MCQ
Q3.A compound with molecular mass 180 is acylated with $C H_{3} C O C l$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:
Chemistry · Compounds Containing Nitrogen · MCQ
Q4.An organic compound A upon reacting with $N H_{3}$ gives $B .$ On heating $B$ gives $C . C$ in presence of $K O H$ reacts with $B r_{2}$ to given $C H_{3} C H_{2} N H_{2} 2. A$ is :
Chemistry · Compounds Containing Nitrogen · MCQ
Q5.Arrange the following compounds in order of decreasing acidity : Includes diagram
Chemistry · Alcohols Phenols and Ethers · MCQ
Q6.Compound $(A), C_{8} H_{9} B r,$ gives a white precipitate when warmed with alcoholic $A g N O_{3} .$ Oxidation of $(A)$ gives an acid $(B), C_{8} H_{6} O_{4} . (B)$ easily forms anhydride on…
Chemistry · Haloalkanes and Haloarenes · MCQ
Q7.The order of stability of the following carbocations : Includes diagram
Chemistry · Basics of Organic Chemistry · MCQ
Q8.Synthesis of each molecule of glucose in photosynthesis involves:
Chemistry · Biomolecules · MCQ
Q9.The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:
Chemistry · Compounds Containing Nitrogen · MCQ
Q10.An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q11.Which of the following complex species is not expected to exhibit optical isomerism?
Chemistry · Coordination Compounds · MCQ
Q12.Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest $E_{M^{3 +} / M^{2 +}}^{0}$ value?
Chemistry · D and F Block Elements · MCQ
Q13.Which of the following arrangements does not represent the correct order of the property stated against it?
Chemistry · D and F Block Elements · MCQ
Q14.The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be:(R = 8.314 JK–1 mol–1 and log 2 = 0.301)
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q15.Given $E_{C r^{2 +} / C r}^{o}$ = -0.74 V; $E_{M n O_{4}^{-} / M n^{2 +}}^{o}$ = 1.51 V $E_{C r_{2} O_{7}^{2 -} / C r^{3 +}}^{o}$ = 1.33 V; $E_{C l / C l^{-}}^{o}$ = 1.36 V Based on the data given above, strongest oxidising agent will be :
Chemistry · Electrochemistry · MCQ
Q16.The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q17.A solution of (– $l$ ) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small amount of $S b C l_{5}$ , due to the formation of :
Chemistry · Haloalkanes and Haloarenes · MCQ
Q18.In which of the following pairs of molecules/ions, both the species are not likely to exist?
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q19.Stability of the species $L i_{2}$ , $L i_{2}^{-}$ and $L i_{2}^{+}$ increases in the order of:
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q20.Which one of the following molecules is expected to exhibit diamagnetic behaviour?
Chemistry · Chemical Bonding and Molecular Structure · Multiple correct
Q21.The first ionization potential of $N a$ is 5.1 eV. The value of electron gain enthalpy of $N a^{+}$ will be:
Chemistry · Periodic Table and Periodicity · MCQ
Q22.Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?
Chemistry · Periodic Table and Periodicity · MCQ
Q23.Energy of an electron is given by $E = - 2.178 \times 1 0^{- 18} J (\frac{Z ^{2}}{n ^{2}})$ . Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be (h = 6.62 × 10−34 Js…
Chemistry · Structure of Atom · MCQ
Q24.Experimentally it was found that a metal oxide has formula $M 0.98 O$ . Metal $M$ , present as $M^{2 +}$ and $M^{3 +}$ in its oxide. Fraction of the metal which exists as $M^{3 +}$ would be
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q25.A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of $C O_{2}$ . The empirical formula of the hydrocarbon is
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q26.Consider the following reaction: $x M n O_{4}^{-} + y C_{2} O_{4}^{2 -}$ + z $H^{+}$ $\to$ x $M n^{2 +}$ + 2y $C O_{2}$ + $\frac{z}{2} H_{2} O$ The value's of x, y and z in the reaction are, respectively :
Chemistry · Redox Reactions · MCQ
Q27.Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A $\times$ B having 3 or more elements is :
Mathematics · Permutations and Combinations · MCQ
Q28.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
Mathematics · Statistics · MCQ
Q29. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production P w.r.t. additional number of workers $x$ is given by $\frac{d p}{d x} = 100 - 12 x .$ If the firm employs $25$ more workers,…
Mathematics · Differential Equations · MCQ
Q31.The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0, x$ -axis, and lying in the first quadrant is :
Mathematics · Area Under the Curves · MCQ
Q32.Statement-1 : The value of the integral $π /6 \int π /3 \frac{d x}{1 + t a n x}$ is equal to $π /6$ Statement-2 : $a \int b f (x) d x = a \int b f (a + b - x) d x .$ …
Mathematics · Definite Integration · MCQ
Q33.If $\int f (x) d x = ψ (x),$ then $\int x^{5} f (x^{3}) d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q34.If $x, y, z$ are in A.P. and $tan^{- 1} x, tan^{- 1} y$ and $tan^{- 1} z$ are also in A.P., then :
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.If $y = sec (tan^{- 1} x),$ then $\frac{d y}{d x}$ at $x = 1$ is equal to :
Mathematics · Differentiation · MCQ
Q36.The equation of the circle passing through the foci of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ , and having centre at $(0, 3)$ is :
Mathematics · Ellipse · MCQ
Q37.The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1) (1, 1)$ and $(1, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.A ray of light along $x + 3 y = 3$ gets reflected upon reaching $X$ -axis, the equation of the reflected ray is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.The term independent of $x$ in expansion of $(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}$ is
Mathematics · Binomial Theorem · MCQ
Q40.Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n + 1} - T_{n}$ = 10, then the value of n is :
Mathematics · Permutations and Combinations · MCQ
Q41.If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R,$ have a common root, then $a : b : c$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.The number of values of $k$ , for which the system of equations : $(k + 1) x + 8 y = 4 k k x + (k + 3) y = 3 k - 1$ has no solution, is
Mathematics · Matrices and Determinants · MCQ
Q43.The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$
Mathematics · Application of Derivatives · MCQ
Q44.If z is a complex number of unit modulus and argument $θ$ , then arg $(\frac{1 + z}{1 + z})$ equals :
Mathematics · Complex Numbers · MCQ
Q45.The expression $\frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A}$ can be written as:
Mathematics · Trigonometric Ratio and Identites · MCQ
Q46.If the vectors $A B = 3 i + 4 k$ and $A C = 5 i - 2 j + 4 k$ are the sides of a triangle $A B C,$ then the length of the median through $A$ is :
Mathematics · Vector Algebra · MCQ
Q47.If the lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}$ and $\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar, then $k$ can have :
Mathematics · 3D Geometry · MCQ
Q48.Diameter of a plano-convex lens is $6 c m$ and thickness at the center is $3 mm$ . If speed of light in material of lens is $2 \times 1 0^{8} m / s,$ the focal length of the lens is
Physics · Geometrical Optics · MCQ
Q49.The $I$ - $V$ characteristic of an $L E D$ is
Physics · Electronic Devices · MCQ
Q50.The anode voltage of a photocell is kept fixed. The wavelength $λ$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows :
Physics · Dual Nature of Radiation · MCQ
Q51.In a hydrogen like atom electron make transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$ . If $n >> 1,$ the frequency of radiation emitted is proportional to :
Physics · Atoms and Nuclei · MCQ
Q52.The magnetic field in a travelling electromagnetic wave has a peak value of $20 n T$ . The peak value of electric field strength is :
Physics · Electromagnetic Waves · MCQ
Q53.A diode detector is used to detect an amplitude modulated wave of $60%$ modulation by using a condenser of capacity $250$ picofarad in parallel with a load resistance $100$ kilo $o hm .$ Find the maximum modulated frequency which could be… Includes diagram
Physics · Electronic Devices · MCQ
Q54.The graph between angle of deviation $(δ)$ and angle of incidence $(i)$ for a triangular prism is represented by
Physics · Geometrical Optics · MCQ
Q55.Two coherent point sources $S_{1}$ and $S_{2}$ are separated by a small distance $^{'} d^{'}$ as shown. The fringes obtained on the screen will be Includes diagram
Physics · Wave Optics · MCQ
Q56.In an $L C R$ circuit as shown below both switches are open initially. Now switch $S_{1}$ is closed, $S_{2}$ kept open. ( $q$ is charge on the capacitor and $τ = R C$ is Capacitance time constant). Which of the following statement is correct… Includes diagram
Physics · Alternating Current · MCQ
Q57.A metallic rod of length $^{'} ℓ^{'}$ is tied to a string of length $2 ℓ$ and made to rotate with angular speed $w$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $^{'} B^{'}$ in the region, the $e . m . f$ … Includes diagram
Physics · Electromagnetic Induction · MCQ
Q58.A beam of unpolarised light of intensity $I_{0}$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $4 5^{\circ}$ relative to that of $A$ . The…
Physics · Wave Optics · MCQ
Q59.A circular loop of radius $0.3 c m$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $15 c m .$ If a current of $2.0 A$ flows through the smaller loop, than the flux linked with bigger loop is
Physics · Electromagnetic Induction · MCQ
Q60.Two short bar magnets of length $1 c m$ each have magnetic moments $1.20 A m^{2}$ and $1.00 A m^{2}$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common…
Physics · Magnetic Properties of Matter · MCQ
Q61.This questions has Statement - $I$ and Statement - $I I$ . Of the four choices given after the Statements, choose the one that best describes into two Statements. Statement - $I$ : Higher the range, greater is the…
Physics · Current Electricity · MCQ
Q62.The supply voltage to room is $120 V .$ The resistance of the lead wires is $6Ω$ . A $60 W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240 W$ heater is switched on in parallel to the bulb?
Physics · Current Electricity · MCQ
Q63.Two capacitors $C_{1}$ and $C_{2}$ are charged to $120 V$ and $200 V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then
Physics · Capacitor · MCQ
Q64.A charge $Q$ is uniformly distributed over a long rod $A B$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is Includes diagram
Physics · Electrostatics · MCQ
Q65.Two charges, each equals to $q,$ are kept at $x = - a$ and $x = a$ on the $x$ -axis. A particle of mass $m$ and charge $q_{0} = \frac{q}{2}$ is placed at the origin. If charge $q_{0}$ is given a small displacement $$\left( {y \lt \lt a}…
Physics · Electrostatics · MCQ
Q66.A sonometer wire of length $1.5 m$ is made of steel. The tension in it produces an elastic strain of $1%$ . What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 1 0^{3} k g / m^{3}$ and $2.2 \times 1 0^{11} N / m^{2}$ …
Physics · Waves · MCQ
Q67.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M .$ The piston and the cylinder have equal cross sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and…
Physics · Simple Harmonic Motion · MCQ
Q68.The above $p$ - $v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q69.Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $T,$ density of liquid is…
Physics · Heat and Thermodynamics · MCQ
Q70.A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $σ$ at equilibrium…
Physics · Properties of Matter · MCQ
Q71.What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ?
Physics · Gravitation · MCQ
Q72.A hoop of radius $r$ and mass $m$ rotating with an angular velocity $ω_{0}$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it…
Physics · Rotational Motion · MCQ
Q73.This question has statement $I$ and statement $I I$ . Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $I$ : A point particle of mass $m$ moving with…
Physics · Center of Mass · MCQ
Q74.A projectile is given an initial velocity of $(i + 2 j)$ m/s, where $i$ is along the ground and $j$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:
Physics · Motion in A Plane · MCQ
Q75.Let [ $ε_{0}$ ] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
Physics · Units and Measurements · MCQ