2011 · Shift 0

79 questions · JEE Main

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JEE Main
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2011 · Shift 0

2011 · Shift 0

79 questions · JEE Main

Chemistry28 questions Mathematics24 questions Physics27 questions

Q1.A 5.2 molal aqueous solution of methyl alcohol, $C H_{3} O H$ , is supplied. What is the mole fraction of methyl alcohol in the solution ?
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q2.The degree of dissociation ( $α$ ) of a weak electrolyte, AxBy is related to van’t Hoff factor (i) by the expression :
Chemistry · Solutions · MCQ
Q3.Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :
Chemistry · Hydrocarbons · MCQ
Q4.Identify the compound that exhibits tautomerism.
Chemistry · Basics of Organic Chemistry · MCQ
Q5.A vessel at 1000 K contains $C O_{2}$ with a pressure of 0.5 atm. Some of the $C O_{2}$ is converted into $C O$ on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is :
Chemistry · Chemical Equilibrium · MCQ
Q6.The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm3 to a volume of 100 dm3 at 27oC is :
Chemistry · Thermodynamics · MCQ
Q7.Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6oC will be : [Kf for water = 1.86 K kg mol−1 , and molar mass of ethylene glycol =…
Chemistry · Solutions · MCQ
Q8.Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q9.The outer electron configuration of $G d$ (Atomic No. $64$ ) is :
Chemistry · D and F Block Elements · MCQ
Q10.Outer electronic configuration of Gd (Atomic no : 64) is -
Chemistry · Periodic Table and Periodicity · MCQ
Q11.The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?
Chemistry · Biomolecules · MCQ
Q12.Silver Mirror test is given by which one of the following compounds ?
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q13.Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The strongest acid amongst the following compounds is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q15.Which of the following reagents may be used to distinguish between phenol and benzoic acid ?
Chemistry · Practical Organic Chemistry · MCQ
Q16.Phenol is heated with a solution of mixture of $K B r$ and $K B r O_{3}$ . The major product obtained in the above reaction is
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.The magnetic moment (spin only) of $[N i C l_{4}]^{2 -}$ is
Chemistry · Coordination Compounds · MCQ
Q18.Which of the following facts about the complex $[C r (N H_{3})_{6}] C l_{3}$ is wrong?
Chemistry · Coordination Compounds · MCQ
Q19.In context of the lanthanoids, which of the following statements is not correct?
Chemistry · D and F Block Elements · MCQ
Q20.Which of the following statement is wrong?
Chemistry · P Block Elements · MCQ
Q21.Which of the following statements regarding sulphur is incorrect?
Chemistry · P Block Elements · MCQ
Q22.The rate of a chemical reaction doubles for every 10oC rise of temperature. If the temperature is raised by 50oC , the rate of the reaction increases by about :
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.The reduction potential of hydrogen half cell will be negative if :
Chemistry · Electrochemistry · MCQ
Q24.The structure of $I F_{7}$ is :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q25.The hybridization of orbitals of N atom in $N O_{3}^{-}$ , $N O_{2}^{+}$ and $N H_{4}^{+}$ are respectively :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q26.Among the following the maximum covalent character is shown by the compound :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q27.Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?
Chemistry · Periodic Table and Periodicity · MCQ
Q28.A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :
Chemistry · Structure of Atom · MCQ
Q29.If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals
Mathematics · Statistics · MCQ
Q30.The value of $p$ and $q$ for which the function $f (x) = ⎩ ⎨ ⎧ \frac{s i n ( p + 1 ) x + s i n x}{x} q \frac{x + x ^{2} - x}{x ^{3/2}}, x < 0, x = 0, x > 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q31. $x \to 2 lim (\frac{1 - c o s { 2 ( x - 2 ) }}{x - 2})$
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.The domain of the function f(x) = $\frac{1}{∣ x ∣ - x}$ is
Mathematics · Functions · MCQ
Q33.Let $α, β$ be real and z be a complex number. If $z^{2} + α z + β = 0$ has two distinct roots on the line Re z = 1, then it is necessary that :
Mathematics · Complex Numbers · MCQ
Q34.For $x \in (0, \frac{5 π}{2}),$ define $f (x) = 0 \int x t sin t d t .$ Then $f$ has
Mathematics · Application of Derivatives · MCQ
Q35.The vectors $a$ and $b$ are not perpendicular and $c$ and $d$ are two vectors satisfying $b \times c = b \times d$ …
Mathematics · Vector Algebra · MCQ
Q36.If $C$ and $D$ are two events such that $C \subset D$ and $P (D) e 0,$ then the correct statement among the following is :
Mathematics · Probability · MCQ
Q37.If $\frac{d y}{d x} = y + 3 > 0$ and $y (0) = 2,$ then $y (ln 2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q38.Let $I$ be the purchase value of an equipment and $V (t)$ be the value after it has been used for $t$ years. The value $V (t)$ depreciates at a rate given by differential equation $\frac{d v ( t )}{d t} = - k (T - t),$ …
Mathematics · Differential Equations · MCQ
Q39.The area of the region enclosed by the curves $y = x, x = e, y = \frac{1}{x}$ and the positive $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q40.The value of $0 \int 1 \frac{8 l o g ( 1 + x )}{1 + x ^{2}} d x$ is
Mathematics · Definite Integration · MCQ
Q41.The number of values of $k$ for which the linear equations $4 x + k y + 2 z = 0, k x + 4 y + z = 0$ and $2 x + 2 y + z = 0$ possess a non-zero solution is :
Mathematics · Matrices and Determinants · MCQ
Q42.Let $A$ and $B$ be two symmetric matrices of order $3$ . Statement - 1 : $A (B A)$ and $(A B) A$ are symmetric matrices. Statement - 2 : $A B$ is symmetric matrix if matrix multiplication of $A$ with $B$ is commutative.
Mathematics · Matrices and Determinants · MCQ
Q43. $\frac{d ^{2} x}{d y ^{2}}$ equals:
Mathematics · Differentiation · MCQ
Q44.Equation of the ellipse whose axes of coordinates and which passes through the point $(- 3, 1)$ and has eccentricity $\frac{2}{5}$ is :
Mathematics · Ellipse · MCQ
Q45.A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increases by ₹ 40 more than the saving of immediately previous month. His total saving from the start of service will be ₹…
Mathematics · Sequences and Series · MCQ
Q46.Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is $^{9} C_{3}$ . Statement - 2: The number of ways of choosing any 3 places from 9 different places is $^{9} C_{3}$ .
Mathematics · Permutations and Combinations · MCQ
Q47.These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:
Mathematics · Permutations and Combinations · MCQ
Q48.If $ω (e 1)$ is a cube root of unity, and $(1 + ω)^{7} = A + B ω$ . Then $(A, B)$ equals :
Mathematics · Complex Numbers · MCQ
Q49.If $A = sin^{2} x + cos^{4} x,$ then for all real $x$ :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q50.Statement - 1 : The point $A (1, 0, 7)$ is the mirror image of the point $B (1, 6, 3)$ in the line : $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ Statement - 2 : The line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ bisects…
Mathematics · 3D Geometry · MCQ
Q51.Let $R$ be the set of real numbers. Statement I : $A = {(x, y) \in R \times R : y - x$ is an integer $}$ is an equivalence relation on $R$ . Statement II : $B = {(x, y) \in R \times R : x = α y$ for some rational number $α}$ is an…
Mathematics · Sets and Relations · MCQ
Q52.Let $a$ , $b$ , $c$ be three non-zero vectors which are pairwise non-collinear. If $a + 3 b$ is collinear with $c$ and $b + 2 c$ …
Mathematics · Vector Algebra · MCQ
Q53.This question has Statement - $1$ and Statement - $2$ . Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $1$ : A metallic surface is irradiated by a monochromatic light of…
Physics · Dual Nature of Radiation · MCQ
Q54.Energy required for the electron excitation in $L i^{++}$ from the first to the third Bohr orbit is :
Physics · Atoms and Nuclei · MCQ
Q55.This question has a paragraph followed by two statements, Statement $- 1$ and Statement $- 2$ . Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex…
Physics · Wave Optics · MCQ
Q56.A car is fitted with a convex side-view mirror of focal length $20 c m$ . A second car $2.8 m$ behind the first car is overtaking the first car at a relative speed of $15 m / s$ . The speed of the image of the second car as seen in the mirror of…
Physics · Geometrical Optics · MCQ
Q57.Let $x$ - $z$ plane be the boundary between two transparent media. Medium $1$ in $z \geq 0$ has a refractive index of $2$ and medium $2$ with $z < 0$ has a refractive index of $3 .$ A ray of light in medium $1$ given by the…
Physics · Geometrical Optics · MCQ
Q58.A resistor $^{'} R^{'}$ and $2 μ F$ capacitor in series is connected through a switch to $200 V$ direct supply. Across the capacitor is a neon bulb that lights up at $120 V .$ Calculate the value of $R$ to make the bulb light up $5 s$ after the…
Physics · Alternating Current · MCQ
Q59.A boat is moving due east in a region where the earth's magnetic fields is $5.0 \times 1 0^{- 5} N A^{- 1} m^{- 1}$ due north and horizontal. The best carries a vertical aerial $2 m$ long. If the speed of the boat is $1.50 m s^{- 1},$ …
Physics · Electromagnetic Induction · MCQ
Q60.A fully charged capacitor $C$ with initial charge $q_{0}$ is connected to a coil of self inductance $L$ at $t = 0.$ The time at which the energy is stored equally between the electric and the magnetic fields is :
Physics · Alternating Current · MCQ
Q61.A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R .$ The magnitude of the magnetic induction along its axis is:
Physics · Magnetics · MCQ
Q62.If a wire is stretched to make it $0.1%$ longer, its resistance will:
Physics · Current Electricity · MCQ
Q63.The electrostatic potential inside a charged spherical ball is given by $ϕ = a r^{2} + b$ where $r$ is the distance from the center and $a, b$ are constants. Then the charge density inside the ball is:
Physics · Electrostatics · MCQ
Q64.Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d (d << 1)$ apart because of their mutual repulsion. The charge begins to leak from both the…
Physics · Electrostatics · MCQ
Q65.Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $ω$ along the $x$ -axis. Their mean position is separated by distance $X_{0} (X_{0} > A)$ . If the maximum separation between…
Physics · Simple Harmonic Motion · MCQ
Q66.The transverse displacement $y (x, t)$ of a wave on a string is given by $y (x, t) = e^{- (a x^{2} + b t^{2} + 2 ab x t)} .$ This represents $a :$
Physics · Waves · MCQ
Q67.A mass $M,$ attached to a horizontal spring, executes $S . H . M .$ with amplitude $A_{1} .$ When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2} .$ The…
Physics · Simple Harmonic Motion · MCQ
Q68. $100 g$ of water is heated from $3 0^{\circ} C$ to $5 0^{\circ} C$ . Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4184 J / k g / K$ ):
Physics · Heat and Thermodynamics · MCQ
Q69.A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $γ .$ It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature…
Physics · Heat and Thermodynamics · MCQ
Q70.Three perfect gases at absolute temperatures $T_{1}, T_{2}$ and $T_{3}$ are mixed. The masses of molecules are $m_{1}, m_{2}$ and $m_{3}$ and the number of molecules are $n_{1}, n_{2}$ and $n_{3}$ respectively. Assuming no loss of energy,…
Physics · Heat and Thermodynamics · MCQ
Q71.Water is flowing continuously from a tap having an internal diameter $8 \times 1 0^{- 3} m .$ The water velocity as it leaves the tap is $0.4 m s^{- 1}$ . The diameter of the water stream at a distance $2 \times 1 0^{- 1} m$ …
Physics · Properties of Matter · MCQ
Q72.Work done in increasing the size of a soap bubble from a radius of $3 c m$ to $5 c m$ is nearly (Surface tension of soap solution $= 0.03 N m^{- 1},$
Physics · Properties of Matter · MCQ
Q73.Two bodies of masses $m$ and $4 m$ are placed at a distance $r .$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:
Physics · Gravitation · MCQ
Q74.A pulley of radius $2 m$ is rotated about its axis by a force $F = (20 t - 5 t^{2})$ newton (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 k g$ - $m^{2}$ …
Physics · Rotational Motion · MCQ
Q75.A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R .$ Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m,$ if the string…
Physics · Rotational Motion · MCQ
Q76.A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the…
Physics · Rotational Motion · MCQ
Q77.A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :
Physics · Motion in A Plane · MCQ
Q78.An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : $\frac{d v}{d t} = - 2.5 v$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be :
Physics · Motion in A Straight Line · MCQ
Q79.A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The…
Physics · Units and Measurements · MCQ

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2011 · Shift 0

79 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
2011 · Shift 0

2011 · Shift 0

79 questions · JEE Main

Chemistry28 questions Mathematics24 questions Physics27 questions

Q1.A 5.2 molal aqueous solution of methyl alcohol, $C H_{3} O H$ , is supplied. What is the mole fraction of methyl alcohol in the solution ?
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q2.The degree of dissociation ( $α$ ) of a weak electrolyte, AxBy is related to van’t Hoff factor (i) by the expression :
Chemistry · Solutions · MCQ
Q3.Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :
Chemistry · Hydrocarbons · MCQ
Q4.Identify the compound that exhibits tautomerism.
Chemistry · Basics of Organic Chemistry · MCQ
Q5.A vessel at 1000 K contains $C O_{2}$ with a pressure of 0.5 atm. Some of the $C O_{2}$ is converted into $C O$ on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is :
Chemistry · Chemical Equilibrium · MCQ
Q6.The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm3 to a volume of 100 dm3 at 27oC is :
Chemistry · Thermodynamics · MCQ
Q7.Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6oC will be : [Kf for water = 1.86 K kg mol−1 , and molar mass of ethylene glycol =…
Chemistry · Solutions · MCQ
Q8.Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q9.The outer electron configuration of $G d$ (Atomic No. $64$ ) is :
Chemistry · D and F Block Elements · MCQ
Q10.Outer electronic configuration of Gd (Atomic no : 64) is -
Chemistry · Periodic Table and Periodicity · MCQ
Q11.The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?
Chemistry · Biomolecules · MCQ
Q12.Silver Mirror test is given by which one of the following compounds ?
Chemistry · Aldehydes Ketones and Carboxylic Acids · Multiple correct
Q13.Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The strongest acid amongst the following compounds is :
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q15.Which of the following reagents may be used to distinguish between phenol and benzoic acid ?
Chemistry · Practical Organic Chemistry · MCQ
Q16.Phenol is heated with a solution of mixture of $K B r$ and $K B r O_{3}$ . The major product obtained in the above reaction is
Chemistry · Alcohols Phenols and Ethers · MCQ
Q17.The magnetic moment (spin only) of $[N i C l_{4}]^{2 -}$ is
Chemistry · Coordination Compounds · MCQ
Q18.Which of the following facts about the complex $[C r (N H_{3})_{6}] C l_{3}$ is wrong?
Chemistry · Coordination Compounds · MCQ
Q19.In context of the lanthanoids, which of the following statements is not correct?
Chemistry · D and F Block Elements · MCQ
Q20.Which of the following statement is wrong?
Chemistry · P Block Elements · MCQ
Q21.Which of the following statements regarding sulphur is incorrect?
Chemistry · P Block Elements · MCQ
Q22.The rate of a chemical reaction doubles for every 10oC rise of temperature. If the temperature is raised by 50oC , the rate of the reaction increases by about :
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.The reduction potential of hydrogen half cell will be negative if :
Chemistry · Electrochemistry · MCQ
Q24.The structure of $I F_{7}$ is :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q25.The hybridization of orbitals of N atom in $N O_{3}^{-}$ , $N O_{2}^{+}$ and $N H_{4}^{+}$ are respectively :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q26.Among the following the maximum covalent character is shown by the compound :
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q27.Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?
Chemistry · Periodic Table and Periodicity · MCQ
Q28.A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :
Chemistry · Structure of Atom · MCQ
Q29.If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals
Mathematics · Statistics · MCQ
Q30.The value of $p$ and $q$ for which the function $f (x) = ⎩ ⎨ ⎧ \frac{s i n ( p + 1 ) x + s i n x}{x} q \frac{x + x ^{2} - x}{x ^{3/2}}, x < 0, x = 0, x > 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q31. $x \to 2 lim (\frac{1 - c o s { 2 ( x - 2 ) }}{x - 2})$
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.The domain of the function f(x) = $\frac{1}{∣ x ∣ - x}$ is
Mathematics · Functions · MCQ
Q33.Let $α, β$ be real and z be a complex number. If $z^{2} + α z + β = 0$ has two distinct roots on the line Re z = 1, then it is necessary that :
Mathematics · Complex Numbers · MCQ
Q34.For $x \in (0, \frac{5 π}{2}),$ define $f (x) = 0 \int x t sin t d t .$ Then $f$ has
Mathematics · Application of Derivatives · MCQ
Q35.The vectors $a$ and $b$ are not perpendicular and $c$ and $d$ are two vectors satisfying $b \times c = b \times d$ …
Mathematics · Vector Algebra · MCQ
Q36.If $C$ and $D$ are two events such that $C \subset D$ and $P (D) e 0,$ then the correct statement among the following is :
Mathematics · Probability · MCQ
Q37.If $\frac{d y}{d x} = y + 3 > 0$ and $y (0) = 2,$ then $y (ln 2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q38.Let $I$ be the purchase value of an equipment and $V (t)$ be the value after it has been used for $t$ years. The value $V (t)$ depreciates at a rate given by differential equation $\frac{d v ( t )}{d t} = - k (T - t),$ …
Mathematics · Differential Equations · MCQ
Q39.The area of the region enclosed by the curves $y = x, x = e, y = \frac{1}{x}$ and the positive $x$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q40.The value of $0 \int 1 \frac{8 l o g ( 1 + x )}{1 + x ^{2}} d x$ is
Mathematics · Definite Integration · MCQ
Q41.The number of values of $k$ for which the linear equations $4 x + k y + 2 z = 0, k x + 4 y + z = 0$ and $2 x + 2 y + z = 0$ possess a non-zero solution is :
Mathematics · Matrices and Determinants · MCQ
Q42.Let $A$ and $B$ be two symmetric matrices of order $3$ . Statement - 1 : $A (B A)$ and $(A B) A$ are symmetric matrices. Statement - 2 : $A B$ is symmetric matrix if matrix multiplication of $A$ with $B$ is commutative.
Mathematics · Matrices and Determinants · MCQ
Q43. $\frac{d ^{2} x}{d y ^{2}}$ equals:
Mathematics · Differentiation · MCQ
Q44.Equation of the ellipse whose axes of coordinates and which passes through the point $(- 3, 1)$ and has eccentricity $\frac{2}{5}$ is :
Mathematics · Ellipse · MCQ
Q45.A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increases by ₹ 40 more than the saving of immediately previous month. His total saving from the start of service will be ₹…
Mathematics · Sequences and Series · MCQ
Q46.Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is $^{9} C_{3}$ . Statement - 2: The number of ways of choosing any 3 places from 9 different places is $^{9} C_{3}$ .
Mathematics · Permutations and Combinations · MCQ
Q47.These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:
Mathematics · Permutations and Combinations · MCQ
Q48.If $ω (e 1)$ is a cube root of unity, and $(1 + ω)^{7} = A + B ω$ . Then $(A, B)$ equals :
Mathematics · Complex Numbers · MCQ
Q49.If $A = sin^{2} x + cos^{4} x,$ then for all real $x$ :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q50.Statement - 1 : The point $A (1, 0, 7)$ is the mirror image of the point $B (1, 6, 3)$ in the line : $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ Statement - 2 : The line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ bisects…
Mathematics · 3D Geometry · MCQ
Q51.Let $R$ be the set of real numbers. Statement I : $A = {(x, y) \in R \times R : y - x$ is an integer $}$ is an equivalence relation on $R$ . Statement II : $B = {(x, y) \in R \times R : x = α y$ for some rational number $α}$ is an…
Mathematics · Sets and Relations · MCQ
Q52.Let $a$ , $b$ , $c$ be three non-zero vectors which are pairwise non-collinear. If $a + 3 b$ is collinear with $c$ and $b + 2 c$ …
Mathematics · Vector Algebra · MCQ
Q53.This question has Statement - $1$ and Statement - $2$ . Of the four choices given after the statements, choose the one that best describes the two statements. Statement - $1$ : A metallic surface is irradiated by a monochromatic light of…
Physics · Dual Nature of Radiation · MCQ
Q54.Energy required for the electron excitation in $L i^{++}$ from the first to the third Bohr orbit is :
Physics · Atoms and Nuclei · MCQ
Q55.This question has a paragraph followed by two statements, Statement $- 1$ and Statement $- 2$ . Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex…
Physics · Wave Optics · MCQ
Q56.A car is fitted with a convex side-view mirror of focal length $20 c m$ . A second car $2.8 m$ behind the first car is overtaking the first car at a relative speed of $15 m / s$ . The speed of the image of the second car as seen in the mirror of…
Physics · Geometrical Optics · MCQ
Q57.Let $x$ - $z$ plane be the boundary between two transparent media. Medium $1$ in $z \geq 0$ has a refractive index of $2$ and medium $2$ with $z < 0$ has a refractive index of $3 .$ A ray of light in medium $1$ given by the…
Physics · Geometrical Optics · MCQ
Q58.A resistor $^{'} R^{'}$ and $2 μ F$ capacitor in series is connected through a switch to $200 V$ direct supply. Across the capacitor is a neon bulb that lights up at $120 V .$ Calculate the value of $R$ to make the bulb light up $5 s$ after the…
Physics · Alternating Current · MCQ
Q59.A boat is moving due east in a region where the earth's magnetic fields is $5.0 \times 1 0^{- 5} N A^{- 1} m^{- 1}$ due north and horizontal. The best carries a vertical aerial $2 m$ long. If the speed of the boat is $1.50 m s^{- 1},$ …
Physics · Electromagnetic Induction · MCQ
Q60.A fully charged capacitor $C$ with initial charge $q_{0}$ is connected to a coil of self inductance $L$ at $t = 0.$ The time at which the energy is stored equally between the electric and the magnetic fields is :
Physics · Alternating Current · MCQ
Q61.A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R .$ The magnitude of the magnetic induction along its axis is:
Physics · Magnetics · MCQ
Q62.If a wire is stretched to make it $0.1%$ longer, its resistance will:
Physics · Current Electricity · MCQ
Q63.The electrostatic potential inside a charged spherical ball is given by $ϕ = a r^{2} + b$ where $r$ is the distance from the center and $a, b$ are constants. Then the charge density inside the ball is:
Physics · Electrostatics · MCQ
Q64.Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d (d << 1)$ apart because of their mutual repulsion. The charge begins to leak from both the…
Physics · Electrostatics · MCQ
Q65.Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $ω$ along the $x$ -axis. Their mean position is separated by distance $X_{0} (X_{0} > A)$ . If the maximum separation between…
Physics · Simple Harmonic Motion · MCQ
Q66.The transverse displacement $y (x, t)$ of a wave on a string is given by $y (x, t) = e^{- (a x^{2} + b t^{2} + 2 ab x t)} .$ This represents $a :$
Physics · Waves · MCQ
Q67.A mass $M,$ attached to a horizontal spring, executes $S . H . M .$ with amplitude $A_{1} .$ When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2} .$ The…
Physics · Simple Harmonic Motion · MCQ
Q68. $100 g$ of water is heated from $3 0^{\circ} C$ to $5 0^{\circ} C$ . Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4184 J / k g / K$ ):
Physics · Heat and Thermodynamics · MCQ
Q69.A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $γ .$ It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature…
Physics · Heat and Thermodynamics · MCQ
Q70.Three perfect gases at absolute temperatures $T_{1}, T_{2}$ and $T_{3}$ are mixed. The masses of molecules are $m_{1}, m_{2}$ and $m_{3}$ and the number of molecules are $n_{1}, n_{2}$ and $n_{3}$ respectively. Assuming no loss of energy,…
Physics · Heat and Thermodynamics · MCQ
Q71.Water is flowing continuously from a tap having an internal diameter $8 \times 1 0^{- 3} m .$ The water velocity as it leaves the tap is $0.4 m s^{- 1}$ . The diameter of the water stream at a distance $2 \times 1 0^{- 1} m$ …
Physics · Properties of Matter · MCQ
Q72.Work done in increasing the size of a soap bubble from a radius of $3 c m$ to $5 c m$ is nearly (Surface tension of soap solution $= 0.03 N m^{- 1},$
Physics · Properties of Matter · MCQ
Q73.Two bodies of masses $m$ and $4 m$ are placed at a distance $r .$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:
Physics · Gravitation · MCQ
Q74.A pulley of radius $2 m$ is rotated about its axis by a force $F = (20 t - 5 t^{2})$ newton (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 k g$ - $m^{2}$ …
Physics · Rotational Motion · MCQ
Q75.A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R .$ Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m,$ if the string…
Physics · Rotational Motion · MCQ
Q76.A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the…
Physics · Rotational Motion · MCQ
Q77.A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :
Physics · Motion in A Plane · MCQ
Q78.An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : $\frac{d v}{d t} = - 2.5 v$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be :
Physics · Motion in A Straight Line · MCQ
Q79.A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The…
Physics · Units and Measurements · MCQ