2014 · Shift 0

74 questions · JEE Main

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JEE Main
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2014 · Shift 0

2014 · Shift 0

74 questions · JEE Main

Chemistry24 questions Mathematics20 questions Physics30 questions

Q1.Resistance of 0.2 M solution of an electrolyte is 50 $Ω$ . The specific conductance of the solution is 1.4 S m-1. The resistance of 0.5 M solution of the same electrolyte is 280 $Ω$ . The molar conductivity of 0.5 M solution of the…
Chemistry · Electrochemistry · MCQ
Q2.Consider separate solutions of 0.500 M $C_{2} H_{5} O H$ (aq), 0.100 M $M g_{3} (P O_{4})_{2}$ (aq), 0.250 M $K B r$ (aq) and 0.125 M $N a_{3} P O_{4}$ (aq) at 25oC. Which statement is true about these solutions, assuming all salts to be strong electrolytes?
Chemistry · Solutions · MCQ
Q3.For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete…
Chemistry · Basics of Organic Chemistry · MCQ
Q4.In which of the following reactions $H_{2} O_{2}$ acts as a reducing agent? 1. $H_{2} O_{2}$ + 2 $H^{+}$ + 2e- $\to$ 2 $H_{2} O$ 2. $H_{2} O_{2}$ - 2e- $\to$ $O_{2}$ + 2 $H^{+}$ 3. $H_{2} O_{2}$ + 2e- $\to$ 2 $O H^{-}$ 4. $H_{2} O_{2}$ + 2 $O H^{-}$ - 2e- $\to$ $O_{2}$ + 2 $H_{2} O$
Chemistry · Redox Reactions · MCQ
Q5.For the reaction $S O_{2}$ (g) + $\frac{1}{2} O_{2} (g) ⇋$ $S O_{3}$ (g). if KP = KC(RT)x where the symbols have usual meaning then the value of x is: (assuming ideality)
Chemistry · Chemical Equilibrium · MCQ
Q6.For complete combustion of ethanol, $C_{2} H_{5} O H$ (l) + 3 $O_{2}$ (g) $\to$ 2 $C O_{2}$ (g) + 3 $H_{2} O$ (l) the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol–1 at 25oC. Assuming ideality the Enthalpy of combustion, $\Delta…
Chemistry · Thermodynamics · MCQ
Q7.Given below are the half-cell reactions: $M n^{2 +}$ + 2e- $\to$ $M n$ ; Eo = -1.18 V 2( $M n^{3 +}$ + e- $\to$ $M n^{2 +}$ ); Eo = +1.51 V The Eo for 3 $M n^{2 +}$ $\to$ $M n$ + 2 $M n^{3 +}$ will be :
Chemistry · Electrochemistry · MCQ
Q8.The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q9.The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q10.Sodium phenoxide when heated with $C O_{2}$ under pressure at $12 5^{\circ} C$ yields a product which on acetylation products $C .$ The major product $C$ would be Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q11.Which one of the following bases is not present in DNA?
Chemistry · Biomolecules · MCQ
Q12.Considering the basic strength of amines in aqueous solution, which one has the smallest pKb value?
Chemistry · Compounds Containing Nitrogen · MCQ
Q13.On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is:
Chemistry · Compounds Containing Nitrogen · MCQ
Q14.The most suitable reagent for the conversion of R - $C H_{2}$ - OH $\to$ R - CHO is:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.In the reaction, the product C is: Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q16.In $S N_{2}$ reactions, the correct order of reactivity for the following compounds: $C H_{3} C l$ , $C H_{3} C H 2 C l$ , $(C H_{3})_{2} C H C l$ and $(C H_{3})_{3} C C l$ is:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q17.The equation which is balanced and represents the correct product(s) is :
Chemistry · Coordination Compounds · MCQ
Q18.The octahedral complex of a metal ion $M^{3 +}$ with four monodentate ligands $L_{1}$ , $L_{2}$ , $L_{3}$ and $L_{4}$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four…
Chemistry · Coordination Compounds · MCQ
Q19.Which series of reactions correctly represents chemical relations related to iron and its compound?
Chemistry · D and F Block Elements · MCQ
Q20.The correct statement for the molecule, $C s I_{3}$ is :
Chemistry · P Block Elements · MCQ
Q21.Which one of the following properties is not shown by NO?
Chemistry · P Block Elements · MCQ
Q22.For the non – stoichiometre reaction 2A + B $\to$ C + D, the following kinetic data were obtained in three separate experiments, all at 298 K. The rate law for the formation of C is: Includes table
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.The equivalent conductance of NaCl at concentration C and at infinite dilution are $λ_{C}$ and $λ_{\infty}$ , respectively. The correct relationship between $λ_{C}$ and $λ_{\infty}$ is given as: (where the…
Chemistry · Electrochemistry · MCQ
Q24.The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:
Chemistry · Structure of Atom · MCQ
Q25.The variance of first 50 even natural numbers is
Mathematics · Statistics · MCQ
Q26. $x \to 0 lim \frac{s i n ( π c o s ^{2} x )}{x ^{2}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let the population of rabbits surviving at time $t$ be governed by the differential equation $\frac{d p ( t )}{d t} = \frac{1}{2} p (t) - 200.$ If $p (0) = 100,$ then $p (t)$ equals:
Mathematics · Differential Equations · MCQ
Q28.The integral $0 \int π 1 + 4 sin^{2} \frac{x}{2} - 4 sin \frac{x}{2} d x$ equals:
Mathematics · Definite Integration · MCQ
Q29.The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1$ and $y^{2} \leq 1 - x}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q31.If $A$ is a $3 \times 3$ non-singular matrix such that $A A^{'} = A^{'} A$ and $B = A^{- 1} A^{'},$ then $B B^{'}$ equals:
Mathematics · Matrices and Determinants · MCQ
Q32.If $α, β e 0,$ and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4)$ …
Mathematics · Matrices and Determinants · MCQ
Q33.If $x = - 1$ and $x = 2$ are extreme points of $f (x) = α lo g ∣ x ∣ + β x^{2} + x$ then
Mathematics · Application of Derivatives · MCQ
Q34.If $g$ is the inverse of a function $f$ and $f^{'} (x) = \frac{1}{1 + x ^{5}},$ then $g^{'} (x)$ is equal to:
Mathematics · Differentiation · MCQ
Q35.Let $A$ and $B$ be two events such that $P (\overline{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}$ and $P (\overline{A}) = \frac{1}{4},$ where $\overline{A}$ stands for the…
Mathematics · Probability · MCQ
Q36.The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2} + 3 y^{2} = 6$ on any tangent to it is :
Mathematics · Ellipse · MCQ
Q37.Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes then :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let $P S$ be the median of the triangle with vertices $P (2, 2)$ , $Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ band parallel to PS is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is :
Mathematics · Sequences and Series · MCQ
Q40.Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p e 0.$ If $p, q, r$ in A.P. and $\frac{1}{α} + \frac{1}{β} = 4,$ then the value of $∣ α - β ∣$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q41.If $a \in R$ and the equation $- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0$ (where [ $x$ ] denotes the greater integer $\leq x$ ) has no integral solution, then all possible values of a…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.If z is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $z + \frac{1}{2}$ :
Mathematics · Complex Numbers · MCQ
Q43.Let $f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ where $x \in R$ and $k \geq 1.$ Then $f_{4} (x) - f_{6} (x)$ equals :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q44.The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ is :
Mathematics · 3D Geometry · MCQ
Q45.The current voltage relation of diode is given by $I = (e^{100 V / T} - 1) m A,$ where the applied voltage $V$ is in volts and the temperature $T$ is in degree kelvin. If a student makes an error measuring $\pm 0.01 V$ …
Physics · Electronic Devices · MCQ
Q46.The forward biased diode connection is:
Physics · Electronic Devices · MCQ
Q47.Match List - $1$ (Electromagnetic wave type ) with List - $2$ (Its association/application) and select the correct option from the choices given below the lists: Includes diagram
Physics · Electromagnetic Waves · MCQ
Q48.The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3 \times 1 0^{- 4} T .$ If the radius of the larger circular…
Physics · Atoms and Nuclei · MCQ
Q49.During the propagation of electromagnetic waves in a medium :
Physics · Electromagnetic Waves · MCQ
Q50.Hydrogen $(_{1} H^{1})$ , Deuterium $(_{1} H^{2})$ , singly ionised Helium $(_{2} H e^{4})^{+}$ and doubly ionised lithium $(_{3} L i^{6})^{++}$ all have one electron…
Physics · Atoms and Nuclei · MCQ
Q51.In the circuit shown here, the point $^{'} C^{'}$ is kept connected to point $^{'} A^{'}$ till the current flowing through the circuit becomes constant. Afterward, suddenly, point $^{'} C^{'}$ is disconnected from point $^{'} A^{'}$ and connected to point $^{'} B^{'}$ at… Includes diagram
Physics · Alternating Current · MCQ
Q52.A green light is incident from the water to the air - water interface at the critical angle $(θ)$ . Select the correct statement.
Physics · Geometrical Optics · MCQ
Q53.A thin convex lens made from crown glass $(μ = \frac{3}{2})$ has focal length $f$ . When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3},$ it has the focal lengths $f_{1}$ …
Physics · Geometrical Optics · MCQ
Q54.Two beams, $A$ and $B$ , of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of…
Physics · Wave Optics · MCQ
Q55.A conductor lies along the $z$ -axis at $- 1.5 \leq z < 1.5 m$ and carries a fixed current of $10.0 A$ in $- a_{z}$ direction (see figure). For a field $B = 3.0 \times 1 0^{- 4} e^{- 0.2 x} a_{y} T,$ … Includes diagram
Physics · Magnetics · MCQ
Q56.The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 1 0^{3} A m^{- 1} .$ The current required to be passed in a solenoid of length $10 c m$ and number of turns $100,$ so that the magnet gets demagnetized…
Physics · Magnetic Properties of Matter · MCQ
Q57.In a large building, three are $15$ bulbs of $40 W$ , $5$ bulbs of $100 W$ , $5$ fans of $80 W$ and $1$ heater of $1 k W .$ The voltage of electric mains is $220 V .$ The minimum capacity of the main fuse of the building will be:
Physics · Current Electricity · MCQ
Q58.An open glass tube is immersed in mercury in such a way that a length of $8 c m$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $46 c m$ . What will be…
Physics · Properties of Matter · MCQ
Q59.A parallel plate capacitor is made of two circular plates separated by a distance $5 mm$ and with a dielectric of dielectric constant $2.2$ between them. When the electric field in the dielectric is $3 \times 1 0^{4} V / m$ the charge density…
Physics · Capacitor · MCQ
Q60.Assume that an electric field $E = 30 x^{2} i$ exists in space. Then the potential difference $V_{A} - V_{O},$ where $V_{O}$ is the potential at the origin and $V_{A}$ the potential at $x = 2 m$ is :
Physics · Electrostatics · MCQ
Q61.A pipe of length $85 c m$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250 H z$ . The velocity of sound in air is $340 m / s$ .
Physics · Waves · MCQ
Q62.A particle moves with simple harmonic motion in a straight line. In first $τ s,$ after starting from rest it travels a distance $a,$ and in next $τ s$ it travels $2 a,$ in same direction, then:
Physics · Simple Harmonic Motion · MCQ
Q63.One mole of a diatomic ideal gas undergoes a cyclic process $A B C$ as shown in figure. The process $B C$ is adiabatic. The temperatures at $A, B$ and $C$ are $400 K$ , $800 K$ and $600 K$ respectively. Choose the correct statement : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q64.There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_{1}$ and $d_{2}$ are filled in the tube. Each liquid subtends $9 0^{\circ}$ angle at center. Radius joining their interface makes an angle $α$ … Includes diagram
Physics · Properties of Matter · MCQ
Q65.On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom $R$ and making a circular contact of radius $r$ … Includes diagram
Physics · Properties of Matter · MCQ
Q66.Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross - section of each rod $= 4 c m^{2} .$ End of copper rod is maintained at $10 0^{\circ} C$ where as ends of brass and steel are kept at $0^{\circ} C$ …
Physics · Heat and Thermodynamics · MCQ
Q67.The pressure that has to be applied to the ends of a steel wire of length $10 c m$ to keep its length constant when its temperature is raised by $10 0^{\circ} C$ is: (For steel Young's modulus is $2 \times 1 0^{11} N m^{- 2}$ and…
Physics · Properties of Matter · MCQ
Q68.A mass $^{'} m^{'}$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R .$ If the string does not slip on the cylinder, with what acceleration will the mass fall or release? Includes diagram
Physics · Rotational Motion · MCQ
Q69.Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is :
Physics · Gravitation · MCQ
Q70.A bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $ω r a d / s$ about the vertical. About the point of suspension:
Physics · Rotational Motion · MCQ
Q71.When a rubber-band is stretched by a distance $x$ , it exerts restoring force of magnitude $F = a x + b x^{2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :
Physics · Work Power and Energy · MCQ
Q72.A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{x ^{3}}{6} .$ If the coefficient of friction is $0.5,$ the maximum height above the ground at which the block can be placed without slipping is:
Physics · Laws of Motion · MCQ
Q73.From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:
Physics · Motion in A Straight Line · MCQ
Q74.A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
Physics · Units and Measurements · MCQ

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2014 · Shift 0

74 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
2014 · Shift 0

2014 · Shift 0

74 questions · JEE Main

Chemistry24 questions Mathematics20 questions Physics30 questions

Q1.Resistance of 0.2 M solution of an electrolyte is 50 $Ω$ . The specific conductance of the solution is 1.4 S m-1. The resistance of 0.5 M solution of the same electrolyte is 280 $Ω$ . The molar conductivity of 0.5 M solution of the…
Chemistry · Electrochemistry · MCQ
Q2.Consider separate solutions of 0.500 M $C_{2} H_{5} O H$ (aq), 0.100 M $M g_{3} (P O_{4})_{2}$ (aq), 0.250 M $K B r$ (aq) and 0.125 M $N a_{3} P O_{4}$ (aq) at 25oC. Which statement is true about these solutions, assuming all salts to be strong electrolytes?
Chemistry · Solutions · MCQ
Q3.For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete…
Chemistry · Basics of Organic Chemistry · MCQ
Q4.In which of the following reactions $H_{2} O_{2}$ acts as a reducing agent? 1. $H_{2} O_{2}$ + 2 $H^{+}$ + 2e- $\to$ 2 $H_{2} O$ 2. $H_{2} O_{2}$ - 2e- $\to$ $O_{2}$ + 2 $H^{+}$ 3. $H_{2} O_{2}$ + 2e- $\to$ 2 $O H^{-}$ 4. $H_{2} O_{2}$ + 2 $O H^{-}$ - 2e- $\to$ $O_{2}$ + 2 $H_{2} O$
Chemistry · Redox Reactions · MCQ
Q5.For the reaction $S O_{2}$ (g) + $\frac{1}{2} O_{2} (g) ⇋$ $S O_{3}$ (g). if KP = KC(RT)x where the symbols have usual meaning then the value of x is: (assuming ideality)
Chemistry · Chemical Equilibrium · MCQ
Q6.For complete combustion of ethanol, $C_{2} H_{5} O H$ (l) + 3 $O_{2}$ (g) $\to$ 2 $C O_{2}$ (g) + 3 $H_{2} O$ (l) the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol–1 at 25oC. Assuming ideality the Enthalpy of combustion, $\Delta…
Chemistry · Thermodynamics · MCQ
Q7.Given below are the half-cell reactions: $M n^{2 +}$ + 2e- $\to$ $M n$ ; Eo = -1.18 V 2( $M n^{3 +}$ + e- $\to$ $M n^{2 +}$ ); Eo = +1.51 V The Eo for 3 $M n^{2 +}$ $\to$ $M n$ + 2 $M n^{3 +}$ will be :
Chemistry · Electrochemistry · MCQ
Q8.The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is:
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q9.The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q10.Sodium phenoxide when heated with $C O_{2}$ under pressure at $12 5^{\circ} C$ yields a product which on acetylation products $C .$ The major product $C$ would be Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q11.Which one of the following bases is not present in DNA?
Chemistry · Biomolecules · MCQ
Q12.Considering the basic strength of amines in aqueous solution, which one has the smallest pKb value?
Chemistry · Compounds Containing Nitrogen · MCQ
Q13.On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is:
Chemistry · Compounds Containing Nitrogen · MCQ
Q14.The most suitable reagent for the conversion of R - $C H_{2}$ - OH $\to$ R - CHO is:
Chemistry · Alcohols Phenols and Ethers · MCQ
Q15.In the reaction, the product C is: Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q16.In $S N_{2}$ reactions, the correct order of reactivity for the following compounds: $C H_{3} C l$ , $C H_{3} C H 2 C l$ , $(C H_{3})_{2} C H C l$ and $(C H_{3})_{3} C C l$ is:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q17.The equation which is balanced and represents the correct product(s) is :
Chemistry · Coordination Compounds · MCQ
Q18.The octahedral complex of a metal ion $M^{3 +}$ with four monodentate ligands $L_{1}$ , $L_{2}$ , $L_{3}$ and $L_{4}$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four…
Chemistry · Coordination Compounds · MCQ
Q19.Which series of reactions correctly represents chemical relations related to iron and its compound?
Chemistry · D and F Block Elements · MCQ
Q20.The correct statement for the molecule, $C s I_{3}$ is :
Chemistry · P Block Elements · MCQ
Q21.Which one of the following properties is not shown by NO?
Chemistry · P Block Elements · MCQ
Q22.For the non – stoichiometre reaction 2A + B $\to$ C + D, the following kinetic data were obtained in three separate experiments, all at 298 K. The rate law for the formation of C is: Includes table
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q23.The equivalent conductance of NaCl at concentration C and at infinite dilution are $λ_{C}$ and $λ_{\infty}$ , respectively. The correct relationship between $λ_{C}$ and $λ_{\infty}$ is given as: (where the…
Chemistry · Electrochemistry · MCQ
Q24.The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:
Chemistry · Structure of Atom · MCQ
Q25.The variance of first 50 even natural numbers is
Mathematics · Statistics · MCQ
Q26. $x \to 0 lim \frac{s i n ( π c o s ^{2} x )}{x ^{2}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let the population of rabbits surviving at time $t$ be governed by the differential equation $\frac{d p ( t )}{d t} = \frac{1}{2} p (t) - 200.$ If $p (0) = 100,$ then $p (t)$ equals:
Mathematics · Differential Equations · MCQ
Q28.The integral $0 \int π 1 + 4 sin^{2} \frac{x}{2} - 4 sin \frac{x}{2} d x$ equals:
Mathematics · Definite Integration · MCQ
Q29.The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1$ and $y^{2} \leq 1 - x}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}} d x$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q31.If $A$ is a $3 \times 3$ non-singular matrix such that $A A^{'} = A^{'} A$ and $B = A^{- 1} A^{'},$ then $B B^{'}$ equals:
Mathematics · Matrices and Determinants · MCQ
Q32.If $α, β e 0,$ and $f (n) = α^{n} + β^{n}$ and $3 1 + f (1) 1 + f (2) 1 + f (1) 1 + f (2) 1 + f (3) 1 + f (2) 1 + f (3) 1 + f (4)$ …
Mathematics · Matrices and Determinants · MCQ
Q33.If $x = - 1$ and $x = 2$ are extreme points of $f (x) = α lo g ∣ x ∣ + β x^{2} + x$ then
Mathematics · Application of Derivatives · MCQ
Q34.If $g$ is the inverse of a function $f$ and $f^{'} (x) = \frac{1}{1 + x ^{5}},$ then $g^{'} (x)$ is equal to:
Mathematics · Differentiation · MCQ
Q35.Let $A$ and $B$ be two events such that $P (\overline{A \cup B}) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}$ and $P (\overline{A}) = \frac{1}{4},$ where $\overline{A}$ stands for the…
Mathematics · Probability · MCQ
Q36.The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2} + 3 y^{2} = 6$ on any tangent to it is :
Mathematics · Ellipse · MCQ
Q37.Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes then :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let $P S$ be the median of the triangle with vertices $P (2, 2)$ , $Q (6, - 1)$ and $R (7, 3)$ . The equation of the line passing through $(1, - 1)$ band parallel to PS is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is :
Mathematics · Sequences and Series · MCQ
Q40.Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p e 0.$ If $p, q, r$ in A.P. and $\frac{1}{α} + \frac{1}{β} = 4,$ then the value of $∣ α - β ∣$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q41.If $a \in R$ and the equation $- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0$ (where [ $x$ ] denotes the greater integer $\leq x$ ) has no integral solution, then all possible values of a…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q42.If z is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $z + \frac{1}{2}$ :
Mathematics · Complex Numbers · MCQ
Q43.Let $f_{k} (x) = \frac{1}{k} (sin^{k} x + cos^{k} x)$ where $x \in R$ and $k \geq 1.$ Then $f_{4} (x) - f_{6} (x)$ equals :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q44.The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^{2} = m^{2} + n^{2}$ is :
Mathematics · 3D Geometry · MCQ
Q45.The current voltage relation of diode is given by $I = (e^{100 V / T} - 1) m A,$ where the applied voltage $V$ is in volts and the temperature $T$ is in degree kelvin. If a student makes an error measuring $\pm 0.01 V$ …
Physics · Electronic Devices · MCQ
Q46.The forward biased diode connection is:
Physics · Electronic Devices · MCQ
Q47.Match List - $1$ (Electromagnetic wave type ) with List - $2$ (Its association/application) and select the correct option from the choices given below the lists: Includes diagram
Physics · Electromagnetic Waves · MCQ
Q48.The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3 \times 1 0^{- 4} T .$ If the radius of the larger circular…
Physics · Atoms and Nuclei · MCQ
Q49.During the propagation of electromagnetic waves in a medium :
Physics · Electromagnetic Waves · MCQ
Q50.Hydrogen $(_{1} H^{1})$ , Deuterium $(_{1} H^{2})$ , singly ionised Helium $(_{2} H e^{4})^{+}$ and doubly ionised lithium $(_{3} L i^{6})^{++}$ all have one electron…
Physics · Atoms and Nuclei · MCQ
Q51.In the circuit shown here, the point $^{'} C^{'}$ is kept connected to point $^{'} A^{'}$ till the current flowing through the circuit becomes constant. Afterward, suddenly, point $^{'} C^{'}$ is disconnected from point $^{'} A^{'}$ and connected to point $^{'} B^{'}$ at… Includes diagram
Physics · Alternating Current · MCQ
Q52.A green light is incident from the water to the air - water interface at the critical angle $(θ)$ . Select the correct statement.
Physics · Geometrical Optics · MCQ
Q53.A thin convex lens made from crown glass $(μ = \frac{3}{2})$ has focal length $f$ . When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3},$ it has the focal lengths $f_{1}$ …
Physics · Geometrical Optics · MCQ
Q54.Two beams, $A$ and $B$ , of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of…
Physics · Wave Optics · MCQ
Q55.A conductor lies along the $z$ -axis at $- 1.5 \leq z < 1.5 m$ and carries a fixed current of $10.0 A$ in $- a_{z}$ direction (see figure). For a field $B = 3.0 \times 1 0^{- 4} e^{- 0.2 x} a_{y} T,$ … Includes diagram
Physics · Magnetics · MCQ
Q56.The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 1 0^{3} A m^{- 1} .$ The current required to be passed in a solenoid of length $10 c m$ and number of turns $100,$ so that the magnet gets demagnetized…
Physics · Magnetic Properties of Matter · MCQ
Q57.In a large building, three are $15$ bulbs of $40 W$ , $5$ bulbs of $100 W$ , $5$ fans of $80 W$ and $1$ heater of $1 k W .$ The voltage of electric mains is $220 V .$ The minimum capacity of the main fuse of the building will be:
Physics · Current Electricity · MCQ
Q58.An open glass tube is immersed in mercury in such a way that a length of $8 c m$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $46 c m$ . What will be…
Physics · Properties of Matter · MCQ
Q59.A parallel plate capacitor is made of two circular plates separated by a distance $5 mm$ and with a dielectric of dielectric constant $2.2$ between them. When the electric field in the dielectric is $3 \times 1 0^{4} V / m$ the charge density…
Physics · Capacitor · MCQ
Q60.Assume that an electric field $E = 30 x^{2} i$ exists in space. Then the potential difference $V_{A} - V_{O},$ where $V_{O}$ is the potential at the origin and $V_{A}$ the potential at $x = 2 m$ is :
Physics · Electrostatics · MCQ
Q61.A pipe of length $85 c m$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250 H z$ . The velocity of sound in air is $340 m / s$ .
Physics · Waves · MCQ
Q62.A particle moves with simple harmonic motion in a straight line. In first $τ s,$ after starting from rest it travels a distance $a,$ and in next $τ s$ it travels $2 a,$ in same direction, then:
Physics · Simple Harmonic Motion · MCQ
Q63.One mole of a diatomic ideal gas undergoes a cyclic process $A B C$ as shown in figure. The process $B C$ is adiabatic. The temperatures at $A, B$ and $C$ are $400 K$ , $800 K$ and $600 K$ respectively. Choose the correct statement : Includes diagram
Physics · Heat and Thermodynamics · MCQ
Q64.There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_{1}$ and $d_{2}$ are filled in the tube. Each liquid subtends $9 0^{\circ}$ angle at center. Radius joining their interface makes an angle $α$ … Includes diagram
Physics · Properties of Matter · MCQ
Q65.On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom $R$ and making a circular contact of radius $r$ … Includes diagram
Physics · Properties of Matter · MCQ
Q66.Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross - section of each rod $= 4 c m^{2} .$ End of copper rod is maintained at $10 0^{\circ} C$ where as ends of brass and steel are kept at $0^{\circ} C$ …
Physics · Heat and Thermodynamics · MCQ
Q67.The pressure that has to be applied to the ends of a steel wire of length $10 c m$ to keep its length constant when its temperature is raised by $10 0^{\circ} C$ is: (For steel Young's modulus is $2 \times 1 0^{11} N m^{- 2}$ and…
Physics · Properties of Matter · MCQ
Q68.A mass $^{'} m^{'}$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R .$ If the string does not slip on the cylinder, with what acceleration will the mass fall or release? Includes diagram
Physics · Rotational Motion · MCQ
Q69.Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is :
Physics · Gravitation · MCQ
Q70.A bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $ω r a d / s$ about the vertical. About the point of suspension:
Physics · Rotational Motion · MCQ
Q71.When a rubber-band is stretched by a distance $x$ , it exerts restoring force of magnitude $F = a x + b x^{2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :
Physics · Work Power and Energy · MCQ
Q72.A block of mass $m$ is placed on a surface with a vertical cross section given by $y = \frac{x ^{3}}{6} .$ If the coefficient of friction is $0.5,$ the maximum height above the ground at which the block can be placed without slipping is:
Physics · Laws of Motion · MCQ
Q73.From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:
Physics · Motion in A Straight Line · MCQ
Q74.A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
Physics · Units and Measurements · MCQ