2015 · Shift 0

69 questions · JEE Main

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JEE Main
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2015 · Shift 0

2015 · Shift 0

69 questions · JEE Main

Chemistry22 questions Mathematics20 questions Physics27 questions

Q1.The vapour pressure of acetone at 20oC is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20oC, its vapour pressure was 183 torr. The molar mass (g mol-1) of the substance is:
Chemistry · Solutions · MCQ
Q2.Which of the following compounds will exhibit geometrical isomerism?
Chemistry · Basics of Organic Chemistry · MCQ
Q3.In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is: (at. Mass Ag = 108; Br = 80)
Chemistry · Basics of Organic Chemistry · MCQ
Q4.The molecular formula of a commercial resin used for exchanging ions in water softening is $C_{8} H_{7} S O_{3} N a$ (Mol. Wt. 206). What would be the maximum uptake of $C a^{2 +}$ ions by the resin when expressed in mole per gram resin?
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q5.The following reaction is performed at 298 K 2 $N O$ (g) + $O_{2}$ (g) $⇋$ 2 $N O_{2}$ (g) The standard free energy of formation of $N O$ (g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of $N O_{2}$ (g) at…
Chemistry · Thermodynamics · MCQ
Q6.The standard Gibbs energy change at 300 K for the reaction 2A $⇋$ B + C is 2494.2 J. At a given time, the composition of the reaction mixture is [A] = 1/2, [B] = 2 and [C] = 1/2. The reaction proceeds in the: [R = 8.314…
Chemistry · Chemical Equilibrium · MCQ
Q7.Two Faraday of electricity is passed through a solution of $C u S O_{4}$ . The mass of copper deposited at the cathode is: (at. mass of Cu = 63.5 amu)
Chemistry · Electrochemistry · MCQ
Q8.The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q9.Match the catalysts to the correct processes : Includes table
Chemistry · D and F Block Elements · MCQ
Q10.In the reaction The product $E$ is : Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q11.Which compound would give $5$ - keto - $2$ - methylhexanal upon ozonolysis?
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q12.Which of the vitamins given below is water soluble?
Chemistry · Biomolecules · MCQ
Q13.In the following sequence of reactions: The product C is Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The synthesis of alkyl fluorides is best accomplished by:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q15.The number of geometric isomers that can exist for square planar $[P t (C l) (p y) (N H_{3}) (N H_{2} O H)]^{+}$ is (py = pyridine) :
Chemistry · Coordination Compounds · MCQ
Q16.The colour of $K M n O_{4}$ is due to :
Chemistry · D and F Block Elements · MCQ
Q17.Which of the following compounds is not colored yellow?
Chemistry · Coordination Compounds · MCQ
Q18.Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : The reaction between nitrogen and oxygen requires high temperature.
Chemistry · P Block Elements · MCQ
Q19.Which one has the highest boiling point?
Chemistry · P Block Elements · MCQ
Q20.Higher order (>3) reactions are rare due to
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q21.The ionic radii (in Å) of $N_{3}^{-}$ , $O^{2 -}$ and $F^{-}$ are respectively:
Chemistry · Periodic Table and Periodicity · MCQ
Q22.Which of the following is the energy of a possible excited state of hydrogen?
Chemistry · Structure of Atom · MCQ
Q23.If the function. $g (x) = {k x + 1, m x + 2, 0 \leq x \leq 3 3 < x \leq 5$ is differentiable, then the value of $k + m$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :
Mathematics · Statistics · MCQ
Q25. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n},$ for $n \geq 1,$ then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.If $12$ different balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :
Mathematics · Probability · MCQ
Q28.Let $y (x)$ be the solution of the differential equation $(x lo g x) \frac{d y}{d x} + y = 2 x lo g x, (x \geq 1) .$ Then $y (e)$ is equal to :
Mathematics · Differential Equations · MCQ
Q29.The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x$ and $y \geq 4 x - 1}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $2 \int 4 \frac{l o g x ^{2}}{l o g x ^{2} + l o g ( 36 - 12 x + x ^{2} )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q31.The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals :
Mathematics · Indefinite Integrals · MCQ
Q32.If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I,$ where $I$ is $3 \times 3$ identity matrix, then the…
Mathematics · Matrices and Determinants · MCQ
Q33.The set of all values of $λ$ for which the system of linear equations: $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1} 2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2} - x_{1} + 2 x_{2} = λ x_{3}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.Let $f (x)$ be a polynomial of degree four having extreme values at $x = 1$ and $x = 2$ . If $x \to 0 lim [1 + \frac{f ( x )}{x ^{2}}] = 3$ , then f $(2)$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q35.Let $tan^{- 1} y = tan^{- 1} x + tan^{- 1} (\frac{2 x}{1 - x ^{2}}),$ where $∣ x ∣ < \frac{1}{3} .$ Then a value of $y$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2} = 8 y$ . If the point $P$ divides the line segment $O Q$ internally in the ratio $1 : 3$ , then locus of $P$ is :
Mathematics · Parabola · MCQ
Q37.Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a :
Mathematics · Circle · MCQ
Q38.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0) (0, 41)$ and $(41, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.If m is the A.M. of two distinct real numbers l and n $(l, n > 1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between $l$ and n, then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals:
Mathematics · Sequences and Series · MCQ
Q40.The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
Mathematics · Permutations and Combinations · MCQ
Q41.A complex number z is said to be unimodular if $∣ z ∣ = 1$ . Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z _{2}}$ is unimodular and $z_{2}$ is not unimodular.…
Mathematics · Complex Numbers · MCQ
Q42.Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are
Mathematics · Sets and Relations · MCQ
Q43.As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :
Physics · Atoms and Nuclei · MCQ
Q44.A red $L E D$ emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1 m$ from the diode is :
Physics · Electronic Devices · MCQ
Q45.Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray, incident at an angle $θ$ . on the face $A B$ would get transmitted through the face $A C$ of the prism… Includes diagram
Physics · Geometrical Optics · MCQ
Q46.An inductor $(L = 0.03 H)$ and a resistor $(R = 0.15 k Ω)$ are connected in series to a battery of $15 V E M F$ in a circuit shown below. The key $K_{1}$ has been kept closed for a long time. Then at $t = 0$ , $K_{1}$ is… Includes diagram
Physics · Alternating Current · MCQ
Q47.An $L C R$ circuit is equivalent to a damped pendulum. In an $L C R$ circuit the capacitor is charged to $Q_{0}$ and then connected to the $L$ and $R$ as shown below : If a student plots graphs of the square of maximum charge $(Q_{M a x}^{2})$ … Includes diagram
Physics · Alternating Current · MCQ
Q48.Assuming human pupil to have a radius of $0.25 c m$ and a comfortable viewing distance of $25 c m$ , the minimum separation between two objects that human eye can resolve at $500 nm$ wavelength is :
Physics · Wave Optics · MCQ
Q49.On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light…
Physics · Wave Optics · MCQ
Q50.Two coaxial solenoids of different radius carry current $I$ in the same direction. $F_{1}$ be the magnetic force on the inner solenoid due to the outer one and $F_{2}$ be the magnetic force on the outer…
Physics · Electromagnetic Induction · MCQ
Q51.A rectangular loop of sides $10 c m$ and $5 c m$ carrying a current $1$ of $12 A$ is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of $0.3 T$ in the positive $z$ direction, in which… Includes diagram
Physics · Magnetics · MCQ
Q52.Two stones are thrown up simultaneously from the edge of a cliff $240 m$ high with initial speed of $10 m / s$ and $40 m / s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone…
Physics · Motion in A Straight Line · MCQ
Q53.In the circuit shown, the current in the $1Ω$ resistor is : Includes diagram
Physics · Current Electricity · MCQ
Q54.Two long current carrying thin wires, both with current $I,$ are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $^{'} θ^{'}$ with the vertical. If wires have mass $λ$ … Includes diagram
Physics · Magnetics · MCQ
Q55.When $5 V$ potential difference is applied across a wire of length $0.1 m,$ the drift speed of electrons is $2.5 \times 1 0^{- 4} m s^{- 1} .$ If the electron density in the wire is $8 \times 1 0^{28} m^{- 3},$ the resistivity…
Physics · Current Electricity · MCQ
Q56.A long cylindrical shell carries positives surfaces change $σ$ in the upper half and negative surface charge - $σ$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are…
Physics · Electrostatics · MCQ
Q57.A uniformly charged solid sphere of radius $R$ has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3 V _{0}}{2}, \frac{5 V _{0}}{4}, \frac{3 V _{0}}{4}$ …
Physics · Electrostatics · Multiple correct
Q58.In the given circuit, charges $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F . Q_{2}$ as a function of $^{'} C^{'}$ is given properly by: $(f i g u r es a r e d r a w n sc h e ma t i c a l l y an d a r e n o t t o sc a l e)$ … Includes diagram
Physics · Capacitor · MCQ
Q59.For a simple pendulum, a graph is plotted between its kinetic energy $(K E)$ and potential energy $(P E)$ against its displacement $d .$ Which one of the following represents these correctly? $(g r a p h s a r esc h e ma t i c an d n o t d r a w n t osc a l e)$
Physics · Simple Harmonic Motion · MCQ
Q60.A pendulum made of a uniform wire of cross sectional area $A$ has time period $T .$ When an additional mass $M$ is added to its bob, the time period changes to $T_{M .}$ If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ …
Physics · Simple Harmonic Motion · MCQ
Q61.From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R /2$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the center of the cavity thus formed is: ( $G = g r a v i t a t i o na l co n s t an t$ … Includes diagram
Physics · Gravitation · MCQ
Q62.Consider a spherical shell of radius $R$ at temperature $T$ . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^{4}$ and pressure $p = \frac{1}{3} (\frac{U}{V})$ …
Physics · Heat and Thermodynamics · MCQ
Q63.Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q},$ where $V$ is the volume of the gas. The value of $q$ is: $(γ = \frac{C _{p}}{C _{v}})$ …
Physics · Heat and Thermodynamics · MCQ
Q64.A solid body of constant heat capacity $1 J /^{\circ} C$ is being heated by keeping it in contact with reservoirs in two ways: $(i)$ Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies…
Physics · Heat and Thermodynamics · MCQ
Q65.Given in the figure are two blocks $A$ and $B$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $B$ and the… Includes diagram
Physics · Laws of Motion · MCQ
Q66.From a solid sphere of mass $M$ and radius $R$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:
Physics · Rotational Motion · MCQ
Q67.Distance of the center of mass of a solid uniform cone from its vertex is $z_{0}$ . If the radius of its base is $R$ and its height is $h$ then $z_{0}$ is equal to :
Physics · Center of Mass · MCQ
Q68.A particle of mass $m$ moving in the $x$ direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ direction with speed $v .$ If the collision is perfectly inelastic, the percentage loss in the energy during the…
Physics · Center of Mass · MCQ
Q69.The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution.…
Physics · Simple Harmonic Motion · MCQ

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2015 · Shift 0

69 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
2015 · Shift 0

2015 · Shift 0

69 questions · JEE Main

Chemistry22 questions Mathematics20 questions Physics27 questions

Q1.The vapour pressure of acetone at 20oC is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20oC, its vapour pressure was 183 torr. The molar mass (g mol-1) of the substance is:
Chemistry · Solutions · MCQ
Q2.Which of the following compounds will exhibit geometrical isomerism?
Chemistry · Basics of Organic Chemistry · MCQ
Q3.In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is: (at. Mass Ag = 108; Br = 80)
Chemistry · Basics of Organic Chemistry · MCQ
Q4.The molecular formula of a commercial resin used for exchanging ions in water softening is $C_{8} H_{7} S O_{3} N a$ (Mol. Wt. 206). What would be the maximum uptake of $C a^{2 +}$ ions by the resin when expressed in mole per gram resin?
Chemistry · Some Basic Concepts of Chemistry · MCQ
Q5.The following reaction is performed at 298 K 2 $N O$ (g) + $O_{2}$ (g) $⇋$ 2 $N O_{2}$ (g) The standard free energy of formation of $N O$ (g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of $N O_{2}$ (g) at…
Chemistry · Thermodynamics · MCQ
Q6.The standard Gibbs energy change at 300 K for the reaction 2A $⇋$ B + C is 2494.2 J. At a given time, the composition of the reaction mixture is [A] = 1/2, [B] = 2 and [C] = 1/2. The reaction proceeds in the: [R = 8.314…
Chemistry · Chemical Equilibrium · MCQ
Q7.Two Faraday of electricity is passed through a solution of $C u S O_{4}$ . The mass of copper deposited at the cathode is: (at. mass of Cu = 63.5 amu)
Chemistry · Electrochemistry · MCQ
Q8.The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:
Chemistry · Chemical Bonding and Molecular Structure · MCQ
Q9.Match the catalysts to the correct processes : Includes table
Chemistry · D and F Block Elements · MCQ
Q10.In the reaction The product $E$ is : Includes diagram
Chemistry · Compounds Containing Nitrogen · MCQ
Q11.Which compound would give $5$ - keto - $2$ - methylhexanal upon ozonolysis?
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q12.Which of the vitamins given below is water soluble?
Chemistry · Biomolecules · MCQ
Q13.In the following sequence of reactions: The product C is Includes diagram
Chemistry · Aldehydes Ketones and Carboxylic Acids · MCQ
Q14.The synthesis of alkyl fluorides is best accomplished by:
Chemistry · Haloalkanes and Haloarenes · MCQ
Q15.The number of geometric isomers that can exist for square planar $[P t (C l) (p y) (N H_{3}) (N H_{2} O H)]^{+}$ is (py = pyridine) :
Chemistry · Coordination Compounds · MCQ
Q16.The colour of $K M n O_{4}$ is due to :
Chemistry · D and F Block Elements · MCQ
Q17.Which of the following compounds is not colored yellow?
Chemistry · Coordination Compounds · MCQ
Q18.Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : The reaction between nitrogen and oxygen requires high temperature.
Chemistry · P Block Elements · MCQ
Q19.Which one has the highest boiling point?
Chemistry · P Block Elements · MCQ
Q20.Higher order (>3) reactions are rare due to
Chemistry · Chemical Kinetics and Nuclear Chemistry · MCQ
Q21.The ionic radii (in Å) of $N_{3}^{-}$ , $O^{2 -}$ and $F^{-}$ are respectively:
Chemistry · Periodic Table and Periodicity · MCQ
Q22.Which of the following is the energy of a possible excited state of hydrogen?
Chemistry · Structure of Atom · MCQ
Q23.If the function. $g (x) = {k x + 1, m x + 2, 0 \leq x \leq 3 3 < x \leq 5$ is differentiable, then the value of $k + m$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :
Mathematics · Statistics · MCQ
Q25. $x \to 0 lim \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n},$ for $n \geq 1,$ then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.If $12$ different balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :
Mathematics · Probability · MCQ
Q28.Let $y (x)$ be the solution of the differential equation $(x lo g x) \frac{d y}{d x} + y = 2 x lo g x, (x \geq 1) .$ Then $y (e)$ is equal to :
Mathematics · Differential Equations · MCQ
Q29.The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x$ and $y \geq 4 x - 1}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.The integral $2 \int 4 \frac{l o g x ^{2}}{l o g x ^{2} + l o g ( 36 - 12 x + x ^{2} )} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q31.The integral $\int \frac{d x}{x ^{2} ( x ^{4} + 1 ) ^{3/4}}$ equals :
Mathematics · Indefinite Integrals · MCQ
Q32.If $A = 12 a 212 2 - 2 b$ is a matrix satisfying the equation $A A^{T} = 9 I,$ where $I$ is $3 \times 3$ identity matrix, then the…
Mathematics · Matrices and Determinants · MCQ
Q33.The set of all values of $λ$ for which the system of linear equations: $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1} 2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2} - x_{1} + 2 x_{2} = λ x_{3}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.Let $f (x)$ be a polynomial of degree four having extreme values at $x = 1$ and $x = 2$ . If $x \to 0 lim [1 + \frac{f ( x )}{x ^{2}}] = 3$ , then f $(2)$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q35.Let $tan^{- 1} y = tan^{- 1} x + tan^{- 1} (\frac{2 x}{1 - x ^{2}}),$ where $∣ x ∣ < \frac{1}{3} .$ Then a value of $y$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2} = 8 y$ . If the point $P$ divides the line segment $O Q$ internally in the ratio $1 : 3$ , then locus of $P$ is :
Mathematics · Parabola · MCQ
Q37.Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a :
Mathematics · Circle · MCQ
Q38.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0) (0, 41)$ and $(41, 0)$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.If m is the A.M. of two distinct real numbers l and n $(l, n > 1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between $l$ and n, then $G_{1}^{4} + 2 G_{2}^{4} + G_{3}^{4}$ equals:
Mathematics · Sequences and Series · MCQ
Q40.The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
Mathematics · Permutations and Combinations · MCQ
Q41.A complex number z is said to be unimodular if $∣ z ∣ = 1$ . Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z _{2}}$ is unimodular and $z_{2}$ is not unimodular.…
Mathematics · Complex Numbers · MCQ
Q42.Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are
Mathematics · Sets and Relations · MCQ
Q43.As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :
Physics · Atoms and Nuclei · MCQ
Q44.A red $L E D$ emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1 m$ from the diode is :
Physics · Electronic Devices · MCQ
Q45.Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray, incident at an angle $θ$ . on the face $A B$ would get transmitted through the face $A C$ of the prism… Includes diagram
Physics · Geometrical Optics · MCQ
Q46.An inductor $(L = 0.03 H)$ and a resistor $(R = 0.15 k Ω)$ are connected in series to a battery of $15 V E M F$ in a circuit shown below. The key $K_{1}$ has been kept closed for a long time. Then at $t = 0$ , $K_{1}$ is… Includes diagram
Physics · Alternating Current · MCQ
Q47.An $L C R$ circuit is equivalent to a damped pendulum. In an $L C R$ circuit the capacitor is charged to $Q_{0}$ and then connected to the $L$ and $R$ as shown below : If a student plots graphs of the square of maximum charge $(Q_{M a x}^{2})$ … Includes diagram
Physics · Alternating Current · MCQ
Q48.Assuming human pupil to have a radius of $0.25 c m$ and a comfortable viewing distance of $25 c m$ , the minimum separation between two objects that human eye can resolve at $500 nm$ wavelength is :
Physics · Wave Optics · MCQ
Q49.On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light…
Physics · Wave Optics · MCQ
Q50.Two coaxial solenoids of different radius carry current $I$ in the same direction. $F_{1}$ be the magnetic force on the inner solenoid due to the outer one and $F_{2}$ be the magnetic force on the outer…
Physics · Electromagnetic Induction · MCQ
Q51.A rectangular loop of sides $10 c m$ and $5 c m$ carrying a current $1$ of $12 A$ is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of $0.3 T$ in the positive $z$ direction, in which… Includes diagram
Physics · Magnetics · MCQ
Q52.Two stones are thrown up simultaneously from the edge of a cliff $240 m$ high with initial speed of $10 m / s$ and $40 m / s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone…
Physics · Motion in A Straight Line · MCQ
Q53.In the circuit shown, the current in the $1Ω$ resistor is : Includes diagram
Physics · Current Electricity · MCQ
Q54.Two long current carrying thin wires, both with current $I,$ are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $^{'} θ^{'}$ with the vertical. If wires have mass $λ$ … Includes diagram
Physics · Magnetics · MCQ
Q55.When $5 V$ potential difference is applied across a wire of length $0.1 m,$ the drift speed of electrons is $2.5 \times 1 0^{- 4} m s^{- 1} .$ If the electron density in the wire is $8 \times 1 0^{28} m^{- 3},$ the resistivity…
Physics · Current Electricity · MCQ
Q56.A long cylindrical shell carries positives surfaces change $σ$ in the upper half and negative surface charge - $σ$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are…
Physics · Electrostatics · MCQ
Q57.A uniformly charged solid sphere of radius $R$ has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3 V _{0}}{2}, \frac{5 V _{0}}{4}, \frac{3 V _{0}}{4}$ …
Physics · Electrostatics · Multiple correct
Q58.In the given circuit, charges $Q_{2}$ on the $2 μ F$ capacitor changes as $C$ is varied from $1 μ F$ to $3 μ F . Q_{2}$ as a function of $^{'} C^{'}$ is given properly by: $(f i g u r es a r e d r a w n sc h e ma t i c a l l y an d a r e n o t t o sc a l e)$ … Includes diagram
Physics · Capacitor · MCQ
Q59.For a simple pendulum, a graph is plotted between its kinetic energy $(K E)$ and potential energy $(P E)$ against its displacement $d .$ Which one of the following represents these correctly? $(g r a p h s a r esc h e ma t i c an d n o t d r a w n t osc a l e)$
Physics · Simple Harmonic Motion · MCQ
Q60.A pendulum made of a uniform wire of cross sectional area $A$ has time period $T .$ When an additional mass $M$ is added to its bob, the time period changes to $T_{M .}$ If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ …
Physics · Simple Harmonic Motion · MCQ
Q61.From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $R /2$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the center of the cavity thus formed is: ( $G = g r a v i t a t i o na l co n s t an t$ … Includes diagram
Physics · Gravitation · MCQ
Q62.Consider a spherical shell of radius $R$ at temperature $T$ . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^{4}$ and pressure $p = \frac{1}{3} (\frac{U}{V})$ …
Physics · Heat and Thermodynamics · MCQ
Q63.Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{q},$ where $V$ is the volume of the gas. The value of $q$ is: $(γ = \frac{C _{p}}{C _{v}})$ …
Physics · Heat and Thermodynamics · MCQ
Q64.A solid body of constant heat capacity $1 J /^{\circ} C$ is being heated by keeping it in contact with reservoirs in two ways: $(i)$ Sequentially keeping in contact with $2$ reservoirs such that each reservoir supplies…
Physics · Heat and Thermodynamics · MCQ
Q65.Given in the figure are two blocks $A$ and $B$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $B$ and the… Includes diagram
Physics · Laws of Motion · MCQ
Q66.From a solid sphere of mass $M$ and radius $R$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:
Physics · Rotational Motion · MCQ
Q67.Distance of the center of mass of a solid uniform cone from its vertex is $z_{0}$ . If the radius of its base is $R$ and its height is $h$ then $z_{0}$ is equal to :
Physics · Center of Mass · MCQ
Q68.A particle of mass $m$ moving in the $x$ direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ direction with speed $v .$ If the collision is perfectly inelastic, the percentage loss in the energy during the…
Physics · Center of Mass · MCQ
Q69.The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution.…
Physics · Simple Harmonic Motion · MCQ