Recent questions in 2015

The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them :

asked Dec 11, 2018 by pady_1

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The reaction $2N_2O_5 (g) \to 4NO_2 (g) +O_2 (g)$ follows first order kinetics. The pressure of a vessel containing only $N_2O_5$ was found to increase from $50\; mm \;Hg$ to $87.5\; mm \;Hg$ in $30\; min$ . The pressure exerted by the gases after $60 \;min$ . will be (Assume temperature remains constant) :

asked Dec 11, 2018 by pady_1

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A variable, opposite external potential $(E_{ext})$ is applied to the cell $Zn|Zn^{2+} \; (1M) || Cu^{2+} \; (1M) | Cu$ , of potential $1.1\;V$ . When $E_{ext} < 1.1\;V$ and $E_{ext} > 1.1 \;V$ , respectively electrons flow from :

asked Dec 11, 2018 by pady_1

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Gaseous $N_2O_4$ dissociates into gaseous $NO_2$ according to the reaction $N_2O_4 (g) \leftrightharpoons 2NO_2 (g)$ At $300\; K$ and $1\; atm \;pressure$ , the degree of dissociation of $N_2O_4$ is $0.2$ . If one mole of $N_2O_4$ gas is contained in a vessel, then the density of the equilibrium mixture is :

asked Dec 11, 2018 by pady_1

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A solution at $20^{\circ}C$ is composed of $1.5\; mol$ of benzene and $3.5\; mol$ of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are $74.7\; torr$ and $22.3\; torr$ , respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively :

asked Dec 11, 2018 by pady_1

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The heat of atomization of methane and ethane are $360\; kJ/mol$ and $620\; kJ/mol$ , respectively. The longest wavelength of light capable of breaking the $C - C$ bond is (Avogadro number = $6.02 \times 10^{23} ,\; h =6.62 \times 10^{-34}\; J s$ ) :

asked Dec 11, 2018 by pady_1

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After understanding the assertion and reason, choose the correct option. Assertion : In the bonding molecular orbital (MO) of $H_2$ , electron density is increased between the nuclei. Reason : The bonding MO is $\Psi_A + \Psi_B$ , which shows destructive interference of the combining electron waves

asked Dec 11, 2018 by pady_1

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If the principal quantum number n56, the correct sequence of filling of electrons will be :

asked Dec 11, 2018 by pady_1

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Which of the following is not an assumption of the kinetic theory of gases ?

asked Dec 11, 2018 by pady_1

1 answer

A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed $52\; g$ . The formula of the hydrated salt is : (atomic mass, $Ba=137 \;amu,\; Cl = 35.5 \;amu$ )

asked Dec 11, 2018 by pady_1

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Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as : If the zero error is 20.03 cm, then mean corrected diameter is :

asked Dec 11, 2018 by pady_1

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In an unbiased n-p junction electrons diffuse from n - region to p - region because :

asked Dec 11, 2018 by pady_1

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If one were to apply Bohr model to a particle of mass $'m'$ and charge $'q'$ moving in a plane under the influence of a magnetic field $'B'$ , the energy of the charged particle in the $n^{th}$ level will be :

asked Dec 11, 2018 by pady_1

0 answers

de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to $(|e| = 1.6 \times 10^{-19} C, m_e = 9.1 \times 10^{-31} kg, \; h = 6.6 \times 10^{-34} Js)$ :

asked Dec 11, 2018 by pady_1

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A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is $\theta$ , then $\theta$ is close to :

asked Dec 11, 2018 by pady_1

0 answers

A parallel beam of electrons travelling in $x$ -direction falls on a slit of width $d$ (see figure). If after passing the slit, an electron acquires momentum $p_{_y}$ in the $y$ -direction then for a majority of electrons passing through the slit ( $h$ is Planck's constant) :

asked Dec 11, 2018 by pady_1

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You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

asked Dec 11, 2018 by pady_1

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An electromagnetic wave travelling in the $x$ -direction has frequency of $2 \times 10^{14}\; Hz$ and electric field amplitude of $27\; Vm^{-1}$ . From the options given below, which one describes the magnetic field for this wave ?

asked Dec 11, 2018 by pady_1

0 answers

In the circuits (a) and (b) switches $S_1$ and $S_2$ are closed at $t = 0$ and are kept closed for a long time. The variation of currents in the two circuits for $t \geq 0$ are roughly shown by (figures are schematic and not drawn to scale) :

asked Dec 11, 2018 by pady_1

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When current in a coil changes from $5\; A$ to $2\; A$ in $0.1 \;s$ , an average voltage of $50\; V$ is produced. The self - inductance of the coil is :

asked Dec 11, 2018 by pady_1

0 answers

A $25 \;cm$ long solenoid has radius $2\; cm$ and $500$ total number of turns. It carries a current of $15\; A$ . If it is equivalent to a magnet of the same size and magnetization $\overrightarrow{M}$ (magnetic moment/volume), then $|\overrightarrow{M}|$ is :

asked Dec 11, 2018 by pady_1

0 answers

A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width $'d'$ . If $'\alpha'$ be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be :

asked Dec 11, 2018 by pady_1

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A $10V$ battery with internal resistance $1 \Omega$ and a $15V$ battery with internal resistance $0.6 \Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to :

asked Dec 11, 2018 by pady_1

0 answers

Suppose the drift velocity $v_{_d}$ in a material varied with the applied electric field $E$ as $v_{_d} \propto \sqrt{E}$ ; . Then $V - I$ graph for a wire made of such a material is best given by :

asked Dec 11, 2018 by pady_1

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If the capacitance of a nanocapacitor is measured in terms of a unit $'u'$ made by combining the electronic charge $'e'$ , Bohr radius $'a_0$ , Planck's constant $'h'$ and speed of light $'c'$ then :

asked Dec 11, 2018 by pady_1

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Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma_1$ is the surface charge on the inner surface and $Q_1$ net charge on it and $\sigma_2$ the surface charge on the outer surface and $Q_2$ net charge on it then :

asked Dec 11, 2018 by pady_1

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A thin disc of radius $b=2a$ has a concentric hole of radius $'a'$ in it (see figure). It carries uniform surface charge $'\sigma'$ on it. If the electric field on its axis at height $'h (h<< a)$ from its centre is given as 'Ch' then value of 'C' is :

asked Dec 11, 2018 by pady_1

0 answers

A bat moving at $10 \;ms^{-1}$ towards a wall sends a sound signal of $8000\; Hz$ towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = $320 \;ms^{-1}$ )$

asked Dec 11, 2018 by pady_1

0 answers

A simple harmonic oscillator of angular frequency $2\; rad\; s^{-1}$ is acted upon by an external force $F = \sin t\; N$ . If the oscillator is at rest in its equilibrium position at $t=0$ , its position at later times is proportional to :

asked Dec 11, 2018 by pady_1

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In an ideal gas at temperature $T$ , the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$ . A good estimate for $q$ is :

asked Dec 11, 2018 by pady_1

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An ideal gas goes through a reversible cycle $a \to b \to c \to d$ has the $V-T$ diagram shown below. Process $d \to a$ and $b \to c$ are adiabatic. The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale) :

asked Dec 11, 2018 by pady_1

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If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by :

asked Dec 11, 2018 by pady_1

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If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}}$ then the Reynolds number for the flow is (density of water $=10^3\; kg/m^3$ and viscosity of water $=10^{-3}$ Pa.s) close to :

asked Dec 11, 2018 by pady_1

0 answers

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R(R << L)$ . A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T, and its distance from the galaxy's axis is $r$ , then :

asked Dec 11, 2018 by pady_1

0 answers

Consider a thin uniform square sheet made of a rigid material. If its side is $'a'$ , mass m and moment of inertia I about one of its diagonals, then :

asked Dec 11, 2018 by pady_1

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A uniform solid cylindrical roller of mass $'m'$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its centre. If the acceleration of the cylinder is $'a'$ and it is rolling without slipping then the value of $'F$ is :

asked Dec 11, 2018 by pady_1

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A block of mass $m=0.1 \;kg$ is connected to a spring of unknown spring constant $k$ . It is compressed to a distance $x$ from its equilibrium position and released from rest. After approaching half the distance $(\frac{x}{2})$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3 \;ms^{-1}$ . The total initial energy of the spring is :

asked Dec 11, 2018 by pady_1

0 answers

A block of mass $m =10\; kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$ . When hit by a bullet of mass $50\; g$ moving with speed $v$ , that gets embedded in it, the block moves and comes to stop after moving a distance of $2\; m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H$ , then neglecting energy losses and taking $g=10\; ms^{-2}$ , the value of $H$ is close to :

asked Dec 11, 2018 by pady_1

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If a body moving in a circular path maintains constant speed of $10\; ms^{-1}$ , then which of the following correctly describes relation between acceleration and radius ?

asked Dec 11, 2018 by pady_1

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$x$ and $y$ displacements of a particle are given as $x(t) = a \sin \omega t$ and $y(t) = a \sin 2 \omega t$ . Its trajectory will look like :

asked Dec 11, 2018 by pady_1

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The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them :

A variable, opposite external potential $(E_{ext})$ is applied to the cell $Zn|Zn^{2+} \; (1M) || Cu^{2+} \; (1M) | Cu$ , of potential $1.1\;V$ . When $E_{ext} < 1.1\;V$ and $E_{ext} > 1.1 \;V$ , respectively electrons flow from :

The heat of atomization of methane and ethane are $360\; kJ/mol$ and $620\; kJ/mol$ , respectively. The longest wavelength of light capable of breaking the $C - C$ bond is (Avogadro number = $6.02 \times 10^{23} ,\; h =6.62 \times 10^{-34}\; J s$ ) :

If the principal quantum number n56, the correct sequence of filling of electrons will be :

Which of the following is not an assumption of the kinetic theory of gases ?

A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed $52\; g$ . The formula of the hydrated salt is : (atomic mass, $Ba=137 \;amu,\; Cl = 35.5 \;amu$ )

In an unbiased n-p junction electrons diffuse from n - region to p - region because :

If one were to apply Bohr model to a particle of mass $'m'$ and charge $'q'$ moving in a plane under the influence of a magnetic field $'B'$ , the energy of the charged particle in the $n^{th}$ level will be :

de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to $(|e| = 1.6 \times 10^{-19} C, m_e = 9.1 \times 10^{-31} kg, \; h = 6.6 \times 10^{-34} Js)$ :

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is $\theta$ , then $\theta$ is close to :

A parallel beam of electrons travelling in $x$ -direction falls on a slit of width $d$ (see figure). If after passing the slit, an electron acquires momentum $p_{_y}$ in the $y$ -direction then for a majority of electrons passing through the slit ( $h$ is Planck's constant) : <br>

You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

An electromagnetic wave travelling in the $x$ -direction has frequency of $2 \times 10^{14}\; Hz$ and electric field amplitude of $27\; Vm^{-1}$ . From the options given below, which one describes the magnetic field for this wave ?

In the circuits (a) and (b) switches $S_1$ and $S_2$ are closed at $t = 0$ and are kept closed for a long time. The variation of currents in the two circuits for $t \geq 0$ are roughly shown by (figures are schematic and not drawn to scale) : <br>

When current in a coil changes from $5\; A$ to $2\; A$ in $0.1 \;s$ , an average voltage of $50\; V$ is produced. The self - inductance of the coil is :

A $25 \;cm$ long solenoid has radius $2\; cm$ and $500$ total number of turns. It carries a current of $15\; A$ . If it is equivalent to a magnet of the same size and magnetization $\overrightarrow{M}$ (magnetic moment/volume), then $|\overrightarrow{M}|$ is :

A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width $'d'$ . If $'\alpha'$ be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be : <br>

A $10V$ battery with internal resistance $1 \Omega$ and a $15V$ battery with internal resistance $0.6 \Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to : <br>

Suppose the drift velocity $v_{_d}$ in a material varied with the applied electric field $E$ as $v_{_d} \propto \sqrt{E}$ ; . Then $V - I$ graph for a wire made of such a material is best given by :

If the capacitance of a nanocapacitor is measured in terms of a unit $'u'$ made by combining the electronic charge $'e'$ , Bohr radius $'a_0$ , Planck's constant $'h'$ and speed of light $'c'$ then :

A thin disc of radius $b=2a$ has a concentric hole of radius $'a'$ in it (see figure). It carries uniform surface charge $'\sigma'$ on it. If the electric field on its axis at height $'h (h<< a)$ from its centre is given as 'Ch' then value of 'C' is : <br>

A bat moving at $10 \;ms^{-1}$ towards a wall sends a sound signal of $8000\; Hz$ towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = $320 \;ms^{-1}$ )$

A simple harmonic oscillator of angular frequency $2\; rad\; s^{-1}$ is acted upon by an external force $F = \sin t\; N$ . If the oscillator is at rest in its equilibrium position at $t=0$ , its position at later times is proportional to :

In an ideal gas at temperature $T$ , the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$ . A good estimate for $q$ is :

An ideal gas goes through a reversible cycle $a \to b \to c \to d$ has the $V-T$ diagram shown below. Process $d \to a$ and $b \to c$ are adiabatic. <br> <br> The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale) :

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}}$ then the Reynolds number for the flow is (density of water $=10^3\; kg/m^3$ and viscosity of water $=10^{-3}$ Pa.s) close to :

Consider a thin uniform square sheet made of a rigid material. If its side is $'a'$ , mass m and moment of inertia I about one of its diagonals, then :

A uniform solid cylindrical roller of mass $'m'$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its centre. If the acceleration of the cylinder is $'a'$ and it is rolling without slipping then the value of $'F$ is :

If a body moving in a circular path maintains constant speed of $10\; ms^{-1}$ , then which of the following correctly describes relation between acceleration and radius ?

$x$ and $y$ displacements of a particle are given as $x(t) = a \sin \omega t$ and $y(t) = a \sin 2 \omega t$ . Its trajectory will look like :