A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table
The block of mass (M) moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is
A ball is projected with a velocity of \[10\sqrt{2}\,m/s\]at angle of \[45{}^\circ \] with the horizontal from the top of a cliff 20 m high, with what velocity does the ball hit the ground?
A heavy circular disc whose plane is vertical is kept at rest on a rough inclined plane by a string parallel to the plane and touching the disc as shown in the figure. The disc starts to slip if:
A particle performs uniform circular motion with an angular momentum L. If the frequency of rotation is doubled and its KE is halved, the angular momentum becomes:
The potential energy of a particle of mass 0.1 kg moving along the \[x-\]axis is given by \[U=5x(x-4)\,J,\]where\[x\]is in metre. It can be concluded that:
A)
the particle is acted upon by a constant force.
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B)
the speed of the particle is maximum at x = 2 m.
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C)
the particle cannot execute simple harmonic motion.
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D)
the period of oscillation of the particle is \[\frac{\pi }{20}s\]
A particle leaves the origin with an initial velocity\[\vec{v}=3\hat{i}\,m/s\]and a constant acceleration \[\vec{a}=(\hat{i}0.5\hat{j})\,m/{{s}^{2}}\]When the particle reaches its maximum\[x-\]coordinate, what is its \[y-\]component of velocity?
A rigid conducting wire bent as shown, is released to fall freely in a horizontal magnetic field, which is perpendicular to the plane of the conductor. If magnetic field strength is B, then the emf induced across the points A and when it has fallen through a height h will be:
A block of mass 8 kg rests on a rough inclined plane of angle\[{{30}^{o}}\]and\[\mu =\frac{3}{4}\]between the block and the plane. The value of the force of friction is: [Take\[g=10\,m/{{s}^{2}}\]]
A tank accelerates uniformly in upward direction with acceleration\[1\,m/{{s}^{2}}\]and contains water. A block of mass 1 kg and density 0.8 g/cc is held stationary inside the tank with the help of the string as shown in the figure. The tension in the string is [Take\[{{\rho }_{\text{water}}}=1000\,kg/{{m}^{3}}\]and\[g=10\,m/{{s}^{2}}\]]
Two blocks of masses 1 kg and 3 kg are attached to a horizontal spring of spring constant 300 N/m as shown in the figure. The natural vibrational frequency of the system is, approximately
The work done against surface tension in blowing a soap bubble from a radius 10 to 20 cm, if the surface tension of solution is \[25\times {{10}^{-3}}N/m,\] is
A cannot engine working between 300 K and 600 K has a work output of 800 J/cycle. The amount of heat energy supplied to the engine from the source in each cycle is
The masses and radii of the earth and moon are\[{{M}_{1}},{{R}_{1}}\]and\[{{M}_{2}},{{R}_{2}},\]respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from the mid-point between their centres, so that the particle goes out from the gravitational influence of both earth and moon, is
A convex lens forms an image at a distance 10 cm when a parallel beam of light is incident on it. Find the position (s) of a concave mirror of radius of curvature 5 cm such that the final image is formed at infinity
A source of sound is moving with constant velocity of 20 m/s emitting a note of frequency 1000 Hz. The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him will be:(Speed of sound v = 340 m/s)
An elevator cable is to have a maximum stress of \[7\times {{10}^{7}}\,N/{{m}^{2}}\]to allow for appropriate safety factors. Its maximum upward acceleration is \[1.5\text{ }m/{{s}^{2}}.\] If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be:
A vertical ring of radius r and resistance R falls vertically. It is in contact with two vertical rails, which are joined at the top. The rails are without friction and resistance. There is a horizontal uniform magnetic field of magnitude B perpendicular to the plane of the ring and the rails. When the speed of the ring is v, the current in the section PQ is
A glass hemisphere of radius R and material having refractive index 1.5 is silvered on its flat face as shown in the figure. A small object of height h is located at a distance 2R from the surface of hemisphere. The final image will be formed
A)
at a distance of R from silvered surface, on right side.
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B)
on the object itself.
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C)
at the hemispherical surface.
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D)
at a distance of 2R from the silvered surface on left side.
A pipe of length 1 m is closed at one end. The velocity of sound in air is 300 m/s. The air column in the pipe will not resonate for sound of frequency
The maximum wavelength for photoelectric emission in tungsten is 230 nm. The wavelength of light, which must be used in order that maximum KE of ejected photoelectrons is 1.5 eV, is
\[{{K}_{\alpha }}\]wave length emitted by an atom of atomic number\[Z=11\]is \[\lambda .\]The atomic number for an atom that emits\[{{K}_{\alpha }}\]radiation with wavelength \[4\lambda ,\] is
At time t = 0. A bullet is fired vertically upwards with-a speed of\[98\text{ }m{{s}^{-1}}.\] A second bullet is fired vertically upwards with the same speed at \[t=5\]s. Then:
A)
the two bullets will be at the same height above the ground at t = 12.5 s.
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B)
the two bullets will reach back their stating point at t = 25 s.
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C)
the two bullets will have the same speed at t = 20 s.
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D)
the maximum height attained by either bullet will be 980 m.
Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in the figure. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7. What is the maximum horizontal force F that can be applied to block M so that the two blocks move without slipping? Take \[g=10\,m{{s}^{-2}}.\]
A uniform solid cylinder rolling with angular velocity \[\omega \] along a plane surface strikes a vertical rigid wall. With what angular velocity the cylinder begins to roll up the wall because of impulsive blow?
A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced in the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?
When two moles of oxygen is heated from \[0{}^\circ C\] to \[10{}^\circ C\] at constant volume, its internal energy changes by 420 J. What is the molar specific heat of oxygen at constant volume?
A wire is bent to from the double loop shown in the figure. There is a uniform magnetic field directed into the plane of the loop. If the magnitude if this field is decreasing, current will flow from
In the hydrogen atom the electron moves around the proton with a speed of\[~2.0\times 106\text{ }m{{s}^{-1}}\]in a circular orbit of radius \[5.0\times {{10}^{11}}m.\]What is the equivalent dipole moment?
A mixture of violet light of wavelength \[3800\,\overset{\text{o}}{\mathop{\text{A}}}\,\] and blue light of wavelength \[4000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] is incident normally on an air film of 0.00029 mm thickness. The colour of the reflected light is
Light of wavelength\[\lambda \]is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. The linear width of the principal maximum is equal to the width of the slit, if D equals
If the binding energy per nucleon in \[\text{L}{{\text{i}}^{\text{7}}}\]and\[\text{H}{{\text{e}}^{\text{4}}}\] nuclei is respectively 5.60 MeV and 7.06 MeV, then the energy of the reaction \[L{{i}^{7}}+p\to {{2}_{2}}H{{e}^{4}}\]
A conducting sphere of radius 10 cm is charged with\[\text{10}\mu \text{C}\text{.}\]Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After, if the spheres are separated, then the surface density of charges on the spheres will be in the ratio of
The potential of the electric field produced by a point charge at any point\[(x,y,z)\] is given by; \[V=3{{x}^{2}}+5,\] where \[x,\text{ }y,\text{ }z\]are in metres and V is in volt. The intensity of the electric field at (-2, 1,0) is
Two identical capacitors 1 and 2 are connected in series to a battery as shown in the figure. Capacitor 2 contains a dielectric slab of dielectric constant K as shown. \[{{Q}_{1}}\]and \[{{Q}_{2}}\]are the charges stored in-the capacitors. Now the dielectric slab is removed and the corresponding charges are \[Q_{1}^{'}\]and\[Q_{2}^{'}.\]Then:
A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by \[\Delta \,T,\] the potential difference V across the capacitance is:
V-I graph for a conductor (Platinum wire) at temperatures\[{{T}_{1}}\]and\[{{T}_{2}}\]is as shown in the figure. \[{{T}_{2}}-{{T}_{1}}\]is proportional to
In the circuit the figure. When key \[{{K}_{1}}\]is closed, the ammeter reads\[{{I}_{0}}\]whether\[{{K}_{2}}\]is open or closed. But, when\[{{K}_{1}}\]is open, the ammeter reads\[{{I}_{0}}/2,\]when\[{{K}_{2}}\]is closed. Assuming that ammeter resistance is much less than \[{{R}_{2}},\]find the values of rand\[{{R}_{1}}\](in ohms)
How many grams of ice at \[0{}^\circ C\] can be melted by the addition of 500 J of heat? (The molar heat of fusion for ice is\[6.02\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\])
A 1.0 g sample of substance A at \[100{}^\circ C\] is added to 100 mL of \[{{\text{H}}_{\text{2}}}\text{O}\]at \[25{}^\circ C\]. Using separate 100 mL portions of\[{{\text{H}}_{\text{2}}}\text{O,}\]the procedure is repeated with substance B and then with substance C. How will the final temperatures of the water compare?
When solid lead iodide is added to water, the equilibrium concentration of \[{{\text{I}}^{-}}\]becomes \[2.6\times {{10}^{-3}}\,M.\] What is the \[{{K}_{sp}}\]for \[Pb{{I}_{2}}?\]
The free energy formation of NO is \[78\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]at the temperature of an automobile engine (1000 K). What is the equilibrium constant for this reaction at 1000 K? \[\frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}^{2}}(g)\Leftrightarrow NO(g)\]
The first order reaction\[2{{N}_{2}}O(g)\to 2{{N}_{2}}(g)+{{O}_{2}}(g)\]has a rate constant of \[1.3\times {{10}^{-11}}{{s}^{-1}}\] at \[207{}^\circ C\] and \[4.5\times {{10}^{-10}}{{s}^{-1}}\]at \[350{}^\circ C\]. What is the activation energy for this reaction?
What will happen to the volume of a bubble of air found underwater in a lake, where the temperature is \[15{}^\circ C\] and the pressure is 1.5 aim, if the bubble then rises to the surface where the temperature is \[25{}^\circ C\] and the pressure is 1.0 atm?
A)
Its volume will become greater by a factor of 2.5.
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B)
Its volume will become greater by, a factor of 1.6.
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C)
Its volume will become greater by a factor of 1.1.
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D)
Its volume will become smaller by a factor of 0.70.
Sodium chloride, NaCI, usually crystallizes in a face- centred cubic lattice. How many ions are in contact with any single \[\text{N}{{\text{a}}^{\text{+}}}\]ion?
What is the osmotic pressure of a \[0.0020\,\text{mol}\,\text{d}{{\text{m}}^{-3}}\]sucrose\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] solution at \[20{}^\circ C\]? (Molar gas constant R\[R=8.314\,J{{K}^{-1}}\,mo{{l}^{-1}};\]\[d{{m}^{3}}=0.001\,{{m}^{3}}\])
Calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule. The \[CI-CI\]bond energy is\[243\,kJ\,mo{{l}^{-1}}\]\[(h=6.6\times {{10}^{-34}}J\,s;\]\[c=3\times {{10}^{8}}\,m/s;)\]Avogadro's number \[=6.02\times {{10}^{23}}\text{mo}{{\text{l}}^{-1}}\]
As\[{{O}_{2}}(l)\]is cooled at 1 atm pressure, it freezes to form solid I at 54.5 K. At a lower temperature, solid I rearranges to solid II, which has a different crystal structure. Thermal measurements show that for the phase transition solid I to solid II, \[\Delta H=-743.1\,J\,mo{{l}^{-1}}\]and \[\Delta S=-17.0\,J{{K}^{-1}}\,mo{{l}^{-1}}.\]At what temperature are solids I and II in equilibrium?
Which one of the following is the correct increasing order of the magnitude of ionic radii of \[C{{e}^{3+}},L{{a}^{3+}},\]\[P{{m}^{3+}}\]and \[Y{{b}^{3+}}?\]
The final product in the following reaction sequence is \[p-Chloroaniline\xrightarrow[0-5{{\,}^{o}}C]{NaN{{O}_{2}},HCl}?\xrightarrow{KCN}?\xrightarrow{LiAl{{H}_{4}}}?\]
The compound with molecular formula \[{{C}_{8}}{{H}_{10}}\]which will give only two isomers on electrophilic substitution with \[C{{l}_{2}}/FeC{{l}_{3}}\]or with\[HN{{O}_{3}}/{{H}_{2}}S{{O}_{4}}\] is
The order of rate of hydrolysis of alkyl halides \[1{}^\circ ,\text{ }2{}^\circ ,\text{ }3{}^\circ \] and \[C{{H}_{3}}X\]by the \[{{S}_{N}}2\]pathway is
A man with a certain disease marries a normal woman. They have eight children (3 daughters and 5 sons). All the daughters suffer from their father's disease but none of the sons are affected. Which of the following mode of inheritance do you suggest for this disease?
Red-green colour blindness in humans is governed by a sex-linked recessive gene. A normal woman whose father has colour blindness marries a colour blind man. What proportion of their daughters is expected to be colour-blind?
Photosynthesis in \[{{\text{C}}_{\text{4}}}\] plants is relatively less and limited by atmospheric \[\text{C}{{\text{O}}_{\text{2}}}\]levels because of
A)
Effective pumping of \[\text{C}{{\text{O}}_{\text{2}}}\]into bundle sheath cells.
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B)
Rubis CO in \[{{\text{C}}_{\text{4}}}\] plants has higher affinity for\[C{{O}_{2}}.\]
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C)
Four carbon acids are the primary initial \[C{{O}_{2}}.\]fixation products.
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D)
The primary fixation of \[C{{O}_{2}}\] is mediated through PEP carboxylase.
Which one of the following triplet codes is correctly matched with its specificity for an amino acid in protein synthesis or as 'start' or 'stop? codon?
At a particular locus, frequency of 'A' allele is 0.6 and that of 'a' is 0.4. What would be the frequency of heterozygotes in a random mating population at equilibrium?
A bottle filled with previously moistened mustard seeds and water was screw capped tightly and kept in a corner. It blew up suddenly after about half an hour. The phenomenon involved is