A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are\[\left( \sqrt{3},\text{ }3 \right)\]. The path of the particle makes with the x-axis an angle of
The resistance of an ammeter is \[13\,\,\Omega \] and its, scale is graduated for a current up to 100 A. After an additional shunt has been connected to this ammeter, it becomes possible to measure currents up to 750 A by this meter. The value of shunt resistance is
The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux \[\phi \] linked with the primary coil is given by \[\phi ={{\phi }_{0}} +4t\], where \[\phi \] is in weber, t is time in second and \[{{\phi }_{0}}\] is a constant, the output voltage across the secondary coil is
A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation As T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
Two radioactive substances A and B have decay constants\[5\,\lambda \,\,and\,\,\lambda \]. respectively. At \[t=0\] they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be \[{{\left( \frac{1}{e} \right)}^{2}}\] after a time interval
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is \[{{L}_{A}}\] when it is at A and \[{{L}_{B}}\] when it is at B, then
A)
\[{{L}_{A}}>{{L}_{B}}\]
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B)
\[{{L}_{A}}={{L}_{B}}\]
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C)
the relationship between \[{{L}_{A}}\,and\,\,{{L}_{B}}\] depends upon the slope of the line AB
A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? \[(Take\,\,g\,\,=\,\,10\,m/{{s}^{2}})\]
A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move
A common emitter amplifier has a voltage gain of 50, an input impedance of \[100\,\,\Omega \] and an output impedance of\[200\,\,\Omega \]. The power gain of the amplifier is
Specific rotation of sugar solution is 0.01 SI units. \[200\text{ }kg\text{ }{{m}^{-}}^{3}\]of impure sugar solution is taken in a polarimeter tube of length 0.25 m and an optical rotation of 0.4 rad is observed. The percentage of purity of sugar in the sample is-
When a body falls in air, the resistance of air depends to a great extent on the shape of the body. Three different shapes are given. Identify the combination of air resistances which truly represents the physical situation? (The cross- sectional areas are the same).
A beam of parallel rays is brought to focus by a plano-convex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is
A)
the focus shifts to infinity
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B)
the focal point shifts towards the lens by a small distance
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C)
the focal point shifts away from the lens by a small distance
An asteroid of mass m is approaching earth, initially at a distance of \[10\,{{R}_{e}}\] with speed \[{{v}_{1}}\]. It hits the earth with a speed \[{{v}_{f}}({{R}_{e}}\,and\,\,{{M}_{e}}\] are radius and mass of earth), then
The figure shows three situations when an electron with velocity \[\vec{\nu }\] travels through a uniform magnetic field\[\vec{B}\]. In each case, what is the direction of magnetic force on the electron?
In the figure, a proton moves a distance d in a uniform electric \[\vec{E}\] as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?
The figure shows three circuits with identical batteries, inductors and resistance. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first.
The figure shows the path of a positively charged particle 1 through a rectangular region of uniform electric field as shown in the figure. What is the direction of electric field and the direction of deflection of particles 2, 3 and 4?
A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
In a detector, output circuit consists of \[\operatorname{R}=10k\Omega \]and\[\operatorname{C} = 100 \mu F\]. The frequency of carrier signal it can detect is
The speed \[\left( \nu \right)\] of ripples on the surface of water depends on surface tension\[\left( \sigma \right)\], density \[\left( \rho \right)\] and wavelength\[\left( \lambda \right)\]. The square of speed \[\left( \nu \right)\] is proportional to
If light of wavelength \[{{\lambda }_{1}}\] is allowed to fall on a metal, then kinetic energy of photoelectrons emitted is\[{{E}_{1}}\]. If wavelength of light changes to \[{{\lambda }_{2}}\], then kinetic energy of electrons changes to \[{{E}_{2}}\], then work function of the metal is
How much work must be done to pull apart the electron and the proton that make up the hydrogen atom, if the atom is initially in the state with \[\operatorname{n}= 2\]
A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If \[\mu \] is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is
Four thin rods of the same mass M and the same length l form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is
The horizontal component of the earth?s magnetic field at a place is \[3 \,\times \, 1{{0}^{-}}^{4}T\] and the dip is\[{{\tan }^{-1}}\,\left( \frac{4}{3} \right)\]. A metal rod of length 0.25 m placed in the north-south position and is moved at a constant speed of 10 cm/s towards the east. The emf induced in the rod will be
Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of helium nucleus is\[{{14}^{1/3}}\]. The atomic number of nucleus will be
In the following four situations charged particles are at equal distance from the origin. Arrange them the magnitude of the net electric field at origin greatest first
(i)
(ii)
(iii)
(iv)
A)
\[\left( i \right)>\left( ii \right)>\left( m \right)>\left( iv \right)\]
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B)
\[\left( ii \right)>\left( i \right)>\left( iii \right)>\left( iv \right)\]
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C)
\[\left( i \right)>\left( iii \right)>\left( ii \right)>\left( iv \right)\]
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D)
\[\left( iv \right)>\left( iii \right)>\left( ii \right)>\left( i \right)\]
A bomb of mass 3 m kg explodes into two pieces of mass m kg and 2 m kg. If the velocity of m kg mass is 16 m/s, the total kinetic energy released in the explosion is
What is the r.m.s. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of 2 amperes in the same resistor
A body of weight 64 N is pushed with just enough force to start it moving across a horizontal floor and the same force continues to act afterwards. If the coefficients of static and dynamic friction are 0.6 and 0.4 respectively, the acceleration of the body will be (acceleration due to gravity = g)
The potential energy between two atoms in a molecule is given by\[U\left( x \right)=\,\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\], where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when
A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of the same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be
The radius of a soap bubble is increased from\[\frac{1}{\sqrt{\pi }}\,cm\,\,to\,\,\frac{2}{\sqrt{\pi }}\]. If the surface tension of water is 30 dynes per cm, men the work done will be
A solution containing 30 g of non-volatile solute in exactly 90 g water has a vapour pressure of 21.85 mm Hg at \[25{}^\circ C\]. Further 18 g of waters then added to the solution. The resulting solution has a vapour pressure of 22.15 mm Hg at\[25{}^\circ C\]. Calculate the molecular weight of the solute.
An aqueous solution of a weak monobasic acid containing 0.1 g in 21.7g of water freezes at 272.813 K. If the value of \[{{K}_{f}}\] for water is \[1.86\,\,K/m\] what is the molecular mass of the monobasic acid
A solid is made of two elements P and Q. A Atoms P are in ccp arrangement and atoms Q occupy all the octahedral voids and half of the tetrahedral voids, then the simplest formula of the compound is
Rate law for a gaseous reaction \[\operatorname{A}\,\,+\,\,B\,\xrightarrow{{}}\,\,C +\,D\] is given by \[Rate=K{{\left[ A \right]}^{2}}\,{{\left[ B \right]}^{0}}\] The volume of reaction vessel containing these gases is suddenly reduced to one-fourth of the initial volume. The rate of reaction relative to original rate would be
On introducing a catalyst at 500 K the rate of a first-order reaction increases by 1.718 times. The activation energy in the presence of catalyst is\[4.15\text{ }kJ\text{ }mo{{l}^{-}}^{1}\]. The slope of the plot of ln k\[(in\,\,se{{c}^{-1}})vs.\,\frac{1}{T}(T\,\,in\,\,Kelvin)\] in the absence of catalyst is \[(R=8.3\,\,J\,mo{{l}^{-1}}\,{{K}^{-1}})\]
An organic halide is shaken with aqueous NaOH followed by the addition of dil. \[HN{{O}_{3}}\] and silver nitrate solution gave white ppt. The substance can be
Mixture \[\operatorname{X}= 0.02\] mol of \[\left[ Co{{(N{{H}_{3}})}_{5}}S{{O}_{4}} \right]\,Br\] and 0.02 mol of \[\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}Br \right]S{{O}_{4}}\] was prepared in 2 litre of solution
1 litre of mixture \[\operatorname{X}+excess AgN{{O}_{3}} \to \,\,Y\].
1 litre of mixture \[\operatorname{X}+excess BaC{{l}_{2}} \to \,\,Z\].
Atoms consists of protons, neutrons and electrons. If the mass of neutrons and electrons were made half and two times respectively to their actual masses, then the atomic mass of \[_{6}{{C}^{12}}\]
Among the following species, identify the iso- structural pairs \[{{\operatorname{NF}}_{3}}, N{{O}_{3}}^{-}, B{{F}_{3}} {{H}_{3}}{{O}^{+}}, H{{N}_{3}}\]
The position of both an electron and a helium atom is known within 1.0 nm and the momentum of the electron is known within\[50 \times 1{{0}^{-}}^{26}kg m{{s}^{-1}}\]. The minimum uncertainty in the measurement of the momentum of the helium atom is
For two gases A and B with molecular weights\[{{M}_{A}}\,\,and\text{ }{{M}_{B}}\], it is observed that at a certain temperature\[{{T}_{1}}\]; the mean velocity of A is equal to the root mean square velocity of B. Thus the mean velocity of A can be made equal to the mean velocity of B if
A)
A is at temperature T and B at \[\operatorname{T}, T> T\]
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B)
A is lowered to a temperature \[{{\operatorname{T}}_{2}}, {{T}_{2}}< T\] while B is at T
Ionisation energy of \[\operatorname{Al}=5137\,kJ mol{{e}^{-}}^{1}\left( \Delta H \right)\] and hydration of \[A{{l}^{3+}}=\,\,-4665\,\,kJ\,\,mol{{e}^{-1}}\]. \[{{(\Delta H)}_{hydration}}\,\,for\,\,C{{l}^{-}}=-\,381\,\,kJ\,\,mole{{\,}^{-}}\,1\]. Which of the following statement is correct?
A)
\[AlC{{l}_{3}}\] would remain covalent in aqueous solution
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B)
Only at infinite dilution \[AlC{{l}_{3}}\] undergoes ionisation
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C)
In aqueous solution \[AlC{{l}_{3}}\] becomes ionic
A vessel has \[{{N}_{2}}\] gas and water vapours at a total pressure of 1 atm. The partial pressure of water vapours is 0.3 atm. The contents of this vessel are transferred to another vessel having one third of the capacity of original volume, completely at the same temperature the total pressure of this system in the new vessel is
\[C{{H}_{3}}COOH(1)\,\,+\,\,{{C}_{2}}{{H}_{5}}OH\,(1)\,\rightleftharpoons \] \[{{\operatorname{CH}}_{3}}COO{{C}_{2}}{{H}_{5}}\left( 1 \right) + {{H}_{2}}O\left( 1 \right).\] In the given reaction, one mole of each of acetic acid and alcohol are heated in the presence of little cone. \[{{H}_{2}}S{{O}_{4}}\]. On equilibrium being attained
What is the amount of heat to be supplied to prepare 128 g of \[Ca{{C}_{2}}\] by using \[CaC{{O}_{3}}\] and followed by reduction with carbon. Reactions are
A mixture of 0.3 mole of \[{{H}_{2}}\] and 0.3 mole of \[{{I}_{2}}\] is allowed to react in a 10 litre evacuated flask at\[500{}^\circ C\]. The reaction is \[{{H}_{2}}+{{I}_{2}}\rightleftharpoons \,\,2HI\], the K is found to be 64. The amount of unreacted \[{{I}_{2}}\] at equilibrium is
The figure given below shows the conversion of a substrate into product by an enzyme. In which one of the four options (a-d) the components or reaction labelled as A, B, C and D are identified correctly?
A)
A - Potential energy, B - Transition state, C - Activation energy with enzyme, D - Activation energy without enzyme
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B)
A - Transition state, B - Potential energy, C - Activation energy without enzyme, D - Activation energy with enzyme
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C)
A - Potential energy, B -Transition state, C - Activation energy with enzyme, D - Activation energy with enzyme
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D)
A - Activation energy with enzyme, B - Transition state, C - Activation energy without enzyme, D - Potential energy
The figure below is the diagrammatic representation of the E. coli vector pBR 322. Which one of the given options correctly identifies its certain component(s)?
The diagram shows an antibody molecule. Identify A to F.
A)
A - Antigen binding site; B - Variable region (of L-Chain); C - Constant region (of L-Chain); D - Light polypeptide chain (L-Chain); E - Heavy polypeptide chain (H-Chain); F - Disulfide (bond)
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B)
A - Antigen binding site; B - Constant region (of L-Chain); C - Variable region (of L-Chain); D - Light polypeptide chain (L-Chain); E - Heavy polypeptide chain (H-Chain); F - Disulfide (bond)
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C)
A - Antigen binding site; B - Variable region (of L-Chain); C - Constant region (of L-Chain); D - Heavy polypeptide chain (L-Chain); E - Light polypeptide chain (H-Chain); F - Hydrogen (bond)
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D)
A - Antigen binding site; B - Variable region (of L-Chain); C - Constant region (of L-Chain); D - Light polypeptide chain (L-Chain); E - Heavy polypeptide chain (H-Chain); F - Hydrogen (bond);
The density of a population in a given habitat during a given period, fluctuates due to changes in four basic process. On this basis fill up A and B boxes in the given diagram with correct options
A)
A = Natality + Immigration, B = Mortality + Emigration
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B)
A = Natality + Mortality, B = Immigration + Emigration
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C)
A = Birth rate + Death rate, B = Migration + Emigration
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D)
A = Natality + Emigration, B = Mortality + Immigration