question_answer2) The potential energy between two atoms, in a molecule, is given by\[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]where a and b are positive and x is the distance between the atoms. The atom is in stable equilibrium, when:
question_answer3) A simple pendulum with a bob of mass in oscillates from A to C and back to A such that PB is H. If the acceleration due to gravity is g, then the velocity of the bob as it passes through B is:
question_answer4) Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is:
question_answer5) The length of a sonometer wire AB is 110 cm. Where should the two bridges be placed from A to divide the wire in 3 segments whose fundamental frequencies are in the ratio 1 : 2 : 3?
question_answer6) A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 MHz. The speed of sound in a tissue is 1.7 km/s. The wavelength of sound in the tissue is close to:
question_answer7) Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be:
question_answer8) In an A.C. circuit, the current flowing is \[I=5\,\sin \,(100\,t-\pi \text{/}2)\] amperes and the potential difference is V = 200 sin (100t) volts. The power consumption is equal to:
question_answer9) A lens is placed between a source of light and a wall. It forms images of area \[{{A}_{1}}\] and \[{{A}_{2}}\] on the wall, for its two different positions. The area of the source of light is:
question_answer10) When the key K is pressed at time \[t=0,\] then which of the following statement about the current I in the resistor AB of the given circuit is true?
question_answer11) The work done in turning a magnet of magnetic moment M by an angle of \[90{}^\circ \] from the meridian, is n times the corresponding work done to turn it through an angle of\[60{}^\circ \]. The value of n is given by:
question_answer12) A straight line conductor of length 0.4 m is moved with a speed of 7 m/s perpendicular to magnetic field of intensity 0.9\[Wb\text{/}{{m}^{2}}.\] The induced e.m.f. across the conductor is:
question_answer13) Two metallic spheres of radii 1 cm and 2 cm are given charges\[{{10}^{-2}}C\]and\[5\times {{10}^{-2}}\,C\]respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is:
question_answer14) A heating coil is labelled 100 W, 220 V. The coil is cut in half and the two pieces are joined in parallel to the same source. The energy now liberated per second is:
question_answer15) Two wires of the same metal have same length, but their cross-sections are in the ratio 3:1. They are joined in series. The resistance of thicker wire is 10 \[\Omega \]. The total resistance of the combination will be:
question_answer16) The focal length of converging lens is measured for violet, green and red colours. It is respectively \[{{f}_{v}},{{f}_{g}},{{f}_{r}}.\] We will get:
question_answer19) The ball whose kinetic energy is E is thrown at an angle of \[45{}^\circ \]with the horizontal. Its K.E. at the highest point of its flight will be:
question_answer21) A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by another wire of 1 mm diameter carrying the same current. The strength of the magnetic field far away is:
question_answer22) The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earths mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes:
question_answer26) A metal ball of mass 2 kg moving with speed of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after collision, both the balls move together, then the loss in K.E. due to collision is:
question_answer28) The primary winding of a transformer has 500 turns whereas its secondary has 5000 turns. The primary is connected to an A.C. supply 20 V, 50 Hz. The secondary will have an output of:
question_answer29) An electromagnetic radiation of frequency n wavelength \[\lambda ,\] travelling with velocity v in air, enters a glass slab of refractive index\[\mu .\] The frequency, wavelength and velocity of light in the glass slab will be respectively:
A)
\[\frac{n}{\mu },\frac{\lambda }{\mu }\] and \[\frac{v}{\mu }\]
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B)
\[n,\,\frac{\lambda }{\mu }\] and \[\frac{v}{\mu }\]
question_answer30) The diode used in the circuit shown in the figure has a constant voltage drop at 0.5 V at all currents and a maximum power rating of 100 milli-watts. What should be the value of the resistor R, connected in series and with diode and obtaining maximum current?
question_answer32) The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be:
question_answer33) A particle starts with S.H.M. from the mean position as shown in the Fig. below. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is this displacement?
question_answer34) A body dropped from a height h with initial velocity zero, strikes the ground with a velocity 3 m/s. Another body of same mass dropped from the same height h with an initial velocity of 4 m/s. Find the final velocity of second mass, with which it strikes the group.
question_answer36) The kinetic energy \[({{E}_{k}})\] of a photoelectron varies with the frequency (v) of the incident radiation as which of the following graph?
question_answer37) A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2 : 1. What will be the ratio of their nuclear size (nuclear radius)?
question_answer39) A diatomic gas initially at \[18{}^\circ C\] is compressed adiabatically to one eighth of its original volume. The temperature after compression will be:
question_answer40) A ray of light from a denser medium strikes a rare medium as shown in figure. The reflected and refracted rays make an angle of \[90{}^\circ \] with each other. The angles of reflection and refraction are r and r. The critical angle would be:
question_answer43) The energy of a hydrogen atom in its ground state is -13.6 eV. The energy of the level corresponding to the quantum number n = 2 in the hydrogen atom is:
question_answer44) Light travels through a glass plate of thickness t and having a refractive index\[\mu \]. If c is the velocity of light in vacuum, the time taken by light to travel this thickness of glass is:
question_answer46) The transfer ratio P of a transistor is 50. The input resistance of the transistor, when used in the common emitter configuration is 1 k\[\Omega \]. The peak value of the collector ac current for an ac input voltage of 0.01 V peak is:
question_answer47) A 5000 kg rocket is set for vertical firing. The exhaust speed is 800\[m{{s}^{-1}}\]. To give an initial upward acceleration of 20\[m{{s}^{-2}},\] the amount of gas ejected per second to supply the needed thrust will be (g = 10 \[m{{s}^{-2}}\]):
question_answer50) A mass 1 kg is suspended by a thread. It is (i) lifted up with an acceleration \[4.9\,m/{{s}^{2}},\] (ii) lowered with an acceleration \[4.9\,m/{{s}^{2}}\]. The ratio of the tensions is:
question_answer51) The speed of a boat is 5 km/h in still water. It crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is:
question_answer52) A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity co. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity of:
question_answer53) A rubber ball is dropped from a height of 5m on a planet where the acceleration due gravity is not known. On bouncing, it rises 1.8 m. The ball loses its velocity on bouncing by a factor of:
question_answer54) The radiant energy from the sun, incident normally at the surface of earth, is \[20\,kcal\text{/}{{m}^{2}}\text{-}\min .\] What would have been the radiant energy incident normally on the earth, if the sun had a temperature twice of the present one?
question_answer55) A vehicle, with a horn of frequency n is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency \[n+{{n}_{1}}.\] Then \[{{n}_{1}}\] is equal to (if the sound velocity in air is 300 m/s):
question_answer56) In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.17 sec The frequency of the wave is:
question_answer57) A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance of 1.21\[\overset{\text{o}}{\mathop{\text{A}}}\,\]between them. The wavelength of the standing wave is:
question_answer58) Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation \[I={{I}_{0}}\]is \[\sin \omega t\]where \[I=10A\]and \[\omega =100\pi \]radian/sec. The maximum value of e.m.f. in the second coil is:
question_answer59) A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is:
question_answer60) A step-up transformer operates on a 230 V line and supplies a load of 2A. The ratio of the primary and secondary windings is 1 : 25. The current in the primary is:
question_answer62) Percentage of Se (at. Mass = 78.4) in peroxidase anhydrase enzyme is 0.5% by weight, then minimum molecular mass of peroxidase anhydrase enzyme is:
question_answer63) 2.5 g of the carbonate of a metal was treated with 100 ml of\[1\,N\]\[{{H}_{2}}S{{O}_{4}}\]. After the completion of the reaction, the solution was boiled off to expel \[C{{O}_{2}}\] and was then titrated against \[1\,N\]\[NaOH\]solution. The volume of alkali that would be consumed, if the equivalent weight of the metal is 20.
question_answer64) A radioactive nuclide decays at such a rate that after 96 min, only 1/8th of the original amount remains. The value of half-life of the nuclide is:
question_answer65) Assume that you are travelling at a speed of 90 km/h in a small car with a mass of 105 kg. If the uncertainty in the velocity of the car is 1% (\[\Delta v\]=0.9 km/h), what is the uncertainty (in meters) in the position of the car?
question_answer70) Critical temperatures for A, B, C and D gases are \[25{}^\circ C,\]\[10{}^\circ C,\]\[-80{}^\circ C\]and\[15{}^\circ C\]respectively. Which gas will be liquefied more easily?
question_answer71) Two flasks X and Y have capacity 1L and 2L respectively and each of them contains 1 mole of a gas. The temperatures of the flasks are so adjusted that average speed of molecules in X is twice as those in Y. The pressure in flask X would be:
question_answer72) The heat liberated when 1.89 g of benzoic acid is burnt in a bomb calorimeter at \[25{}^\circ C\] and it increases the temperature of 18.94 kg of water by\[~0.632{}^\circ C\]. If the specific heat of water at \[25{}^\circ C\] is 0.998 cal/g-deg, the value of the heat of combustion of benzoic acid is:
question_answer73) If enthalpies of formation for \[{{C}_{2}}{{H}_{4(g)}},C{{O}_{2(g)}}\]and \[{{H}_{2}}O(l)\] at \[25{}^\circ C\] and 1 atm pressure are 52, -394 and -286 kJ/mol respectively, then enthalpy of combustion of \[{{C}_{2}}{{H}_{4}}(g)\]will be:
question_answer74) One gram sample of \[N{{H}_{4}}N{{O}_{3}}\] is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by 6.12 K. The heat capacity of the system is 1.23 kJ/g/deg. What is the molar heat of decomposition for\[N{{H}_{4}}N{{O}_{3}}\]?
question_answer76) Of the following which change will shift the reaction towards the product? \[{{I}_{2}}(g)\rightleftharpoons 2I(g),\]\[\Delta H_{r}^{\text{o}}(298\,K)=+150\,kJ\]
question_answer86) Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains:
question_answer89) Vapour pressure of benzene at \[30{}^\circ C\] is 121.8 mm when 15 g of a non-volatile solute is dissolved in 250 g of benzene, its vapour pressure is decreased to 120.2 mm. The molecular weight of the solute is:
question_answer94) The potential energy diagram for a reaction \[R\to P\]is given in the figure. \[\Delta H{}^\circ \]of the reaction corresponds to the energy:
question_answer100) On dissolving moderate amount of sodium metal in liquid\[N{{H}_{3}}\]at low temperature, which one of the following does not occur?
A)
Blue coloured solution is obtained
doneclear
B)
\[N{{a}^{+}}\]ions are formed in the solution.
doneclear
C)
Liquid \[N{{H}_{3}}\] becomes good conductor of electricity.
question_answer101) What is the correct relationship between the pHs of isomolar solutions of sodium oxide\[(p{{H}_{1}}),\]sodium sulphide\[(p{{H}_{2}}),\]sodium selenide\[(p{{H}_{3}})\] and sodium telluride\[(p{{H}_{4}})\]?
question_answer108) A complex \[PtC{{l}_{4}}.5N{{H}_{3}}\] shows a molar conductance of \[402\,oh{{m}^{-1}}\,c{{m}^{2}}\,mo{{l}^{-1}}\] in water and precipitates three moles of \[AgCl\] with \[AgN{{O}_{3}}\] solution. The formula of the complex is:
question_answer131) Select one of the following pairs of important features distinguishing Gnetum from Cycas and Pinus and showing affinities with angiosperms.
A)
perianth and two integuments.
doneclear
B)
embryo development and apical meristem.
doneclear
C)
absence of resin duct and leaf venation.
doneclear
D)
presence of vessel elements and absence of archegonia.
question_answer143) The figure given below shows three velocity- substrate concentration curves for an enzyme reaction. What do the curves x, y, and z depict respectively?
question_answer145) There is an irregular mating population. If the frequency of an autosomal recessive lethal gene is 0.4, then the frequency of the carriers in a population of 200 individuals is:
question_answer146) When a tall and red flowered individual is crossed with a dwarf and white flowered individual, phenotype in the progeny is dwarf and white. What will be the genotype of tall and red flowered individual?
question_answer160) Carbon dioxide is necessary for photo- synthesis. The chemical used to remove this gas most effectively from entering a control apparatus is:
question_answer177) A cricket player is lastly chasing a ball in the field. Which one of the following groups of bones are directly contributing in this movement?
question_answer181) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer182) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer183) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer184) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer185) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer186) Directions: Select the most appropriate word from the options against each number: Those living in the slums are 1 and tough because they are totally 2 to the vagaries and hardships of life. The rising sun 3 the day and the setting sun closes the day for them. It is like a drama where the curtain 4 up in the morning and comes down in the evening. They dont 5 hypertension and heart attacks because there is, after all 6 to worry about.
question_answer191) Directions: Choose the word which is nearly opposite in meaning to the given word. Which of the following diagrams indicates the best relation between Hockey, Football and Cricket?
question_answer200) Statement: Clearly, the judiciary cannot provide all answers. But it seems the public, weary of an inactive Executive, is turning to the Supreme Court as a last resort - an article. Assumptions:
(i) The Supreme Court is above the Executive.
(ii) The Supreme Court is more active than the Executive.
(iii) The Executive does not have sufficient powers.