question_answer1) If M is the mass of the earth and R its radius, the ratio of the gravitational acceleration and the gravitational constant is:
A) \[\frac{{{R}^{2}}}{M}\]
B) \[\frac{M}{{{R}^{2}}}\]
C) \[M{{R}^{2}}\]
D) \[\frac{M}{R}\]
View Answer play_arrowquestion_answer2) A student unable to answer a question on Newtons laws of motion attempts to pull himself up by tugging on his hair. He will not succeed:
A) as the force exerted is small
B) the frictional force while gripping, is small
C) Newtons law of inertia is not applicable to living beings
D) as the force applied is internal to the system
View Answer play_arrowquestion_answer3) From the adjacent figure, the correct observation is:
A) the pressure on the bottom of tank A is greater than at the bottom of B
B) the pressure on the bottom of the tank A is smaller than at the bottom of B
C) the pressure depends on the shape of the container
D) the pressure on the bottom of A and B is the same
View Answer play_arrowquestion_answer4) Which one of the following is not a unit of Youngs modulus?
A) \[N{{m}^{-1}}\]
B) \[N{{m}^{-2}}\]
C) dyne \[c{{m}^{-2}}\]
D) mega pascal
View Answer play_arrowquestion_answer5) A piece of blue glass heated to a high temperature and a piece of red glass at room temperature, are taken inside a dimly lit room, then:
A) the blue piece will look blue and red will look as usual
B) red looks brighter red and blue looks ordinary blue
C) blue shines like brighter red compared to the red piece
D) both the pieces will look equally red
View Answer play_arrowquestion_answer6) Three long, straight parallel wires, carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is:
A) \[{{10}^{-3}}N\]
B) \[2.5\times {{10}^{-3}}N\]
C) zero
D) \[1.5\times {{10}^{-3}}N\]
View Answer play_arrowquestion_answer7) A 5.0 amp current is setup in an external circuit by a 6.0 volt storage battery for 6.0 minutes. The chemical energy of the battery is reduced by:
A) \[1.08\times {{10}^{4}}J\]
B) \[1.08\times {{10}^{4}}J\]
C) \[1.8\times {{10}^{4}}J\]
D) \[1.8\times {{10}^{4}}J\]
View Answer play_arrowquestion_answer8) The current in a simple series circuit is 5.0 amp. When an additional resistance of 2.0 ohms is inserted, the current drops to 4.0 amp. The original resistance of the circuit in ohms was:
A) 1.25
B) 8
C) 10
D) 20
View Answer play_arrowquestion_answer9) In the circuit given \[E=6.0\]volt, \[{{R}_{1}}=100\,\Omega \]\[{{R}_{2}}={{R}_{3}}=50\,\,\Omega ,{{R}_{4}}=75\,\,\Omega \]. The equivalent resistance of the circuit, in ohms, is:
A) 11.875
B) 26.31
C) 118.75
D) none of these
View Answer play_arrowquestion_answer10) Two resistances are connected in two gaps of a metre bridge. The balance point is 20 cm from the zero end. A resistance of 15 ohms is connected in series with the smaller of the two. The null point shifts to 40 cm. The value of the smaller resistance in ohms is:
A) 3
B) 6
C) 9
D) 12
View Answer play_arrowquestion_answer11) If the potential difference across the internal resistance \[{{r}_{1}}\] is equal to the emf E of die battery, then:
A) \[R={{r}_{1}}+{{r}_{2}}\]
B) \[R=\frac{{{r}_{1}}}{{{r}_{2}}}\]
C) \[R={{r}_{1}}-{{r}_{2}}\]
D) \[R=\frac{{{r}_{2}}}{{{r}_{1}}}\]
View Answer play_arrowquestion_answer12) By using only two resistance coils-singly, in series or ill parallel one should be able to obtain resistances of 3, 4, 12 and 16 ohms. The separate resistances of the coil are:
A) 3 and 4
B) 4 and 12
C) 12 and 16
D) 16 and 3
View Answer play_arrowquestion_answer13) The electrons in the beam of a television tube move horizontally from south to north. The vertical component of the earths magnetic field points down. The electron is deflected towards:
A) west
B) no deflection
C) east
D) north to south
View Answer play_arrowquestion_answer14) A tangent galvanometer has a reduction factor of 1 A and it is placed with the plane of its coil perpendicular to the magnetic meridian. The deflection produced when a current of 1 A is passed through it is:
A) \[{{60}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{30}^{o}}\]
D) none of these
View Answer play_arrowquestion_answer15) In the given circuit, the voltmeter records 5 volts. The resistance of the voltmeter in ohms is:
A) 200
B) 100
C) 10
D) 50
View Answer play_arrowquestion_answer16) The wavelength of the radiation emitted by a body depends upon:
A) the nature of the surface
B) the area of the surface
C) the temperature of the surface
D) all of the above factors
View Answer play_arrowquestion_answer17) Which mirror is to be used to obtain a parallel beam of light from a small lamp?
A) Plane mirror
B) Convex mirror
C) Concave mirror
D) Any one of the above
View Answer play_arrowquestion_answer18) An ideal monoatomic gas is taken around the cycle ABCDA as shown in the PV diagram. The work done during the cycle is given by:
A) \[\frac{1}{2}PV\]
B) PV
C) 2 PV
D) 4 PV
View Answer play_arrowquestion_answer19) Which of the following is a wrong statement?
A) \[D=1\text{ }/f\] where f is the focal length and D is called the refractive power of a lens.
B) Power is expressed in a diopter when f is in metres
C) Power is expressed in diopter and does not depend on the system of unit used to measure f
D) D is positive for convergent lens and negative for divergent lens.
View Answer play_arrowquestion_answer20) Identify the wrong description of the above figures:
A) 1 represents far-sightedness
B) 2 correction for short sightedness
C) 3 represents far-sightedness
D) 4 correction for far-sightedness
View Answer play_arrowquestion_answer21) An electric field of 1500 V/m and a magnetic field of 0.40 weber/\[metr{{e}^{2}}\] act on a moving electron. The minimum uniform speed along a straight line the electron could have is:
A) \[1.6\times {{10}^{15}}m/s\]
B) \[1.6\times {{10}^{15}}m/s\]
C) \[3.75\times {{10}^{3}}m/s\]
D) \[3.75\times {{10}^{2}}m/s\]
View Answer play_arrowquestion_answer22) In an ammeter 10% of main current is passing through the galvanometer. If the resistance of the galvanometer is G, then the shunt resistance, in ohms is:
A) 9 G
B) \[\frac{G}{9}\]
C) 90 G
D) \[\frac{G}{90}\]
View Answer play_arrowquestion_answer23) Among the following properties describing diamagnetism identify the property that is wrongly stated:
A) Diamagnetic material do not have permanent magnetic moment
B) Ddiamagnetism is explained in terms of electromagnetic induction
C) Diamagnetic materials have a small positive susceptibility
D) The magnetic moment of individual electrons neutralize each other
View Answer play_arrowquestion_answer24) The induction coil works on the principle of:
A) self - induction
B) mutual induction
C) Amperes rule
D) Flemings right hand rule
View Answer play_arrowquestion_answer25) The square root of the product of inductance and capacitance has the dimension of:
A) length
B) mass
C) time
D) no dimension
View Answer play_arrowquestion_answer26) When a body falls in air, the resistance of air depends to a great extent on the shape of the body. 3 different shapes are given. Identify the combination of air resistances which truly represents the physical situation. (The cross sectional areas are the same).
A) \[1<2<3\]
B) \[2<3<1\]
C) \[3<2<1\]
D) \[3<1<2\]
View Answer play_arrowquestion_answer27) The adjacent figure is the part of a horizontally stretched net. Section AB is stretched with a force of 10 N. The tensions in the sections BC and BF are:
A) 10 N, 11 N
B) 10 N, 6 N
C) 10 N, 10 N
D) cant be calculated due to insufficient data
View Answer play_arrowquestion_answer28) Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant?
A) Acceleration due to gravity
B) Surface tension of water
C) Weight of a standard kilogram mass
D) The velocity of light hi vacuum
View Answer play_arrowquestion_answer29) The relationship between the force F and position x of a body is as shown in figure. The work done in displacing the body from \[x=1\]m to \[x=5\,m\] will be:
A) 30 J
B) 15 J
C) 25 J
D) 20 J
View Answer play_arrowquestion_answer30) From the top of a tower of two stones, whose masses are in the ratio \[1:2\] are thrown on straight up with an initial speed k and the second straight down with the same speed it. Then neglecting air resistance:
A) the heavier stone hits the ground with a higher speed
B) the lighter stone hits the ground with a higher speed
C) both the stones will have the same speed when they hit the ground
D) the speed cant be determined with the given data
View Answer play_arrowquestion_answer31) Infrared radiation was discovered in 1800 by:
A) William Wollaston
B) William Herschel
C) Wilhelm Roentgen
D) Thomas Young
View Answer play_arrowquestion_answer32) A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period)
A) T/2
B) T/4
C) T
D) 2 T
View Answer play_arrowquestion_answer33) The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency:
A) 10 Hz
B) 360 Hz
C) 216 Hz
D) 60 Hz
View Answer play_arrowquestion_answer34) The ratio of velocity of sound in hydrogen and oxygen at STP is:
A) \[16:1\]
B) \[8:1\]
C) \[4:1\]
D) \[2:1\]
View Answer play_arrowquestion_answer35) In an experiment with sonometer a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. Tension of the string remaining constant the frequency of the second tuning fork is:
A) 163.84 Hz
B) 400 Hz
C) 320 Hz
D) 204.8 Hz
View Answer play_arrowquestion_answer36) The apparent frequency of a note is 200 Hz, when a listener is moving with a velocity of \[40\text{ }m{{s}^{-1}}\] towards a stationary source. When he moves away from the same source with the same speed, the apparent frequency of the same note is 160 Hz. The velocity of sound in air in m/s is:
A) 340
B) 330
C) 360
D) 320
View Answer play_arrowquestion_answer37) The wave theory of light, in its original form, was first postulated by:
A) Isaac Newton
B) Christian Huygens
C) Thomas Young
D) Augustin Jean Fresnel
View Answer play_arrowquestion_answer38) If a liquid does not wet glass, its angle of contact is:
A) zero
B) acute
C) obtuse
D) right angle
View Answer play_arrowquestion_answer39) The magnitude of J in ampere is:
A) 0.1
B) 0.3
C) 0.6
D) none of these
View Answer play_arrowquestion_answer40) Electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field of intensity B. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius:
A) 2 r
B) 4 r
C) r/4
D) r/2
View Answer play_arrowquestion_answer41) From the figure describing photoelectric effect we may infer correctly that:
A) Na and Al both have the same threshold frequency
B) maximum kinetic energy for both the metals depend linearly on the frequency
C) the stopping potentials are different for Na and Al for the same change m frequency
D) Al is a better photo sensitive material than Na.
View Answer play_arrowquestion_answer42) Two coherent light beams of intensity \[I\]and \[4I\] are superposed. The maximum and minimum possible intensities in the resulting beam are:
A) \[9I\] and \[I\]
B) \[9I\] and \[3I\]
C) \[5I\] and \[I\]
D) \[5I\] and \[3I\]
View Answer play_arrowquestion_answer43) The electron in a hydrogen atom makes a transition from \[n={{n}_{1}}\] to \[n={{n}_{2}}\] state. The time period of the electron in the initial state \[({{n}_{1}})\] is eight times that in the final state \[({{n}_{2}})\]. The possible values of \[{{n}_{1}}\] and \[{{n}_{2}}\]are:
A) \[{{n}_{1}}=8,{{n}_{2}}=1\]
B) \[{{n}_{1}}=4,{{n}_{2}}=2\]
C) \[{{n}_{1}}=2,{{n}_{2}}=4\]
D) \[{{n}_{1}}=1,{{n}_{2}}=8\]
View Answer play_arrowquestion_answer44) If the forward voltage in a diode is increased, the width of the depletion region:
A) increases
B) decreases
C) fluctuates
D) no change
View Answer play_arrowquestion_answer45) Two nucleons are at a separation of one Fermi. Protons have a charge of\[+1.6\times {{10}^{-19}}C\]. The net nuclear force between them is \[{{F}_{1}}\], if both are neutrons, \[{{F}_{2}}\]if both are protons and \[{{F}_{3}}\] if one is proton and the other is neutron. Then:
A) \[{{F}_{1}}={{F}_{2}}>{{F}_{3}}\]
B) \[{{F}_{1}}={{F}_{2}}={{F}_{3}}\]
C) \[{{F}_{1}}<{{F}_{2}}<{{F}_{3}}\]
D) \[{{F}_{1}}>{{F}_{2}}>{{F}_{3}}\]
View Answer play_arrowquestion_answer46) The electric flux for Gaussian surface A that enclose the charged particles in free space is (given \[{{q}_{1}}=14nC,{{q}_{2}}=78.85nC,{{q}_{3}}=-56nC\])
A) \[{{10}^{3}}N{{m}^{2}}{{C}^{-1}}\]
B) \[{{10}^{3}}C{{N}^{-1}}{{m}^{-2}}\]
C) \[6.32\times {{10}^{3}}N{{m}^{2}}{{C}^{-1}}\]
D) \[6.32\times {{10}^{3}}C{{N}^{-1}}{{m}^{-2}}\]
View Answer play_arrowquestion_answer47) Four metal conductors having different shapes (a) a sphere (b) cylinder (c) pear (d) lightning conductor are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is:
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer48) The potential to which a conductor is raised, depends on:
A) the amount of charge
B) geometry and size of the conductor
C) both (a) and (b)
D) only on (a)
View Answer play_arrowquestion_answer49) The work done in carrying a charge q once round a circle of radius r with a charge Q at die centre is:
A) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}r}\]
B) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}^{2}{{r}^{2}}}\]
C) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\]
D) none of these
View Answer play_arrowquestion_answer50) An air filled parallel plate condenser has a capacity of 2 pF. The separation of the plates is doubled and the interspace between the plates is filled with wax. If the capacity is increased to 6 pF, the dielectric constant of wax is:
A) 2
B) 3
C) 4
D) 6
View Answer play_arrowquestion_answer51) The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 rim is:
A) four times the initial energy
B) equal to the initial energy
C) twice the initial energy
D) thrice the initial energy
View Answer play_arrowquestion_answer52) Mean life of a radioactive sample is 100 seconds. Then its half-life (in minutes) is:
A) 0.693
B) 1
C) \[{{10}^{-4}}\]
D) 1.155
View Answer play_arrowquestion_answer53) Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion 5 billion years ago. The other was created in a nuclear reactor 5 minutes ago. The probability of decay during the next time is:
A) different for each nuclei
B) nuclei created in explosion decays first
C) nuclei created in the reactor decays first
D) independent of the time of creation
View Answer play_arrowquestion_answer54) Bohrs atom model assumes:
A) the nucleus is of infinite mass and is at rest
B) electrons in a quantized orbit will not radiate energy
C) mass of electron remains constant
D) all the above conditions
View Answer play_arrowquestion_answer55) Identify the property which is not characteristic for a semiconductor?
A) At a very low temperatures, it behaves like an insulator
B) At higher temperatures two types of charge carriers will cause conductivity
C) The charge carriers are electrons and holes in the valence band at higher temperatures
D) The semiconductor is electrically neutral.
View Answer play_arrowquestion_answer56) Identify the wrong statement in the following. Coulombs law correctly described the electric force that:
A) binds the electrons of an atom to its nucleus
B) binds the protons and neutrons in the nucleus of an atom
C) binds atoms together to form molecules
D) binds atoms and molecules to form solids
View Answer play_arrowquestion_answer57) A single slit of width d is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as y. When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm, the width of the diffraction pattern is:
A) the pattern vanishes and the width is zero
B) \[y/3\]
C) 3 y
D) none of these
View Answer play_arrowquestion_answer58) At Kavalur in India, the astronomers using a telescope whose objective had a diameter of one metre started using telescope of diameter 2.54 m. This resulted in:
A) the increase m the resolving power by 2.54 times for the same \[\lambda \]
B) the increase in the limiting angle by 2.54 times for the same \[\lambda \]
C) decrease in the resolving power
D) no effect on the limiting angle
View Answer play_arrowquestion_answer59) When unpolarised light beam is incident from air onto glass \[(n=1.5)\] at the polarizing angle:
A) reflected beam is polarised 100 percent
B) reflected and refracted beams are partially polarized
C) the reason for (a) is that almost all the light is reflected
D) all of the above
View Answer play_arrowquestion_answer60) Select the right option in the following:
A) Christian Huygens, a contemporary of Newton established the wave theory of light by assuming that light waves were transverse.
B) Maxwell provided the theoretical evidence that light is transverse wave
C) Thomas Young experimentally proved the wave behaviour of light and Huygens assumption
D) All the statements given above, correctly answers the question what is light?
View Answer play_arrowquestion_answer61) 15 moles of \[{{H}_{2}}\] and 5.2 moles of \[{{I}_{2}}\] are mixed and allowed to attain equilibrium at \[{{500}^{o}}C\]. At equilibrium, the concentration of HI is found to be 10 moles. The equilibrium constant for the formation of HI is :
A) 50
B) 15
C) 100
D) 25
View Answer play_arrowquestion_answer62) If, in the reaction \[{{N}_{2}}{{O}_{4}}2N{{O}_{2}},\,\,x\] is that part of \[{{N}_{2}}{{O}_{4}}\] which dissociates, then the number of molecules at equilibrium will be :
A) 1
B) 3
C) \[(1+x)\]
D) \[{{(1+x)}^{2}}\]
View Answer play_arrowquestion_answer63) Which of these does not influence the rate of reaction?
A) Nature of the reactants
B) Concentration of the reactants
C) - Temperature of the reaction
D) Molecularity of die reaction
View Answer play_arrowquestion_answer64) For the reaction \[A+B\to C\], it is found that doubling the concentration of A increases the rate by 4 times, and doubling the concentration of B doubles the reaction rate. What is the overall order of the reaction?
A) 4
B) 3/2
C) 3
D) 1
View Answer play_arrowquestion_answer65) The rate at which a substance reacts depends on its :
A) atomic weight
B) atomic number
C) molecular weight
D) active mass
View Answer play_arrowquestion_answer66) A compound A has a molecular formula\[{{C}_{2}}C{{l}_{3}}OH\]. It reduces Fehlings solution and on oxidation, gives a monocarboxylic acid B.A can be obtained by the action of chlorine on ethyl alcohol. A is :
A) chloroform
B) chloral
C) methyl chloride
D) monochloroacetic acid
View Answer play_arrowquestion_answer67) Which of the following haloalkanes is most reactive?
A) 1-chloropropane
B) 1-bromopropane
C) 2-chloropropane
D) 2-bromopropane
View Answer play_arrowquestion_answer68) The reaction in which phenol differs from alcohol is :
A) it undergoes esterification with carboxylic acid
B) it reacts with ammonia
C) it forms yellow crystals of iodoform
D) it liberates \[{{H}_{2}}\] with Na metal.
View Answer play_arrowquestion_answer69) An organic compound A containing C, H and O has a pleasant odour with boiling point of\[{{78}^{o}}C\]. On boiling A with concentrated \[{{H}_{2}}S{{O}_{4}}\], a colourless gas is produced which decolourises bromine water and alkaline\[KMn{{O}_{4}}\]. The organic liquid A is :
A) \[{{C}_{2}}{{H}_{5}}Cl\]
B) \[{{C}_{2}}{{H}_{5}}COOC{{H}_{3}}\]
C) \[{{C}_{2}}{{H}_{5}}OH\]
D) \[{{C}_{2}}{{H}_{6}}\]
View Answer play_arrowquestion_answer70) Which of the following is an amphoteric acid?
A) Glycine
B) Salicylic acid
C) Benzoic acid
D) Citric acid
View Answer play_arrowquestion_answer71) Gold is extracted by hydrometallurgical process, based on its property :
A) of being electropositive
B) of being less reactive
C) to form complexes which are water soluble
D) to form salts which are water soluble
View Answer play_arrowquestion_answer72) In blast furnace, iron oxide is reduced by:
A) hot blast of air
B) carbon monoxide
C) carbon
D) silica
View Answer play_arrowquestion_answer73) Which of the following pairs of elements cannot form an alloy?
A) Zn, Cu
B) Fe, Hg
C) Fe, C
D) Hg, Na
View Answer play_arrowquestion_answer74) Which compound is zero valent metal complex?
A) \[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\]
B) \[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]
C) \[[Ni{{(CO)}_{4}}]\]
D) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]
View Answer play_arrowquestion_answer75) Alum is a water purifier because it :
A) coagulates the impurities
B) softens hard water
C) gives taste
D) destroys the pathogenic bacteria
View Answer play_arrowquestion_answer76) For the reaction\[{{N}_{2(g)}}+{{O}_{2(g)}}2N{{O}_{(g)}}\], the value of \[{{K}_{c}}\] at \[{{800}^{o}}C\] is 0.1. When the equilibrium concentration of both die reactants is 0.5 mol, what is the value of \[{{K}_{p}}\] at the same temperature?
A) 0.5
B) 0.1
C) 0.01
D) 0.025
View Answer play_arrowquestion_answer77) The extent of adsorption of a gas on a solid depends on :
A) nature of the gas
B) pressure of the gas
C) temperature of the gas
D) all of the above
View Answer play_arrowquestion_answer78) A emulsifier is a substance which :
A) stabilises the emulsion
B) homogenises the emulsion
C) coagulates the emulsion
D) accelerates the dispersion of liquid in liquid
View Answer play_arrowquestion_answer79) Which of the following types of metals form the most efficient catalysts?
A) -Alkali metals
B) -Alkaline earth metals
C) Transition metals
D) All of the above
View Answer play_arrowquestion_answer80) The species among the following, which can act as an acid and a base is :
A) \[HSO_{4}^{-}\]
B) \[SO_{4}^{2-}\]
C) \[{{H}_{3}}{{O}^{+}}\]
D) \[C{{l}^{-}}\]
View Answer play_arrowquestion_answer81) Benzyl alcohol and sodium benzoate is obtained by the action of sodium hydroxide on benzaldehyde. This reaction is known as :
A) Perkins reaction
B) Cannizaros reaction
C) Sandmeyers reaction
D) Claisen condensation
View Answer play_arrowquestion_answer82) Ethyl chloride on heating with \[AgCN\] forms a compound X. The functional isomer of X is :
A) \[{{C}_{2}}{{H}_{5}}NC\]
B) \[{{C}_{2}}{{H}_{5}}N{{H}_{2}}\]
C) \[{{C}_{2}}{{H}_{5}}CN\]
D) none of these
View Answer play_arrowquestion_answer83) A compound, containing only carbon, hydrogen and oxygen, has a molecular weight of 44. On complete oxidation it is converted into a compound of molecular weight 60. The original compound is :
A) an aldehyde
B) an acid
C) ail alcohol
D) an ether
View Answer play_arrowquestion_answer84) Grignard reagent adds to :
A) \[<C=O\]
B) \[C=N\]
C) \[<C=S\]
D) all of these
View Answer play_arrowquestion_answer85) Which of the following biomolecules contain non-transition metal ion?
A) Vitamin \[{{B}_{12}}\]
B) Chlorophyll
C) Haemoglobin
D) Insulin
View Answer play_arrowquestion_answer86) A mixture of two moles of carbon monoxide and one mole of oxygen, in a closed vessel is ignited to convert the carbon monoxide to carbon dioxide. If \[\Delta H\] is the enthalpy change and \[\Delta E\] is the change in internal energy, then:
A) \[\Delta H>\Delta E\]
B) \[\Delta H<\Delta E\]
C) \[\Delta H=\Delta E\]
D) the relationship depends on the capacity of the vessel
View Answer play_arrowquestion_answer87) The cooling in refrigerator is due to :
A) reaction of the refrigerator gas
B) expansion of ice
C) the expansion of the gas in die refrigerator
D) the work of die compressor
View Answer play_arrowquestion_answer88) For a system in equilibrium, \[\Delta G=0\], under conditions of constant .........
A) temperature and pressure
B) temperature arid volume
C) pressure and volume
D) energy and volume
View Answer play_arrowquestion_answer89) Molar heat of vaporisation of a liquid is\[6\,kJ\,mo{{l}^{-1}}\]. If die entropy change is \[16\,J\,mo{{l}^{-1}}{{K}^{-1}}\], the boiling point of the liquid is:
A) \[{{375}^{o}}C\]
B) 375K
C) 273 K
D) \[{{102}^{o}}C\]
View Answer play_arrowquestion_answer90) The temperature of the system decreases in an :
A) adiabatic compression
B) isothermal compression
C) isothermal expansion
D) adiabatic expansion
View Answer play_arrowquestion_answer91) A buffer solution has equal volumes of 0.2 M \[N{{H}_{4}}OH\] and 0.02 M \[N{{H}_{4}}Cl\]. The \[p{{K}_{b}}\], of the base is 5. The pH is :
A) 10
B) 9
C) 4
D) 7
View Answer play_arrowquestion_answer92) The hydrogen electrode is dipped in a solution of pH 3 at \[{{25}^{o}}C\]. The potential would be (the value of 2.303 RT/F is 0.059 V) :
A) 0.177 V
B) 0.087 V
C) 0.059V
D) -0.177V
View Answer play_arrowquestion_answer93) 20 mL of 0.5 N \[HCl\] and 35 mL of 0.1 N \[NaOH\]are mixed. The resulting solution will :
A) be neutral
B) be basic
C) turn phenolphthalein solution pink
D) turn methyl orange red
View Answer play_arrowquestion_answer94) Corrosion of iron is essentially an electrochemical phenomenon where the cell reactions are :
A) Fe is oxidised to \[F{{e}^{2+}}\]and dissolved oxygen in water is reduced to \[O{{H}^{-}}\]
B) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{2-}\]
C) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{-}\]
D) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[{{O}_{2}}\]
View Answer play_arrowquestion_answer95) The standard electrode potential is measured by :
A) electrometer
B) voltmeter
C) pyrometer
D) galvanometer
View Answer play_arrowquestion_answer96) A precipitate of \[AgCl\] is formed when equal volumes of the following are mixed : [\[{{K}_{sp}}\] for\[AgCl={{10}^{-10}}\]]
A) \[{{10}^{-4}}M\,AgN{{O}_{3}}\] and \[{{10}^{-7}}M\,HCl\]
B) \[{{10}^{-5}}M\,AgN{{O}_{3}}\] and \[{{10}^{-6}}M\,HCl\]
C) \[{{10}^{-5}}M\,AgN{{O}_{3}}\] and \[{{10}^{-4}}M\,HCl\]
D) \[{{10}^{-6}}M\,AgN{{O}_{3}}\] and \[{{10}^{-6}}M\,HCl\]
View Answer play_arrowquestion_answer97) Which one of the following defects in the crystals lowers its density?
A) Frenkel defect
B) Schottky defect
C) F-centres
D) Interstitial defect
View Answer play_arrowquestion_answer98) A radioactive isotope has a half-life of 10 days. If today 125 mg is left over, what was its original weight 40 days earlier?
A) 2 g
B) 600 mg
C) 1 g
D) 1.5 g
View Answer play_arrowquestion_answer99) Which of the following cannot be accelerated?
A) \[\alpha \]-particle
B) \[\beta \]-particle
C) Protons
D) Neutrons
View Answer play_arrowquestion_answer100) In which of the following nuclear reaction neutrons is emitted?
A) \[_{13}^{27}Al+_{2}^{4}He\to _{15}^{30}P\]
B) \[_{6}^{27}C+_{1}^{1}H\to _{7}^{13}N\]
C) \[_{15}^{30}P\to _{14}^{30}Si\]
D) \[_{96}^{241}Am+_{2}^{4}He\to _{97}^{245}Bk\]
View Answer play_arrowquestion_answer101) Molarity of \[0.2\,N\,{{H}_{2}}S{{O}_{4}}\] is :
A) 0.2
B) 0.4
C) 0.6
D) 0.1
View Answer play_arrowquestion_answer102) In the equation of state of an ideal gas\[PV=nRT\], the value of the universal gas constant would depend only on :
A) the nature of the gas
B) the pressure of the gas
C) the units of the measurement
D) none of the above
View Answer play_arrowquestion_answer103) A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage strength is nearly :
A) 1%
B) 3%
C) 10%
D) 90%
View Answer play_arrowquestion_answer104) Activated charcoal is used to remove colouring matter from pure substances. It works by :
A) oxidation
B) reduction
C) bleaching
D) adsorption
View Answer play_arrowquestion_answer105) When plants and animals decay, the organic nitrogen is converted into inorganic nitrogen. The inorganic nitrogen is in the form of:
A) ammonia
B) elements of nitrogen
C) nitrates
D) nitrides
View Answer play_arrowquestion_answer106) Three dimensional molecules with cross links are formed in the case of a :
A) thermoplastic
B) thermosetting plastic
C) both (a) and (b)
D) none of the above
View Answer play_arrowquestion_answer107) Sucrose molecule is made up of :
A) a gluco pyranose and a fructo pyranose
B) a gluco pyranose and a fructo furanose
C) a gluco furanose and a fructo pyranose
D) a gluco furanose and a fructo furanose
View Answer play_arrowquestion_answer108) Water insoluble component of starch is :
A) amylopectin
B) amylose
C) cellulose
D) none of these
View Answer play_arrowquestion_answer109) An example for a saturated fatty acid, present in nature is :
A) oleic acid
B) linoleic acid
C) linolenic acid
D) palmitic acid
View Answer play_arrowquestion_answer110) A nanopeptide contains......peptide linkages :
A) 10
B) 8
C) 9
D) 18
View Answer play_arrowquestion_answer111) A gas decolourised by \[KMn{{O}_{4}}\] solution but gives no precipitate with ammoniacal cuprous chloride is :
A) ethane
B) methane
C) ethane
D) acetylene
View Answer play_arrowquestion_answer112) \[{{H}_{3}}C-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C}}\,=CH-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
A) 2-chloro-4-methyl-2pentene
B) 4-chloro-2-methyl-3-pentene
C) 4-methyl-2-chloro-2-pentene
D) 2-chloro-4,4-dimethyl-2-butene
View Answer play_arrowquestion_answer113) Amongst the following the compound that can most readily get sulphonated is :
A) benzene
B) toluene
C) nitrobenzene
D) chlorobenzene
View Answer play_arrowquestion_answer114) Household gaseous fuel (LPG) mainly con tarns:
A) \[C{{H}_{4}}\]
B) \[{{C}_{2}}{{H}_{2}}\]
C) \[{{C}_{2}}{{H}_{4}}\]
D) \[{{C}_{4}}{{H}_{10}}\]
View Answer play_arrowquestion_answer115) Use of chlorofluoro carbons is not encouraged because :
A) they are harmful to the eyes of people that use it
B) they damage the refrigerators and air conditioners
C) they eat away the ozone in the atmosphere
D) they destroy the oxygen layer
View Answer play_arrowquestion_answer116) An example of a sulphur containing amino acid is :
A) lysine
B) serine
C) cysteine
D) tyrosine
View Answer play_arrowquestion_answer117) Which of the following is not present in a nucleotide?
A) Cytosine
B) Guanine
C) Adenine
D) Tyrosine
View Answer play_arrowquestion_answer118) Antiseptic chloroxylenol is :
A) 4-chloro-3,5-dimethyl phenol
B) 3-chloro-4,5-dimethyl phenol
C) 4-chloro-2,5-dimethyl phenol
D) 5-chloro-3,4-dimethyl phenol
View Answer play_arrowquestion_answer119) An atom of an element A has three electrons in its outermost orbit and that of B has six electrons in its outermost orbit. The formula of the compound between these two will be :
A) \[{{A}_{3}}{{B}_{6}}\]
B) \[{{A}_{2}}{{B}_{3}}\]
C) \[{{A}_{3}}{{B}_{2}}\]
D) \[{{A}_{2}}B\]
View Answer play_arrowquestion_answer120) Among \[N{{a}^{+}},\,Na,\,Mg\] and \[M{{g}^{2+}}\], the largest particle is :
A) \[M{{g}^{2+}}\]
B) Mg
C) Na
D) \[N{{a}^{+}}\]
View Answer play_arrowquestion_answer121) When \[{{2}^{301}}\] is divided by 5, the least positive remainder is :
A) 4
B) 8
C) 2
D) 6
View Answer play_arrowquestion_answer122) The contrapositive of If two triangles are identical, then these are similar is :
A) If two triangles are not similar, then these are not identical
B) If two triangles are not identical, then these are not similar
C) If two triangles are not identical, then these are similar
D) If two. triangles are not similar, then these are identical
View Answer play_arrowquestion_answer123) The contrapositive of the inverse of \[p\to \,\sim \,\,q\]is :
A) \[\sim q\to p\]
B) \[p\to q\]
C) \[\sim q\to \sim p\]
D) \[\sim p\to \sim q\]
View Answer play_arrowquestion_answer124) The converse of the contrapositive of \[p\to q\] is :
A) \[\sim p\to q\]
B) \[p\to \sim q\]
C) \[\sim p\to \sim q\]
D) \[\sim q\to p\]
View Answer play_arrowquestion_answer125) If \[\omega \] is a complex cube-root of unity, then\[\left| \begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix} \right|\] is equal to :
A) -1
B) 1
C) 0
D) \[\omega \]
View Answer play_arrowquestion_answer126) The ends of the latus rectum of the conic\[{{x}^{2}}+10x-16y+25=0\] are :
A) (3,-4), (13, 4)
B) (-3,-4), (13,-4)
C) (3, 4), (-13, 4)
D) (5,-8), (-5, 8)
View Answer play_arrowquestion_answer127) The equation to die hyperbola having its eccentricity 2 and the distance between its foci is 8, is :
A) \[\frac{{{x}^{2}}}{12}-\frac{{{y}^{2}}}{4}=1\]
B) \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\]
C) \[\frac{{{x}^{2}}}{8}-\frac{{{y}^{2}}}{2}=1\]
D) \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\]
View Answer play_arrowquestion_answer128) The solution of \[{{\sin }^{-1}}x-{{\sin }^{-1}}2x=\pm \frac{\pi }{3}\] is :
A) \[\pm \frac{1}{3}\]
B) \[\pm \frac{1}{3}\]
C) \[\pm \frac{\sqrt{3}}{2}\]
D) \[\pm \frac{1}{2}\]
View Answer play_arrowquestion_answer129) In a \[\Delta ABC\] if the sides are \[a=3,b=5\] and\[c=4\], then \[\sin \frac{B}{2}+\cos \frac{B}{2}\] is equal to :
A) \[\sqrt{2}\]
B) \[\frac{\sqrt{3}+1}{2}\]
C) \[\frac{\sqrt{3}-1}{2}\]
D) 1
View Answer play_arrowquestion_answer130) The value of\[\cos \left( {{270}^{o}}+\theta \right)\cos \left( {{90}^{o}}-\theta \right)-\sin \left( {{270}^{o}}-\theta \right)\cos \theta \]is :
A) 0
B) - 1
C) 1/2
D) 1
View Answer play_arrowquestion_answer131) The two circles \[{{x}^{2}}+{{y}^{2}}-2x+22y+5=0\] and \[{{x}^{2}}+{{y}^{2}}+14x+6y+k=0\] intersect orthogonally provided k is equal to :
A) 47
B) -47
C) 49
D) -49
View Answer play_arrowquestion_answer132) The radius of the circle \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] is ;
A) \[\sqrt{26}\]
B) \[\sqrt{13}\]
C) \[\sqrt{23}\]
D) 0
View Answer play_arrowquestion_answer133) The centre of the circle \[x=2+3\cos \theta ,\]\[y=3\text{ }\sin \theta -1\] is :
A) (3, 3)
B) (2,-1)
C) (-2,1)
D) (-1,2)
View Answer play_arrowquestion_answer134) The sum of the focal distances of any point on the conic \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] is :
A) 10
B) 9
C) 41
D) 18
View Answer play_arrowquestion_answer135) The eccentricity of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\] is:
A) \[\frac{3}{4}\]
B) \[\frac{3}{5}\]
C) \[\frac{\sqrt{41}}{4}\]
D) \[\frac{\sqrt{41}}{5}\]
View Answer play_arrowquestion_answer136) The solutions of me equation \[\left| \begin{matrix} x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x \\ \end{matrix} \right|=0\] are:
A) 3,-1
B) -3, 1
C) 3, 1
D) -3,-1
View Answer play_arrowquestion_answer137) If \[A=\left[ \begin{matrix} 3 & 5 \\ 2 & 0 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 1 & 17 \\ 0 & -10 \\ \end{matrix} \right]\], then \[|AB|\] is equal to :
A) 80
B) 100
C) - 110
D) 92
View Answer play_arrowquestion_answer138) The inverse of the matrix \[\left[ \begin{matrix} 5 & -2 \\ 3 & 1 \\ \end{matrix} \right]\] is :
A) \[\frac{1}{11}\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\]
C) \[\frac{1}{13}\left[ \begin{matrix} -2 & 5 \\ 1 & 3 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 3 \\ -2 & 5 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer139) The projection of the vector \[2\hat{i}+\hat{j}-3\hat{k}\] on the vector \[\hat{i}-2\hat{j}+\hat{k}\] is :
A) \[-\frac{3}{\sqrt{14}}\]
B) \[\frac{3}{\sqrt{14}}\]
C) \[-\frac{\sqrt{3}}{2}\]
D) \[\frac{3}{\sqrt{2}}\]
View Answer play_arrowquestion_answer140) A unit vector perpendicular to the plane containing the vectors \[\hat{i}-\hat{j}+\hat{k}\] and \[-\hat{i}+\hat{j}+\hat{k}\] is :
A) \[\pm \frac{\hat{j}-\hat{j}}{\sqrt{2}}\]
B) \[\pm \frac{\hat{j}+\hat{k}}{\sqrt{2}}\]
C) \[\pm \frac{\hat{j}-\hat{k}}{\sqrt{2}}\]
D) \[\pm \frac{\hat{i}+\hat{j}}{\sqrt{2}}\]
View Answer play_arrowquestion_answer141) If \[12\,{{\cot }^{2}}\theta -31\cos ec\theta +32=0\], then the value of \[\sin \theta \] is
A) \[\frac{3}{5}\]or 1
B) \[\frac{2}{3}\] or \[-\frac{2}{3}\]
C) \[\frac{4}{5}\] or \[\frac{3}{4}\]
D) \[\pm \frac{1}{2}\]
View Answer play_arrowquestion_answer142) The circus-radius of the triangle whose sides are 13, 12 and 5, is :
A) 15
B) 13/2
C) 15/2
D) 6
View Answer play_arrowquestion_answer143) If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\frac{\pi }{4}\], then :
A) \[x+y+xy=1\]
B) \[x+y-xy=1\]
C) \[x+y+xy+1=0\]
D) \[~x+y-xy+1=0\]
View Answer play_arrowquestion_answer144) The general solution of \[\sin x-\cos x=\sqrt{2}\] for any integer n is :
A) \[n\pi \]
B) \[2n\pi +\frac{3\pi }{4}\]
C) \[2n\pi \]
D) \[(2n\pi +1)\]
View Answer play_arrowquestion_answer145) The amplitude of \[\frac{1+i\sqrt{3}}{\sqrt{3}+i}\] is :
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer146) The sum to infinity of the progression\[9-3+\frac{1}{3}+.........\] is :
A) 9
B) 9/2
C) 27/4
D) 15/2
View Answer play_arrowquestion_answer147) If\[{{\,}^{n}}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\]
A) 72
B) 153
C) 306
D) 2556
View Answer play_arrowquestion_answer148) The middle term in the expansion of \[{{\left( x-\frac{1}{x} \right)}^{18}}\]
A) \[^{18}{{C}_{9}}\]
B) \[\,{{-}^{18}}{{C}_{9}}\]
C) \[^{18}{{C}_{10}}\]
D) \[{{-}^{18}}{{C}_{10}}\]
View Answer play_arrowquestion_answer149) If \[\alpha ,\,\beta ,\,\,\gamma \] are the roots of the equation\[2{{x}^{3}}-3{{x}^{2}}+6x+1=0\], then \[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}\] is equal to :
A) \[-\frac{15}{4}\]
B) \[\frac{15}{4}\]
C) \[\frac{9}{4}\]
D) 4
View Answer play_arrowquestion_answer150) The digit in the units place in the number \[{{7}^{289}}\] is :
A) 9
B) 7
C) 1
D) 3
View Answer play_arrowquestion_answer151) If \[\hat{a},\,\,\hat{b}\] and \[\hat{c}\] are mutually perpendicular unit vectors, then \[|\hat{a}+\hat{b}+\hat{c}\,|\] is equal to :
A) 3
B) \[\sqrt{3}\]
C) \[(\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{3}})}/3\]
D) 1
View Answer play_arrowquestion_answer152) The identity element ill die group\[M=\left\{ \left[ \begin{matrix} x & x \\ x & x \\ \end{matrix} \right]\,\,\left| x\in R\,;\,x\ne 0 \right. \right\}\,\]with respect to matrix multiplication is :
A) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]
B) \[\frac{1}{2}\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer153) In the group \[G=\{1,3,7,9\}\] under multiplication modulo 10, the inverse of 3 is :
A) 1
B) 3
C) 7
D) 9
View Answer play_arrowquestion_answer154) In the group (0,1, 2, 4, 5} under addition modulo 6 a subgroup is :
A) { 0, 2, 5}
B) ( 1, 4, 5}
C) ( 0, 1, 3)
D) ( 0..2, 4}
View Answer play_arrowquestion_answer155) In the group \[({{Q}^{+}},*)\] of positive rational numbers w.r.t. the binary operation * defined by \[a*b=\frac{ab}{3}\,\,\forall \,\,a,b\in {{Q}^{+}}\] the solution of the equation \[5*x={{4}^{-1}}\] in \[{{Q}^{+}}\] is :
A) \[\frac{27}{20}\]
B) \[\frac{20}{27}\]
C) \[\frac{1}{20}\]
D) 20
View Answer play_arrowquestion_answer156) (0, -1) and (0, 3) are two opposite vertices of a square. The other two vertices are:
A) (0,1),(0,-3)
B) (3,-1),(0,0)
C) (2,1), (-2,1)
D) (2, 2), (1,1)
View Answer play_arrowquestion_answer157) The equation to the line bisecting the join of (3, - 4) and (5, 2) and having its intercepts on the ^-axis and the y-axis in the ratio \[2:1\] is :
A) \[x+y-3=0\]
B) \[2x-y=9\]
C) \[x+2y=2\]
D) \[2x+y=7\]
View Answer play_arrowquestion_answer158) The distance between the pair of parallel lines \[{{x}^{2}}+2xy+{{y}^{2}}-8ax-8ay-9{{a}^{2}}=0\] is :
A) \[2\sqrt{5}\,a\]
B) \[\sqrt{10}\,a\]
C) 10 a
D) \[5\sqrt{2}\,a\]
View Answer play_arrowquestion_answer159) The equation to the circle with centre (2,1) and touching the line \[3x+4y=5\] is :
A) \[{{x}^{2}}+{{y}^{2}}-4y-2y+5=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4x-2y-5=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\]
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y-4=0\]
View Answer play_arrowquestion_answer160) The condition for a line \[y=2x+c\] to touch the circle \[{{x}^{2}}+{{y}^{2}}=16\] is :
A) \[c=10\]
B) \[{{c}^{2}}=80\]
C) \[c=12\]
D) \[{{c}^{2}}=64\]
View Answer play_arrowquestion_answer161) \[\int{\frac{\sin \,\,(2x)}{1+{{\cos }^{2}}x}d\,x=}\]
A) \[-\frac{1}{2}\log \,(1+{{\cos }^{2}}x)+c\]
B) \[2\,\,\log \,(1+{{\cos }^{2}}x)+c\]
C) \[\frac{1}{2}\,\,\log \,(1+{{\cos }^{2}}2x)+c\]
D) \[c-\,\log \,\,(1+{{\cos }^{2}}x)\]
View Answer play_arrowquestion_answer162) \[\int{\frac{{{e}^{x}}(1+\sin x)}{1+\cos x}dx=}\]
A) \[{{e}^{x}}\tan \left( \frac{x}{2} \right)+c\]
B) \[{{e}^{x}}\tan x+c\]
C) \[{{e}^{x}}\left( \frac{1+\sin x}{1-\cos x} \right)+c\]
D) \[c-{{e}^{x}}\cot \left( \frac{x}{2} \right)\]
View Answer play_arrowquestion_answer163) \[\int{\frac{1+\tan x}{{{e}^{-x}}\cos x}d\,x}=\]
A) \[{{e}^{-x}}\tan x+c\]
B) \[{{e}^{-x}}\sec x+c\]
C) \[{{e}^{x}}\sec x+c\]
D) \[{{e}^{x}}\tan x+c\]
View Answer play_arrowquestion_answer164) \[\int\limits_{\pi /4}^{\pi /2}{\cos e{{c}^{2}}x\,dx=}\]
A) -1
B) 1
C) 0
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer165) \[\int\limits_{0}^{\pi /4}{\log \,(1+\tan x)d\,x=}\]
A) \[\frac{\pi }{8}{{\log }_{e}}2\]
B) \[\frac{\pi }{4}{{\log }_{2}}e\]
C) \[\frac{\pi }{4}{{\log }_{e}}2\]
D) \[\frac{\pi }{4}{{\log }_{e}}\left( \frac{1}{2} \right)\]
View Answer play_arrowquestion_answer166) The modulus and amplitude of \[\frac{1+2i}{1-{{(1-i)}^{2}}}\], are :
A) \[\sqrt{2}\] and \[\frac{\pi }{6}\]
B) 1 and 0
C) 1 and \[\frac{\pi }{3}\]
D) 1 and \[\frac{\pi }{4}\]
View Answer play_arrowquestion_answer167) The real part of \[\frac{1}{1+\cos \theta +i\sin \theta }\] is :
A) \[-\frac{1}{2}\]
B) \[\frac{1}{2}\]
C) \[\sqrt{2}\]
D) \[\frac{1}{\sqrt{2}}\]
View Answer play_arrowquestion_answer168) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\] is equal to :
A) \[\frac{1}{2}\]
B) \[-\frac{1}{2}\]
C) 0
D) 1
View Answer play_arrowquestion_answer169) If \[y=\frac{{{e}^{x}}+{{e}^{-x}}}{{{e}^{x}}-{{e}^{-x}}}\], then \[\frac{dy}{dx}\] is equal to :
A) \[\sec \,{{h}^{2}}x\]
B) \[\cos ec\,{{h}^{2}}x\]
C) \[\sec \,\,{{h}^{2}}x\]
D) \[-\cos ec\,{{h}^{2}}x\]
View Answer play_arrowquestion_answer170) If \[f(x)=\left\{ \begin{matrix} \frac{\sin \,5x}{{{x}^{2}}+2x}, & x\ne 0 \\ k+\frac{1}{2}, & x=0 \\ \end{matrix} \right.\] is continuous at\[x=0\], then the value of k is :
A) 1
B) -2
C) 2
D) 1/2
View Answer play_arrowquestion_answer171) The area bounded by the parabola \[{{y}^{2}}=4\text{ }ax\] and the line \[x=a\] and \[x=4\,a\] is :
A) \[\frac{35\,{{a}^{2}}}{3}\]
B) \[\frac{4\,{{a}^{2}}}{3}\]
C) \[\frac{7\,{{a}^{2}}}{3}\]
D) \[\frac{56\,{{a}^{2}}}{3}\]
View Answer play_arrowquestion_answer172) A population p (t) of 1000 bacteria introduced into nutrient medium grows according to the relation \[p\,(t)=1000+\frac{1000\,t}{100+{{t}^{2}}}\]. The maximum size of this bacterial population is :
A) 1100
B) 1250
C) 1050
D) 5250
View Answer play_arrowquestion_answer173) The differential equation representing a family of circles touching the y-axis at the origin is :
A) \[{{x}^{2}}+{{y}^{2}}-2xy\frac{dy}{dx}=0\]
B) \[{{x}^{2}}+{{y}^{2}}+2xy\frac{dy}{dx}=0\]
C) \[{{x}^{2}}-{{y}^{2}}-2xy\frac{dy}{dx}=0\]
D) \[{{x}^{2}}-{{y}^{2}}+2xy\frac{dy}{dx}=0\]
View Answer play_arrowquestion_answer174) The area of the region bounded by tile curve \[9{{x}^{2}}+4{{y}^{2}}-36=0\] is :
A) \[9\pi \]
B) \[4\pi \]
C) \[36\pi \]
D) \[6\pi \]
View Answer play_arrowquestion_answer175) The general solution of the differential equation \[(2x-y+1)\,dx+(2y-x+1)\,\,dy=0\] is:
A) \[{{x}^{2}}+{{y}^{2}}+xy-x+y=c\]
B) \[{{x}^{2}}+{{y}^{2}}-xy+x+y=c\]
C) \[{{x}^{2}}-{{y}^{2}}+2xy-x+y=c\]
D) \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\]
View Answer play_arrowquestion_answer176) If \[y={{\tan }^{-1}}\frac{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}\], then \[\frac{dy}{dx}\] is equal to :
A) \[\frac{{{x}^{2}}}{\sqrt{1-{{x}^{4}}}}\]
B) \[\frac{{{x}^{2}}}{\sqrt{1+{{x}^{4}}}}\]
C) \[\frac{{{x}^{2}}}{\sqrt{1+{{x}^{4}}}}\]
D) \[\frac{x}{\sqrt{1-{{x}^{4}}}}\]
View Answer play_arrowquestion_answer177) If \[x=\sin \,t,\,y=\cos \,pt\], then :
A) \[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}+{{p}^{2}}y=0\]
B) \[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}-{{p}^{2}}y=0\]
C) \[(1+{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\]
D) \[(1-{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\]
View Answer play_arrowquestion_answer178) If ST and SN are the lengths of the sub tangent and the subnormal at the point \[\theta =\frac{\pi }{2}\] on the curve \[x=a\,(\theta +\sin \theta )\], \[y=a\,(1-\cos \theta ),\,a\ne 1\], then :
A) \[ST=SN\]
B) \[Sr=2SN\]
C) \[S{{T}^{2}}=a\,S{{N}^{3}}\]
D) \[S{{T}^{3}}=a\,SN\]
View Answer play_arrowquestion_answer179) If \[\theta \] is the acute angle of intersection at a real point of intersection of the circle \[x+y=5\]and the parabola \[y=4x\], then \[\tan \theta \] is equal to :
A) 1
B) \[\sqrt{3}\]
C) 3
D) \[\frac{1}{\sqrt{3}}\]
View Answer play_arrowquestion_answer180) A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase of the surface area of the balloon when its diameter is 14 cm, is :
A) 7 sq.cm/min
B) 10 sq.cm/min
C) 17.5 sq.cm/min
D) 28 sq.cm/min
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