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) \[\frac{{{R}^{2}}}{M}\] done clear
B) \[\frac{M}{{{R}^{2}}}\] done clear
C) \[M{{R}^{2}}\] done clear
D) \[\frac{M}{R}\] done clear
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 done clear
B) the frictional force while gripping, is small done clear
C) Newtons law of inertia is not applicable to living beings done clear
D) as the force applied is internal to the system done clear
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 done clear
B) the pressure on the bottom of the tank A is smaller than at the bottom of B done clear
C) the pressure depends on the shape of the container done clear
D) the pressure on the bottom of A and B is the same done clear
View Answer play_arrowquestion_answer4) Which one of the following is not a unit of Youngs modulus?
A) \[N{{m}^{-1}}\] done clear
B) \[N{{m}^{-2}}\] done clear
C) dyne \[c{{m}^{-2}}\] done clear
D) mega pascal done clear
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 done clear
B) red looks brighter red and blue looks ordinary blue done clear
C) blue shines like brighter red compared to the red piece done clear
D) both the pieces will look equally red done clear
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) \[{{10}^{-3}}N\] done clear
B) \[2.5\times {{10}^{-3}}N\] done clear
C) zero done clear
D) \[1.5\times {{10}^{-3}}N\] done clear
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) \[1.08\times {{10}^{4}}J\] done clear
B) \[1.08\times {{10}^{4}}J\] done clear
C) \[1.8\times {{10}^{4}}J\] done clear
D) \[1.8\times {{10}^{4}}J\] done clear
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 done clear
B) 8 done clear
C) 10 done clear
D) 20 done clear
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 done clear
B) 26.31 done clear
C) 118.75 done clear
D) none of these done clear
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 done clear
B) 6 done clear
C) 9 done clear
D) 12 done clear
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) \[R={{r}_{1}}+{{r}_{2}}\] done clear
B) \[R=\frac{{{r}_{1}}}{{{r}_{2}}}\] done clear
C) \[R={{r}_{1}}-{{r}_{2}}\] done clear
D) \[R=\frac{{{r}_{2}}}{{{r}_{1}}}\] done clear
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 done clear
B) 4 and 12 done clear
C) 12 and 16 done clear
D) 16 and 3 done clear
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 done clear
B) no deflection done clear
C) east done clear
D) north to south done clear
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) \[{{60}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer15) In the given circuit, the voltmeter records 5 volts. The resistance of the voltmeter in ohms is:
A) 200 done clear
B) 100 done clear
C) 10 done clear
D) 50 done clear
View Answer play_arrowquestion_answer16) The wavelength of the radiation emitted by a body depends upon:
A) the nature of the surface done clear
B) the area of the surface done clear
C) the temperature of the surface done clear
D) all of the above factors done clear
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 done clear
B) Convex mirror done clear
C) Concave mirror done clear
D) Any one of the above done clear
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) \[\frac{1}{2}PV\] done clear
B) PV done clear
C) 2 PV done clear
D) 4 PV done clear
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. done clear
B) Power is expressed in a diopter when f is in metres done clear
C) Power is expressed in diopter and does not depend on the system of unit used to measure f done clear
D) D is positive for convergent lens and negative for divergent lens. done clear
View Answer play_arrowquestion_answer20) Identify the wrong description of the above figures:
A) 1 represents far-sightedness done clear
B) 2 correction for short sightedness done clear
C) 3 represents far-sightedness done clear
D) 4 correction for far-sightedness done clear
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) \[1.6\times {{10}^{15}}m/s\] done clear
B) \[1.6\times {{10}^{15}}m/s\] done clear
C) \[3.75\times {{10}^{3}}m/s\] done clear
D) \[3.75\times {{10}^{2}}m/s\] done clear
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 done clear
B) \[\frac{G}{9}\] done clear
C) 90 G done clear
D) \[\frac{G}{90}\] done clear
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 done clear
B) Ddiamagnetism is explained in terms of electromagnetic induction done clear
C) Diamagnetic materials have a small positive susceptibility done clear
D) The magnetic moment of individual electrons neutralize each other done clear
View Answer play_arrowquestion_answer24) The induction coil works on the principle of:
A) self - induction done clear
B) mutual induction done clear
C) Amperes rule done clear
D) Flemings right hand rule done clear
View Answer play_arrowquestion_answer25) The square root of the product of inductance and capacitance has the dimension of:
A) length done clear
B) mass done clear
C) time done clear
D) no dimension done clear
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) \[1<2<3\] done clear
B) \[2<3<1\] done clear
C) \[3<2<1\] done clear
D) \[3<1<2\] done clear
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 done clear
B) 10 N, 6 N done clear
C) 10 N, 10 N done clear
D) cant be calculated due to insufficient data done clear
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 done clear
B) Surface tension of water done clear
C) Weight of a standard kilogram mass done clear
D) The velocity of light hi vacuum done clear
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 done clear
B) 15 J done clear
C) 25 J done clear
D) 20 J done clear
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 done clear
B) the lighter stone hits the ground with a higher speed done clear
C) both the stones will have the same speed when they hit the ground done clear
D) the speed cant be determined with the given data done clear
View Answer play_arrowquestion_answer31) Infrared radiation was discovered in 1800 by:
A) William Wollaston done clear
B) William Herschel done clear
C) Wilhelm Roentgen done clear
D) Thomas Young done clear
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 done clear
B) T/4 done clear
C) T done clear
D) 2 T done clear
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 done clear
B) 360 Hz done clear
C) 216 Hz done clear
D) 60 Hz done clear
View Answer play_arrowquestion_answer34) The ratio of velocity of sound in hydrogen and oxygen at STP is:
A) \[16:1\] done clear
B) \[8:1\] done clear
C) \[4:1\] done clear
D) \[2:1\] done clear
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 done clear
B) 400 Hz done clear
C) 320 Hz done clear
D) 204.8 Hz done clear
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 done clear
B) 330 done clear
C) 360 done clear
D) 320 done clear
View Answer play_arrowquestion_answer37) The wave theory of light, in its original form, was first postulated by:
A) Isaac Newton done clear
B) Christian Huygens done clear
C) Thomas Young done clear
D) Augustin Jean Fresnel done clear
View Answer play_arrowquestion_answer38) If a liquid does not wet glass, its angle of contact is:
A) zero done clear
B) acute done clear
C) obtuse done clear
D) right angle done clear
View Answer play_arrowquestion_answer39) The magnitude of J in ampere is:
A) 0.1 done clear
B) 0.3 done clear
C) 0.6 done clear
D) none of these done clear
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 done clear
B) 4 r done clear
C) r/4 done clear
D) r/2 done clear
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 done clear
B) maximum kinetic energy for both the metals depend linearly on the frequency done clear
C) the stopping potentials are different for Na and Al for the same change m frequency done clear
D) Al is a better photo sensitive material than Na. done clear
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 \[I\] done clear
B) \[9I\] and \[3I\] done clear
C) \[5I\] and \[I\] done clear
D) \[5I\] and \[3I\] done clear
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) \[{{n}_{1}}=8,{{n}_{2}}=1\] done clear
B) \[{{n}_{1}}=4,{{n}_{2}}=2\] done clear
C) \[{{n}_{1}}=2,{{n}_{2}}=4\] done clear
D) \[{{n}_{1}}=1,{{n}_{2}}=8\] done clear
View Answer play_arrowquestion_answer44) If the forward voltage in a diode is increased, the width of the depletion region:
A) increases done clear
B) decreases done clear
C) fluctuates done clear
D) no change done clear
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) \[{{F}_{1}}={{F}_{2}}>{{F}_{3}}\] done clear
B) \[{{F}_{1}}={{F}_{2}}={{F}_{3}}\] done clear
C) \[{{F}_{1}}<{{F}_{2}}<{{F}_{3}}\] done clear
D) \[{{F}_{1}}>{{F}_{2}}>{{F}_{3}}\] done clear
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) \[{{10}^{3}}N{{m}^{2}}{{C}^{-1}}\] done clear
B) \[{{10}^{3}}C{{N}^{-1}}{{m}^{-2}}\] done clear
C) \[6.32\times {{10}^{3}}N{{m}^{2}}{{C}^{-1}}\] done clear
D) \[6.32\times {{10}^{3}}C{{N}^{-1}}{{m}^{-2}}\] done clear
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 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer48) The potential to which a conductor is raised, depends on:
A) the amount of charge done clear
B) geometry and size of the conductor done clear
C) both (a) and (b) done clear
D) only on (a) done clear
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) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}r}\] done clear
B) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}^{2}{{r}^{2}}}\] done clear
C) \[\frac{qQ}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\] done clear
D) none of these done clear
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 done clear
B) 3 done clear
C) 4 done clear
D) 6 done clear
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 done clear
B) equal to the initial energy done clear
C) twice the initial energy done clear
D) thrice the initial energy done clear
View Answer play_arrowquestion_answer52) Mean life of a radioactive sample is 100 seconds. Then its half-life (in minutes) is:
A) 0.693 done clear
B) 1 done clear
C) \[{{10}^{-4}}\] done clear
D) 1.155 done clear
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 done clear
B) nuclei created in explosion decays first done clear
C) nuclei created in the reactor decays first done clear
D) independent of the time of creation done clear
View Answer play_arrowquestion_answer54) Bohrs atom model assumes:
A) the nucleus is of infinite mass and is at rest done clear
B) electrons in a quantized orbit will not radiate energy done clear
C) mass of electron remains constant done clear
D) all the above conditions done clear
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 done clear
B) At higher temperatures two types of charge carriers will cause conductivity done clear
C) The charge carriers are electrons and holes in the valence band at higher temperatures done clear
D) The semiconductor is electrically neutral. done clear
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 done clear
B) binds the protons and neutrons in the nucleus of an atom done clear
C) binds atoms together to form molecules done clear
D) binds atoms and molecules to form solids done clear
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 done clear
B) \[y/3\] done clear
C) 3 y done clear
D) none of these done clear
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 \[\lambda \] done clear
B) the increase in the limiting angle by 2.54 times for the same \[\lambda \] done clear
C) decrease in the resolving power done clear
D) no effect on the limiting angle done clear
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 done clear
B) reflected and refracted beams are partially polarized done clear
C) the reason for (a) is that almost all the light is reflected done clear
D) all of the above done clear
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. done clear
B) Maxwell provided the theoretical evidence that light is transverse wave done clear
C) Thomas Young experimentally proved the wave behaviour of light and Huygens assumption done clear
D) All the statements given above, correctly answers the question what is light? done clear
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 done clear
B) 15 done clear
C) 100 done clear
D) 25 done clear
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 done clear
B) 3 done clear
C) \[(1+x)\] done clear
D) \[{{(1+x)}^{2}}\] done clear
View Answer play_arrowquestion_answer63) Which of these does not influence the rate of reaction?
A) Nature of the reactants done clear
B) Concentration of the reactants done clear
C) - Temperature of the reaction done clear
D) Molecularity of die reaction done clear
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 done clear
B) 3/2 done clear
C) 3 done clear
D) 1 done clear
View Answer play_arrowquestion_answer65) The rate at which a substance reacts depends on its :
A) atomic weight done clear
B) atomic number done clear
C) molecular weight done clear
D) active mass done clear
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 done clear
B) chloral done clear
C) methyl chloride done clear
D) monochloroacetic acid done clear
View Answer play_arrowquestion_answer67) Which of the following haloalkanes is most reactive?
A) 1-chloropropane done clear
B) 1-bromopropane done clear
C) 2-chloropropane done clear
D) 2-bromopropane done clear
View Answer play_arrowquestion_answer68) The reaction in which phenol differs from alcohol is :
A) it undergoes esterification with carboxylic acid done clear
B) it reacts with ammonia done clear
C) it forms yellow crystals of iodoform done clear
D) it liberates \[{{H}_{2}}\] with Na metal. done clear
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) \[{{C}_{2}}{{H}_{5}}Cl\] done clear
B) \[{{C}_{2}}{{H}_{5}}COOC{{H}_{3}}\] done clear
C) \[{{C}_{2}}{{H}_{5}}OH\] done clear
D) \[{{C}_{2}}{{H}_{6}}\] done clear
View Answer play_arrowquestion_answer70) Which of the following is an amphoteric acid?
A) Glycine done clear
B) Salicylic acid done clear
C) Benzoic acid done clear
D) Citric acid done clear
View Answer play_arrowquestion_answer71) Gold is extracted by hydrometallurgical process, based on its property :
A) of being electropositive done clear
B) of being less reactive done clear
C) to form complexes which are water soluble done clear
D) to form salts which are water soluble done clear
View Answer play_arrowquestion_answer72) In blast furnace, iron oxide is reduced by:
A) hot blast of air done clear
B) carbon monoxide done clear
C) carbon done clear
D) silica done clear
View Answer play_arrowquestion_answer73) Which of the following pairs of elements cannot form an alloy?
A) Zn, Cu done clear
B) Fe, Hg done clear
C) Fe, C done clear
D) Hg, Na done clear
View Answer play_arrowquestion_answer74) Which compound is zero valent metal complex?
A) \[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\] done clear
B) \[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\] done clear
C) \[[Ni{{(CO)}_{4}}]\] done clear
D) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\] done clear
View Answer play_arrowquestion_answer75) Alum is a water purifier because it :
A) coagulates the impurities done clear
B) softens hard water done clear
C) gives taste done clear
D) destroys the pathogenic bacteria done clear
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 done clear
B) 0.1 done clear
C) 0.01 done clear
D) 0.025 done clear
View Answer play_arrowquestion_answer77) The extent of adsorption of a gas on a solid depends on :
A) nature of the gas done clear
B) pressure of the gas done clear
C) temperature of the gas done clear
D) all of the above done clear
View Answer play_arrowquestion_answer78) A emulsifier is a substance which :
A) stabilises the emulsion done clear
B) homogenises the emulsion done clear
C) coagulates the emulsion done clear
D) accelerates the dispersion of liquid in liquid done clear
View Answer play_arrowquestion_answer79) Which of the following types of metals form the most efficient catalysts?
A) -Alkali metals done clear
B) -Alkaline earth metals done clear
C) Transition metals done clear
D) All of the above done clear
View Answer play_arrowquestion_answer80) The species among the following, which can act as an acid and a base is :
A) \[HSO_{4}^{-}\] done clear
B) \[SO_{4}^{2-}\] done clear
C) \[{{H}_{3}}{{O}^{+}}\] done clear
D) \[C{{l}^{-}}\] done clear
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 done clear
B) Cannizaros reaction done clear
C) Sandmeyers reaction done clear
D) Claisen condensation done clear
View Answer play_arrowquestion_answer82) Ethyl chloride on heating with \[AgCN\] forms a compound X. The functional isomer of X is :
A) \[{{C}_{2}}{{H}_{5}}NC\] done clear
B) \[{{C}_{2}}{{H}_{5}}N{{H}_{2}}\] done clear
C) \[{{C}_{2}}{{H}_{5}}CN\] done clear
D) none of these done clear
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 done clear
B) an acid done clear
C) ail alcohol done clear
D) an ether done clear
View Answer play_arrowquestion_answer84) Grignard reagent adds to :
A) \[<C=O\] done clear
B) \[C=N\] done clear
C) \[<C=S\] done clear
D) all of these done clear
View Answer play_arrowquestion_answer85) Which of the following biomolecules contain non-transition metal ion?
A) Vitamin \[{{B}_{12}}\] done clear
B) Chlorophyll done clear
C) Haemoglobin done clear
D) Insulin done clear
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) \[\Delta H>\Delta E\] done clear
B) \[\Delta H<\Delta E\] done clear
C) \[\Delta H=\Delta E\] done clear
D) the relationship depends on the capacity of the vessel done clear
View Answer play_arrowquestion_answer87) The cooling in refrigerator is due to :
A) reaction of the refrigerator gas done clear
B) expansion of ice done clear
C) the expansion of the gas in die refrigerator done clear
D) the work of die compressor done clear
View Answer play_arrowquestion_answer88) For a system in equilibrium, \[\Delta G=0\], under conditions of constant .........
A) temperature and pressure done clear
B) temperature arid volume done clear
C) pressure and volume done clear
D) energy and volume done clear
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) \[{{375}^{o}}C\] done clear
B) 375K done clear
C) 273 K done clear
D) \[{{102}^{o}}C\] done clear
View Answer play_arrowquestion_answer90) The temperature of the system decreases in an :
A) adiabatic compression done clear
B) isothermal compression done clear
C) isothermal expansion done clear
D) adiabatic expansion done clear
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 done clear
B) 9 done clear
C) 4 done clear
D) 7 done clear
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 done clear
B) 0.087 V done clear
C) 0.059V done clear
D) -0.177V done clear
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 done clear
B) be basic done clear
C) turn phenolphthalein solution pink done clear
D) turn methyl orange red done clear
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 \[O{{H}^{-}}\] done clear
B) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{2-}\] done clear
C) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[O_{2}^{-}\] done clear
D) Fe is oxidised to \[F{{e}^{2+}}\] and \[{{H}_{2}}O\] is reduced to \[{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer95) The standard electrode potential is measured by :
A) electrometer done clear
B) voltmeter done clear
C) pyrometer done clear
D) galvanometer done clear
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 \[{{10}^{-7}}M\,HCl\] done clear
B) \[{{10}^{-5}}M\,AgN{{O}_{3}}\] and \[{{10}^{-6}}M\,HCl\] done clear
C) \[{{10}^{-5}}M\,AgN{{O}_{3}}\] and \[{{10}^{-4}}M\,HCl\] done clear
D) \[{{10}^{-6}}M\,AgN{{O}_{3}}\] and \[{{10}^{-6}}M\,HCl\] done clear
View Answer play_arrowquestion_answer97) Which one of the following defects in the crystals lowers its density?
A) Frenkel defect done clear
B) Schottky defect done clear
C) F-centres done clear
D) Interstitial defect done clear
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 done clear
B) 600 mg done clear
C) 1 g done clear
D) 1.5 g done clear
View Answer play_arrowquestion_answer99) Which of the following cannot be accelerated?
A) \[\alpha \]-particle done clear
B) \[\beta \]-particle done clear
C) Protons done clear
D) Neutrons done clear
View Answer play_arrowquestion_answer100) In which of the following nuclear reaction neutrons is emitted?
A) \[_{13}^{27}Al+_{2}^{4}He\to _{15}^{30}P\] done clear
B) \[_{6}^{27}C+_{1}^{1}H\to _{7}^{13}N\] done clear
C) \[_{15}^{30}P\to _{14}^{30}Si\] done clear
D) \[_{96}^{241}Am+_{2}^{4}He\to _{97}^{245}Bk\] done clear
View Answer play_arrowquestion_answer101) Molarity of \[0.2\,N\,{{H}_{2}}S{{O}_{4}}\] is :
A) 0.2 done clear
B) 0.4 done clear
C) 0.6 done clear
D) 0.1 done clear
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 done clear
B) the pressure of the gas done clear
C) the units of the measurement done clear
D) none of the above done clear
View Answer play_arrowquestion_answer103) A commercial sample of hydrogen peroxide is labelled as 10 volume. Its percentage strength is nearly :
A) 1% done clear
B) 3% done clear
C) 10% done clear
D) 90% done clear
View Answer play_arrowquestion_answer104) Activated charcoal is used to remove colouring matter from pure substances. It works by :
A) oxidation done clear
B) reduction done clear
C) bleaching done clear
D) adsorption done clear
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 done clear
B) elements of nitrogen done clear
C) nitrates done clear
D) nitrides done clear
View Answer play_arrowquestion_answer106) Three dimensional molecules with cross links are formed in the case of a :
A) thermoplastic done clear
B) thermosetting plastic done clear
C) both (a) and (b) done clear
D) none of the above done clear
View Answer play_arrowquestion_answer107) Sucrose molecule is made up of :
A) a gluco pyranose and a fructo pyranose done clear
B) a gluco pyranose and a fructo furanose done clear
C) a gluco furanose and a fructo pyranose done clear
D) a gluco furanose and a fructo furanose done clear
View Answer play_arrowquestion_answer108) Water insoluble component of starch is :
A) amylopectin done clear
B) amylose done clear
C) cellulose done clear
D) none of these done clear
View Answer play_arrowquestion_answer109) An example for a saturated fatty acid, present in nature is :
A) oleic acid done clear
B) linoleic acid done clear
C) linolenic acid done clear
D) palmitic acid done clear
View Answer play_arrowquestion_answer110) A nanopeptide contains......peptide linkages :
A) 10 done clear
B) 8 done clear
C) 9 done clear
D) 18 done clear
View Answer play_arrowquestion_answer111) A gas decolourised by \[KMn{{O}_{4}}\] solution but gives no precipitate with ammoniacal cuprous chloride is :
A) ethane done clear
B) methane done clear
C) ethane done clear
D) acetylene done clear
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 done clear
B) 4-chloro-2-methyl-3-pentene done clear
C) 4-methyl-2-chloro-2-pentene done clear
D) 2-chloro-4,4-dimethyl-2-butene done clear
View Answer play_arrowquestion_answer113) Amongst the following the compound that can most readily get sulphonated is :
A) benzene done clear
B) toluene done clear
C) nitrobenzene done clear
D) chlorobenzene done clear
View Answer play_arrowquestion_answer114) Household gaseous fuel (LPG) mainly con tarns:
A) \[C{{H}_{4}}\] done clear
B) \[{{C}_{2}}{{H}_{2}}\] done clear
C) \[{{C}_{2}}{{H}_{4}}\] done clear
D) \[{{C}_{4}}{{H}_{10}}\] done clear
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 done clear
B) they damage the refrigerators and air conditioners done clear
C) they eat away the ozone in the atmosphere done clear
D) they destroy the oxygen layer done clear
View Answer play_arrowquestion_answer116) An example of a sulphur containing amino acid is :
A) lysine done clear
B) serine done clear
C) cysteine done clear
D) tyrosine done clear
View Answer play_arrowquestion_answer117) Which of the following is not present in a nucleotide?
A) Cytosine done clear
B) Guanine done clear
C) Adenine done clear
D) Tyrosine done clear
View Answer play_arrowquestion_answer118) Antiseptic chloroxylenol is :
A) 4-chloro-3,5-dimethyl phenol done clear
B) 3-chloro-4,5-dimethyl phenol done clear
C) 4-chloro-2,5-dimethyl phenol done clear
D) 5-chloro-3,4-dimethyl phenol done clear
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) \[{{A}_{3}}{{B}_{6}}\] done clear
B) \[{{A}_{2}}{{B}_{3}}\] done clear
C) \[{{A}_{3}}{{B}_{2}}\] done clear
D) \[{{A}_{2}}B\] done clear
View Answer play_arrowquestion_answer120) Among \[N{{a}^{+}},\,Na,\,Mg\] and \[M{{g}^{2+}}\], the largest particle is :
A) \[M{{g}^{2+}}\] done clear
B) Mg done clear
C) Na done clear
D) \[N{{a}^{+}}\] done clear
View Answer play_arrowquestion_answer121) When \[{{2}^{301}}\] is divided by 5, the least positive remainder is :
A) 4 done clear
B) 8 done clear
C) 2 done clear
D) 6 done clear
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 done clear
B) If two triangles are not identical, then these are not similar done clear
C) If two triangles are not identical, then these are similar done clear
D) If two. triangles are not similar, then these are identical done clear
View Answer play_arrowquestion_answer123) The contrapositive of the inverse of \[p\to \,\sim \,\,q\]is :
A) \[\sim q\to p\] done clear
B) \[p\to q\] done clear
C) \[\sim q\to \sim p\] done clear
D) \[\sim p\to \sim q\] done clear
View Answer play_arrowquestion_answer124) The converse of the contrapositive of \[p\to q\] is :
A) \[\sim p\to q\] done clear
B) \[p\to \sim q\] done clear
C) \[\sim p\to \sim q\] done clear
D) \[\sim q\to p\] done clear
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 done clear
B) 1 done clear
C) 0 done clear
D) \[\omega \] done clear
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) done clear
B) (-3,-4), (13,-4) done clear
C) (3, 4), (-13, 4) done clear
D) (5,-8), (-5, 8) done clear
View Answer play_arrowquestion_answer127) The equation to die hyperbola having its eccentricity 2 and the distance between its foci is 8, is :
A) \[\frac{{{x}^{2}}}{12}-\frac{{{y}^{2}}}{4}=1\] done clear
B) \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{12}=1\] done clear
C) \[\frac{{{x}^{2}}}{8}-\frac{{{y}^{2}}}{2}=1\] done clear
D) \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] done clear
View Answer play_arrowquestion_answer128) The solution of \[{{\sin }^{-1}}x-{{\sin }^{-1}}2x=\pm \frac{\pi }{3}\] is :
A) \[\pm \frac{1}{3}\] done clear
B) \[\pm \frac{1}{3}\] done clear
C) \[\pm \frac{\sqrt{3}}{2}\] done clear
D) \[\pm \frac{1}{2}\] done clear
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) \[\sqrt{2}\] done clear
B) \[\frac{\sqrt{3}+1}{2}\] done clear
C) \[\frac{\sqrt{3}-1}{2}\] done clear
D) 1 done clear
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 done clear
B) - 1 done clear
C) 1/2 done clear
D) 1 done clear
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 done clear
B) -47 done clear
C) 49 done clear
D) -49 done clear
View Answer play_arrowquestion_answer132) The radius of the circle \[{{x}^{2}}+{{y}^{2}}+4x+6y+13=0\] is ;
A) \[\sqrt{26}\] done clear
B) \[\sqrt{13}\] done clear
C) \[\sqrt{23}\] done clear
D) 0 done clear
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) done clear
B) (2,-1) done clear
C) (-2,1) done clear
D) (-1,2) done clear
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 done clear
B) 9 done clear
C) 41 done clear
D) 18 done clear
View Answer play_arrowquestion_answer135) The eccentricity of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1\] is:
A) \[\frac{3}{4}\] done clear
B) \[\frac{3}{5}\] done clear
C) \[\frac{\sqrt{41}}{4}\] done clear
D) \[\frac{\sqrt{41}}{5}\] done clear
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 done clear
B) -3, 1 done clear
C) 3, 1 done clear
D) -3,-1 done clear
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 done clear
B) 100 done clear
C) - 110 done clear
D) 92 done clear
View Answer play_arrowquestion_answer138) The inverse of the matrix \[\left[ \begin{matrix} 5 & -2 \\ 3 & 1 \\ \end{matrix} \right]\] is :
A) \[\frac{1}{11}\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\] done clear
B) \[\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\] done clear
C) \[\frac{1}{13}\left[ \begin{matrix} -2 & 5 \\ 1 & 3 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 1 & 3 \\ -2 & 5 \\ \end{matrix} \right]\] done clear
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) \[-\frac{3}{\sqrt{14}}\] done clear
B) \[\frac{3}{\sqrt{14}}\] done clear
C) \[-\frac{\sqrt{3}}{2}\] done clear
D) \[\frac{3}{\sqrt{2}}\] done clear
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) \[\pm \frac{\hat{j}-\hat{j}}{\sqrt{2}}\] done clear
B) \[\pm \frac{\hat{j}+\hat{k}}{\sqrt{2}}\] done clear
C) \[\pm \frac{\hat{j}-\hat{k}}{\sqrt{2}}\] done clear
D) \[\pm \frac{\hat{i}+\hat{j}}{\sqrt{2}}\] done clear
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 done clear
B) \[\frac{2}{3}\] or \[-\frac{2}{3}\] done clear
C) \[\frac{4}{5}\] or \[\frac{3}{4}\] done clear
D) \[\pm \frac{1}{2}\] done clear
View Answer play_arrowquestion_answer142) The circus-radius of the triangle whose sides are 13, 12 and 5, is :
A) 15 done clear
B) 13/2 done clear
C) 15/2 done clear
D) 6 done clear
View Answer play_arrowquestion_answer143) If \[{{\tan }^{-1}}x+{{\tan }^{-1}}y=\frac{\pi }{4}\], then :
A) \[x+y+xy=1\] done clear
B) \[x+y-xy=1\] done clear
C) \[x+y+xy+1=0\] done clear
D) \[~x+y-xy+1=0\] done clear
View Answer play_arrowquestion_answer144) The general solution of \[\sin x-\cos x=\sqrt{2}\] for any integer n is :
A) \[n\pi \] done clear
B) \[2n\pi +\frac{3\pi }{4}\] done clear
C) \[2n\pi \] done clear
D) \[(2n\pi +1)\] done clear
View Answer play_arrowquestion_answer145) The amplitude of \[\frac{1+i\sqrt{3}}{\sqrt{3}+i}\] is :
A) \[\frac{\pi }{3}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[\frac{2\pi }{3}\] done clear
D) \[\frac{\pi }{6}\] done clear
View Answer play_arrowquestion_answer146) The sum to infinity of the progression\[9-3+\frac{1}{3}+.........\] is :
A) 9 done clear
B) 9/2 done clear
C) 27/4 done clear
D) 15/2 done clear
View Answer play_arrowquestion_answer147) If\[{{\,}^{n}}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\]
A) 72 done clear
B) 153 done clear
C) 306 done clear
D) 2556 done clear
View Answer play_arrowquestion_answer148) The middle term in the expansion of \[{{\left( x-\frac{1}{x} \right)}^{18}}\]
A) \[^{18}{{C}_{9}}\] done clear
B) \[\,{{-}^{18}}{{C}_{9}}\] done clear
C) \[^{18}{{C}_{10}}\] done clear
D) \[{{-}^{18}}{{C}_{10}}\] done clear
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) \[-\frac{15}{4}\] done clear
B) \[\frac{15}{4}\] done clear
C) \[\frac{9}{4}\] done clear
D) 4 done clear
View Answer play_arrowquestion_answer150) The digit in the units place in the number \[{{7}^{289}}\] is :
A) 9 done clear
B) 7 done clear
C) 1 done clear
D) 3 done clear
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 done clear
B) \[\sqrt{3}\] done clear
C) \[(\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{3}})}/3\] done clear
D) 1 done clear
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) \[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] done clear
B) \[\frac{1}{2}\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] done clear
C) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done clear
D) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done clear
View Answer play_arrowquestion_answer153) In the group \[G=\{1,3,7,9\}\] under multiplication modulo 10, the inverse of 3 is :
A) 1 done clear
B) 3 done clear
C) 7 done clear
D) 9 done clear
View Answer play_arrowquestion_answer154) In the group (0,1, 2, 4, 5} under addition modulo 6 a subgroup is :
A) { 0, 2, 5} done clear
B) ( 1, 4, 5} done clear
C) ( 0, 1, 3) done clear
D) ( 0..2, 4} done clear
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) \[\frac{27}{20}\] done clear
B) \[\frac{20}{27}\] done clear
C) \[\frac{1}{20}\] done clear
D) 20 done clear
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) done clear
B) (3,-1),(0,0) done clear
C) (2,1), (-2,1) done clear
D) (2, 2), (1,1) done clear
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) \[x+y-3=0\] done clear
B) \[2x-y=9\] done clear
C) \[x+2y=2\] done clear
D) \[2x+y=7\] done clear
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) \[2\sqrt{5}\,a\] done clear
B) \[\sqrt{10}\,a\] done clear
C) 10 a done clear
D) \[5\sqrt{2}\,a\] done clear
View Answer play_arrowquestion_answer159) The equation to the circle with centre (2,1) and touching the line \[3x+4y=5\] is :
A) \[{{x}^{2}}+{{y}^{2}}-4y-2y+5=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-4x-2y-5=0\] done clear
C) \[{{x}^{2}}+{{y}^{2}}-4x-2y+4=0\] done clear
D) \[{{x}^{2}}+{{y}^{2}}-4x-2y-4=0\] done clear
View Answer play_arrowquestion_answer160) The condition for a line \[y=2x+c\] to touch the circle \[{{x}^{2}}+{{y}^{2}}=16\] is :
A) \[c=10\] done clear
B) \[{{c}^{2}}=80\] done clear
C) \[c=12\] done clear
D) \[{{c}^{2}}=64\] done clear
View Answer play_arrowquestion_answer161) \[\int{\frac{\sin \,\,(2x)}{1+{{\cos }^{2}}x}d\,x=}\]
A) \[-\frac{1}{2}\log \,(1+{{\cos }^{2}}x)+c\] done clear
B) \[2\,\,\log \,(1+{{\cos }^{2}}x)+c\] done clear
C) \[\frac{1}{2}\,\,\log \,(1+{{\cos }^{2}}2x)+c\] done clear
D) \[c-\,\log \,\,(1+{{\cos }^{2}}x)\] done clear
View Answer play_arrowquestion_answer162) \[\int{\frac{{{e}^{x}}(1+\sin x)}{1+\cos x}dx=}\]
A) \[{{e}^{x}}\tan \left( \frac{x}{2} \right)+c\] done clear
B) \[{{e}^{x}}\tan x+c\] done clear
C) \[{{e}^{x}}\left( \frac{1+\sin x}{1-\cos x} \right)+c\] done clear
D) \[c-{{e}^{x}}\cot \left( \frac{x}{2} \right)\] done clear
View Answer play_arrowquestion_answer163) \[\int{\frac{1+\tan x}{{{e}^{-x}}\cos x}d\,x}=\]
A) \[{{e}^{-x}}\tan x+c\] done clear
B) \[{{e}^{-x}}\sec x+c\] done clear
C) \[{{e}^{x}}\sec x+c\] done clear
D) \[{{e}^{x}}\tan x+c\] done clear
View Answer play_arrowquestion_answer164) \[\int\limits_{\pi /4}^{\pi /2}{\cos e{{c}^{2}}x\,dx=}\]
A) -1 done clear
B) 1 done clear
C) 0 done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer165) \[\int\limits_{0}^{\pi /4}{\log \,(1+\tan x)d\,x=}\]
A) \[\frac{\pi }{8}{{\log }_{e}}2\] done clear
B) \[\frac{\pi }{4}{{\log }_{2}}e\] done clear
C) \[\frac{\pi }{4}{{\log }_{e}}2\] done clear
D) \[\frac{\pi }{4}{{\log }_{e}}\left( \frac{1}{2} \right)\] done clear
View Answer play_arrowquestion_answer166) The modulus and amplitude of \[\frac{1+2i}{1-{{(1-i)}^{2}}}\], are :
A) \[\sqrt{2}\] and \[\frac{\pi }{6}\] done clear
B) 1 and 0 done clear
C) 1 and \[\frac{\pi }{3}\] done clear
D) 1 and \[\frac{\pi }{4}\] done clear
View Answer play_arrowquestion_answer167) The real part of \[\frac{1}{1+\cos \theta +i\sin \theta }\] is :
A) \[-\frac{1}{2}\] done clear
B) \[\frac{1}{2}\] done clear
C) \[\sqrt{2}\] done clear
D) \[\frac{1}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer168) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\] is equal to :
A) \[\frac{1}{2}\] done clear
B) \[-\frac{1}{2}\] done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowquestion_answer169) If \[y=\frac{{{e}^{x}}+{{e}^{-x}}}{{{e}^{x}}-{{e}^{-x}}}\], then \[\frac{dy}{dx}\] is equal to :
A) \[\sec \,{{h}^{2}}x\] done clear
B) \[\cos ec\,{{h}^{2}}x\] done clear
C) \[\sec \,\,{{h}^{2}}x\] done clear
D) \[-\cos ec\,{{h}^{2}}x\] done clear
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 done clear
B) -2 done clear
C) 2 done clear
D) 1/2 done clear
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) \[\frac{35\,{{a}^{2}}}{3}\] done clear
B) \[\frac{4\,{{a}^{2}}}{3}\] done clear
C) \[\frac{7\,{{a}^{2}}}{3}\] done clear
D) \[\frac{56\,{{a}^{2}}}{3}\] done clear
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 done clear
B) 1250 done clear
C) 1050 done clear
D) 5250 done clear
View Answer play_arrowquestion_answer173) The differential equation representing a family of circles touching the y-axis at the origin is :
A) \[{{x}^{2}}+{{y}^{2}}-2xy\frac{dy}{dx}=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}+2xy\frac{dy}{dx}=0\] done clear
C) \[{{x}^{2}}-{{y}^{2}}-2xy\frac{dy}{dx}=0\] done clear
D) \[{{x}^{2}}-{{y}^{2}}+2xy\frac{dy}{dx}=0\] done clear
View Answer play_arrowquestion_answer174) The area of the region bounded by tile curve \[9{{x}^{2}}+4{{y}^{2}}-36=0\] is :
A) \[9\pi \] done clear
B) \[4\pi \] done clear
C) \[36\pi \] done clear
D) \[6\pi \] done clear
View Answer play_arrowquestion_answer175) The general solution of the differential equation \[(2x-y+1)\,dx+(2y-x+1)\,\,dy=0\] is:
A) \[{{x}^{2}}+{{y}^{2}}+xy-x+y=c\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-xy+x+y=c\] done clear
C) \[{{x}^{2}}-{{y}^{2}}+2xy-x+y=c\] done clear
D) \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\] done clear
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) \[\frac{{{x}^{2}}}{\sqrt{1-{{x}^{4}}}}\] done clear
B) \[\frac{{{x}^{2}}}{\sqrt{1+{{x}^{4}}}}\] done clear
C) \[\frac{{{x}^{2}}}{\sqrt{1+{{x}^{4}}}}\] done clear
D) \[\frac{x}{\sqrt{1-{{x}^{4}}}}\] done clear
View Answer play_arrowquestion_answer177) If \[x=\sin \,t,\,y=\cos \,pt\], then :
A) \[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}+{{p}^{2}}y=0\] done clear
B) \[(1-{{x}^{2}}){{y}_{2}}+x{{y}_{1}}-{{p}^{2}}y=0\] done clear
C) \[(1+{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\] done clear
D) \[(1-{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\] done clear
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) \[ST=SN\] done clear
B) \[Sr=2SN\] done clear
C) \[S{{T}^{2}}=a\,S{{N}^{3}}\] done clear
D) \[S{{T}^{3}}=a\,SN\] done clear
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 done clear
B) \[\sqrt{3}\] done clear
C) 3 done clear
D) \[\frac{1}{\sqrt{3}}\] done clear
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 done clear
B) 10 sq.cm/min done clear
C) 17.5 sq.cm/min done clear
D) 28 sq.cm/min done clear
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