Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2005

done CET - Karnataka Engineering Solved Paper-2005

  • 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) \[\frac{M}{R}\]

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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) \[1.5\times {{10}^{-3}}N\]

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  • question_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) \[1.8\times {{10}^{4}}J\]

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  • question_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

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  • question_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

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  • question_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

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  • question_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) \[R=\frac{{{r}_{2}}}{{{r}_{1}}}\]

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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.

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  • question_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

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  • question_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) \[3.75\times {{10}^{2}}m/s\]

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  • question_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) \[\frac{G}{90}\]

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  • question_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

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  • question_answer24) The induction coil works on the principle of:

    A) self - induction

    B) mutual induction

    C) Amperes rule

    D) Flemings right hand rule

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  • question_answer25) The square root of the product of inductance and capacitance has the dimension of:

    A) length

    B) mass

    C) time

    D) no dimension

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  • question_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) \[3<1<2\]

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_answer31) Infrared radiation was discovered in 1800 by:

    A) William Wollaston

    B) William Herschel

    C) Wilhelm Roentgen

    D) Thomas Young

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  • question_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

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  • question_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

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  • question_answer34) The ratio of velocity of sound in hydrogen and oxygen at STP is:

    A) \[16:1\]

    B) \[8:1\]

    C) \[4:1\]

    D) \[2:1\]

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  • question_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

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  • question_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

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  • question_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

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  • question_answer38) If a liquid does not wet glass, its angle of contact is:

    A) zero

    B) acute

    C) obtuse

    D) right angle

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  • question_answer39) The magnitude of J in ampere is:

    A) 0.1

    B) 0.3

    C) 0.6

    D) none of these

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  • question_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

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  • question_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.

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  • question_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 \[3I\]

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  • question_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) \[{{n}_{1}}=1,{{n}_{2}}=8\]

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  • question_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

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  • question_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) \[{{F}_{1}}>{{F}_{2}}>{{F}_{3}}\]

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  • question_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) \[6.32\times {{10}^{3}}C{{N}^{-1}}{{m}^{-2}}\]

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  • question_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

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  • question_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)

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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.

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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?

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  • question_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

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  • question_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) \[{{(1+x)}^{2}}\]

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  • question_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

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  • question_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

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  • question_answer65) The rate at which a substance reacts depends on its :

    A) atomic weight

    B) atomic number

    C) molecular weight

    D) active mass

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  • question_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

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  • question_answer67) Which of the following haloalkanes is most reactive?

    A) 1-chloropropane

    B) 1-bromopropane

    C) 2-chloropropane

    D) 2-bromopropane

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  • question_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.

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  • question_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) \[{{C}_{2}}{{H}_{6}}\]

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  • question_answer70) Which of the following is an amphoteric acid?

    A) Glycine

    B) Salicylic acid

    C) Benzoic acid

    D) Citric acid

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  • question_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

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  • question_answer72) In blast furnace, iron oxide is reduced by:

    A) hot blast of air

    B) carbon monoxide

    C) carbon

    D) silica

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  • question_answer73) Which of the following pairs of elements cannot form an alloy?

    A) Zn, Cu

    B) Fe, Hg

    C) Fe, C

    D) Hg, Na

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  • question_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) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]

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  • question_answer75) Alum is a water purifier because it :

    A) coagulates the impurities

    B) softens hard water

    C) gives taste

    D) destroys the pathogenic bacteria

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  • question_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

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  • question_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

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  • question_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

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  • question_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

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  • question_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) \[C{{l}^{-}}\]

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  • question_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

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  • question_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

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  • question_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

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  • question_answer84) Grignard reagent adds to :

    A) \[<C=O\]

    B) \[C=N\]

    C) \[<C=S\]

    D) all of these

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  • question_answer85) Which of the following biomolecules contain non-transition metal ion?

    A) Vitamin \[{{B}_{12}}\]

    B) Chlorophyll

    C) Haemoglobin

    D) Insulin

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  • question_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

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  • question_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

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  • question_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

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  • question_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) \[{{102}^{o}}C\]

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  • question_answer90) The temperature of the system decreases in an :

    A) adiabatic compression

    B) isothermal compression

    C) isothermal expansion

    D) adiabatic expansion

    View Answer play_arrow
  • question_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_arrow
  • question_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

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  • question_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_arrow
  • question_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 \[{{O}_{2}}\]

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  • question_answer95) The standard electrode potential is measured by :

    A) electrometer

    B) voltmeter

    C) pyrometer

    D) galvanometer

    View Answer play_arrow
  • question_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 \[{{10}^{-6}}M\,HCl\]

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  • question_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

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  • question_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

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  • question_answer99) Which of the following cannot be accelerated?

    A) \[\alpha \]-particle

    B) \[\beta \]-particle

    C) Protons

    D) Neutrons

    View Answer play_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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

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  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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

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  • question_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

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  • question_answer108) Water insoluble component of starch is :

    A) amylopectin

    B) amylose

    C) cellulose

    D) none of these

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  • question_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_arrow
  • question_answer110) A nanopeptide contains......peptide linkages :

    A) 10

    B) 8

    C) 9

    D) 18

    View Answer play_arrow
  • question_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_arrow
  • question_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

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  • question_answer113) Amongst the following the compound that can most readily get sulphonated is :

    A) benzene

    B) toluene

    C) nitrobenzene

    D) chlorobenzene

    View Answer play_arrow
  • question_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_arrow
  • question_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_arrow
  • question_answer116) An example of a sulphur containing amino acid is :

    A) lysine

    B) serine

    C) cysteine

    D) tyrosine

    View Answer play_arrow
  • question_answer117) Which of the following is not present in a nucleotide?

    A) Cytosine

    B) Guanine

    C) Adenine

    D) Tyrosine

    View Answer play_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_answer121) When \[{{2}^{301}}\] is divided by 5, the least positive remainder is :

    A) 4

    B) 8

    C) 2

    D) 6

    View Answer play_arrow
  • question_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

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  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_answer147) If\[{{\,}^{n}}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\]

    A) 72

    B) 153

    C) 306

    D) 2556

    View Answer play_arrow
  • question_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_arrow
  • question_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_arrow
  • question_answer150) The digit in the units place in the number \[{{7}^{289}}\] is :

    A) 9

    B) 7

    C) 1

    D) 3

    View Answer play_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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_arrow
  • question_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

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  • question_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) \[\frac{56\,{{a}^{2}}}{3}\]

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  • question_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

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  • question_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) \[{{x}^{2}}-{{y}^{2}}+2xy\frac{dy}{dx}=0\]

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  • question_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) \[6\pi \]

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  • question_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) \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\]

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  • question_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) \[\frac{x}{\sqrt{1-{{x}^{4}}}}\]

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  • question_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) \[(1-{{x}^{2}}){{y}_{2}}-x{{y}_{1}}+{{p}^{2}}y=0\]

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  • question_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) \[S{{T}^{3}}=a\,SN\]

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  • question_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) \[\frac{1}{\sqrt{3}}\]

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  • question_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

    B) 10

    C) 17.5

    D) 28

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